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The Surface of the Earth
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Lesson 1: Why is the interior of the Earth hot? The interior of Earth is very hot (the temperature of the core reaches more than 5,000 degrees Celsius) for two main reasons: . The heat from when the planet formed, . The heat from the decay of radioactive elements. The Earth was formed by the process of accretion. After the creation of our solar system, meteorites gravitationally attracted each other and formed bigger objects, which attracted bigger masses, until our planets reach their current size. This process accumulated a lot of heat; when two objects collide, heat is generated. That is why your hands will get hot when you clap them for too long, or a nail gets very hot when you hammer it for a long time. This heat has not dissipated totally and represents about 10% of the total heat inside the Earth. The main source of heat is the decay of radioactive elements. Radioactive decay is a natural process; unstable elements like 238U (Uranium) or 40K (Potassium) stabilize with time and produce what we call daughter products: 206P (Lead) for Uranium and 40Ar (Argon) for Potassium. This process produces heat, which represents about 90% of the total heat inside the Earth. Lesson 2: How Magma Forms Magma is a molten and semi-molten rock mixture found under the surface of the Earth. This mixture is usually made up the of four parts: hot liquid base, called a melt; minerals crystallized by the melt; solid rocks incorporated into the melt from the surrounding confines; and dissolved gases. When magma is ejected by a volcano or other vent, the material is called lava. Magma that has cooled into a solid isWeathering describes the breaking down or dissolving of rocks and minerals on the surface of the Earth. Water, ice, acids, salts, plants, animals, and changes in temperature are all agents of weathering. Once a rock has been broken down, a process called erosion transports the bits of rock and mineral away. No rock on Earth is hard enough to resist the forces of weathering and erosion. Together, these processes carved landmarks such as the Grand Canyon, in the U.S. state of Arizona. This massive canyon is 446 kilometers (277 miles) long, as much as 29 kilometers (18 miles) wide, and 1,600 meters (1 mile) deep. Weathering and erosion constantly change the rocky landscape of Earth. Weathering wears away exposed surfaces over time. The length of exposure often contributes to how vulnerable a rock is to weathering. Rocks, such as lavas, that are quickly buried beneath other rocks are less vulnerable to weathering and erosion than rocks that are exposed to agents such as wind and water, As it smoothes rough, sharp rock surfaces, weathering is often the first step in the production of soils. Tiny bits of weathered minerals mix with plants, animal remains, fungi, bacteria, and other organisms. A single type of weathered rock often produces infertile soil, while weathered materials from a collection of rocks is richer in mineral diversity and contributes to more fertile soil. Soils types associated with a mixture of weathered rock include glacial till, loess, and alluvial sediments. Weathering is often divided into the processes of mechanical weathering and chemical weathering. Biological weathering, in whichWeathering describes the breaking down or dissolving of rocks and minerals on the surface of the Earth. Water, ice, acids, salts, plants, animals, and changes in temperature are all agents of weathering. Once a rock has been broken down, a process called erosion transports the bits of rock and mineral away. No rock on Earth is hard enough to resist the forces of weathering and erosion. Together, these processes carved landmarks such as the Grand Canyon, in the U.S. state of Arizona. This massive canyon is 446 kilometers (277 miles) long, as much as 29 kilometers (18 miles) wide, and 1,600 meters (1 mile) deep. Weathering and erosion constantly change the rocky landscape of Earth. Weathering wears away exposed surfaces over time. The length of exposure often contributes to how vulnerable a rock is to weathering. Rocks, such as lavas, that are quickly buried beneath other rocks are less vulnerable to weathering and erosion than rocks that are exposed to agents such as wind and water, As it smoothes rough, sharp rock surfaces, weathering is often the first step in the production of soils. Tiny bits of weathered minerals mix with plants, animal remains, fungi, bacteria, and other organisms. A single type of weathered rock often produces infertile soil, while weathered materials from a collection of rocks is richer in mineral diversity and contributes to more fertile soil. Soils types associated with a mixture of weathered rock include glacial till, loess, and alluvial sediments. Weathering is often divided into the processes of mechanical weathering and chemical weathering. Biological weathering, in whichliving or once-living organisms contribute to weathering, can be a part of both processes. Mechanical Weathering Mechanical weathering, also called physical weathering and disaggregation, causes rocks to crumble. Water, in either liquid or solid form, is often a key agent of mechanical weathering. For instance, liquid water can seep into cracks and crevices in rock. If temperatures drop low enough, the water will freeze. When water freezes, it expands. The ice then works as a wedge. It slowly widens the cracks and splits the rock. When ice melts, liquid water performs the act of erosion by carrying away the tiny rock fragments lost in the split. This specific process (the freeze-thaw cycle) is called frost weathering or cryofracturing. Figure 4.3 Frost Wedging Temperature changes can also contribute to mechanical weathering in a process called thermal stress. Changes in temperature cause rock to expand (with heat) and contract (with cold). As this happens over and over again. the structure of the rock weakens. Over time, it crumbles. Rocky desert landscapes are particularly vulnerable to thermal stress. The outer layer of desert rocks undergo repeated stress as the temperature changes from day Eventually, Lo outer night. layersflake off in thin sheets, a process called exfoliation. Exfoliation contributes to the formation of bornhardts, one of the most dramatic features in landscapes formed by weathering and erosion. Bornhardts are tall, domed, isolated rocks often found areas. in tropical Sugarloaf Mountain, an iconic landmark in Rio de Janeiro, Brazil, is bornhardt. a Salt also works to weather rock in a process called haloclasty. Saltwater sometimes gets into the cracks and pores of rock. If the saltwater evaporates, salt crystals are left behind. As the crystals grow, they put pressure on the rock, slowly breaking it apart. Plants and animals can be agents of mechanical weathering. The seed of a tree may sprout in soil that has collected in a cracked rock. As the roots grow, they widen the cracks, eventually breaking the rock into pieces. Over time, trees can break apart even large rocks. Even small plants, such as mosses, can enlarge tiny cracks as they grow. Animals that tunnel underground, such as moles and prairie dogs, also work to break apart rock and soil. Other animals dig and trample rock aboveground, causing rock to slowly crumble. Chemical Weathering Chemical weathering changes the molecular structure of rocks and soil.For instance, carbon dioxide from the air or soil sometimes combines with water in a process called carbonation. This produces a weak acid, called carbonic acid, that can dissolve rock. Carbonic acid is especially effective at dissolving limestone. When carbonic acid seeps through limestone underground, it can open up huge cracks or hollow out vast networks of caves. Carlsbad Caverns National Park, in the U.S. state of New Mexico, includes more than 119 limestone caves created by weathering and erosion. The largest is called the Big Room.. With an area of about 33,210 square meters (357,469 square feet), the Big Room is the size of six football fields. Another type of chemical weathering works on rocks that contain iron. These rocks turn to rust in a process called oxidation. Rust is a compound created by the interaction of oxygen and iron in the presence of water. As rust expands, it weakens rock and helps break it apart. Another familiar form of chemical weathering is hydrolysis. In the process of hydrolysis, a new solution (a mixture of two or more substances) is formed as chemicals in rock interact with water. In many rocks, for example, sodium minerals interact with water to form a saltwater solution. Hydration and hydrolysis contribute to flared slopes, another dramatic example of a landscape formed by weathering and erosion. Flared slopes are sometimes nicknamed "wave rocks." Their c-shape is largely concave rock formations a result of subsurface weathering, in which hydration and hydrolysis wear away rocks beneath the landscape's surfaceWeathering and People Weathering is a natural process, but human activities can speed it up. For example, certain kinds of air pollution increase the rate of weathering Burning coal, natural and petroleum releases chemicals such as nitrogen oxide and gas, sulfur dioxide into the atmosphere. When these chemicals combine with sunlight and moisture, they change into acids. They then fall back to Earth as acid rain. Acid rain rapidly weathers limestone, marble, and other kinds of stone. The effects of acid rain can often be seen on gravestones, making names and other inscriptions impossible to read. Acid rain has also damaged many historic buildings and monuments. For example, at 71 meters (233 feet) tall, the Leshan Giant Buddha at Mount Emei, China is the world's largest statue of the Buddha. It was carved 1,300 years ago and sat unharmed for centuries. An innovative drainage system mitigates the natural process of erosion But in recent years, acid rain has turned the statue's nose black and made some of its hair crumble and fall.What is the relationship between faults and earthquakes? What happens to a fault when an earthquake occurs? Earthquakes occur on faults - strike-slip earthquakes occur on strike-slip faults, normal earthquakes occur on normal faults, and thrust earthquakes occur on reverse or thrust faults. When an earthquake occurs on one of these faults, the rock on one side of the fault slips with respect to the other. The fault surface can be vertical, horizontal, or at some angle to the surface of the earth. The slip direction can also be at any angle. What is a fault and what are the different types? A fault is a fracture or zone of fractures between two blocks of rock. Faults allow the blocks to move relative to each other. This movement may occur rapidly, in the form of an earthquake - or may occur slowly, in the form of creep. Faults may range in length from a few millimeters to thousands of kilometers. Most faults produce repeated displacements over geologic time. During an earthquake, the rock on one side of the fault suddenly slips with respect to the other. The fault surface can be horizontal or vertical or some arbitrary angle in between. Earth scientists use the angle of the fault with respect to the surface (known as the dip) and the direction of slip along the fault to classify faults. Faults which move along the direction of the dip plane are dip-slip faults and described as either normal or reverse (thrust), depending on their motion. Faults which move horizontally are known as strike-slip faults and are classified as either right-lateral or left-lateral. Faults which show both dip-slip and strike-slip motion are known as oblique-slip faults. The following definitions are adapted from The Earth by Press and Siever. normal fault - a dip-slip fault in which the block above the fault has moved downward relative to the block below. This type of faulting occurs in response to extension and is often observed in the Western United States Basin and Range Province and along oceanic ridge systems. Normal Fault Animation reverse (thrust) fault - a dip-slip fault in which the upper block, above the fault plane, moves up and over the lower block. This type of faulting is common in areas of compression, such as regions where one plate is being subducted under another as in Japan. When the dip angle is shallow, a reverse fault is often described as a thrust fault. Thrust Fault Animation Blind Thrust Fault Animation strike-slip fault - a fault on which the two blocks slide past one another. The San Andreas Fault is an example of a right lateral fault. Strike-slip Fault Animation A left-lateral strike-slip fault is one on which the displacement of the far block is to the left when viewed from either side. A right-lateral strike-slip fault is one on which the displacement of the far block is to the right when viewed from either side.Introduction to Free Fall A free-falling object is an object that is falling under the sole influence of gravity. Any object that is being acted upon only by the force of gravity is said to be in a state of free fall. There are two important motion characteristics that are true of free-falling objects: ⢠Free-falling objects do not encounter air resistance. ⢠All free-falling objects (on Earth) accelerate downwards at a rate of 9.8 m/s/s (often approximated as 10 m/s/s for back-of-the-envelope calculations) Because free-falling objects are accelerating downwards at a rate of 9.8 m/s/s, a ticker tape trace or dot diagram of its motion would depict an acceleration. The dot diagram at the right depicts the acceleration of a free-falling object. The position of the object at regular time intervals - say, every 0.1 second - is shown. The fact that the distance that the object travels every interval of time is increasing is a sure sign that the ball is speeding up as it falls downward. Recall from an earlier lesson, that if an object travels downward and speeds up, then its acceleration is downward. Free-fall acceleration is often witnessed in a physics classroom by means of an ever-popular strobe light demonstration. The room is darkened and a jug full of water is connected by a tube to a medicine dropper. The dropper drips water and the strobe illuminate the falling droplets at a regular rate - say once every 0.2 seconds. Instead of seeing a stream of water free-falling from the medicine dropper, several consecutive drops with increasing separation distance are seen. The pattern of drops resembles the dot diagram shown in the graphic at the right. The Acceleration of Gravity It was learned in the previous part of this lesson that a free-falling object is an object that is falling under the sole influence of gravity. A free-falling object has an acceleration of 9.8 m/s/s, downward (on Earth). This numerical value for the acceleration of a free-falling object is such an important value that it is given a special name. It is known as the acceleration of gravity - the acceleration for any object moving under the sole influence of gravity. A matter of fact, this quantity known as the acceleration of gravity is such an important quantity that physicists have a special symbol to denote it - the symbol g. The numerical value for the acceleration of gravity is most accurately known as 9.8 m/s2. There are slight variations in this numerical value (to the second decimal place) that are dependent primarily upon on altitude. We will occasionally use the approximated value of 10 m/s2 in order to reduce the complexity of the many mathematical tasks that we will perform with this number. By so doing, we will be able to better focus on the conceptual nature of physics without too much of a sacrifice in numerical accuracy. g = 9.8 m/s2, downward Look It Up! Even on the surface of the Earth, there are local variations in the value of the acceleration of gravity (g). These variations are due to latitude, altitude and the local geological structure of the region. Recall from an earlier lesson that acceleration is the rate at which an object changes its velocity. It is the ratio of velocity change to time between any two points in an object's path. To accelerate at 9.8 m/s2 means to change the velocity by 9.8 m/s each second. If the velocity and time for a free-falling object being dropped from a position of rest were tabulated, then one would note the following pattern. Time (s) Velocity (m/s) 0 0 1 - 9.8 2 - 19.6 3 - 29.4 4 - 39.2 5 - 49.0 . Observe that the velocity-time data above reveal that the object's velocity is changing by 9.8 m/s each consecutive second. That is, the free-falling object has an acceleration of approximately 9.8 m/s2. Another way to represent this acceleration of 9.8 m/s2 is to add numbers to our dot diagram that we saw earlier in this lesson. The velocity of the ball is seen to increase as depicted in the diagram at the right. (NOTE: The diagram is not drawn to scale - in two seconds, the object would drop considerably further than the distance from shoulder to toes.) Representing Free Fall by Graphs ⢠Early in Lesson 1 it was mentioned that there are a variety of means of describing the motion of objects. One such means of describing the motion of objects is through the use of graphs - position versus time and velocity vs. time graphs. In this part of Lesson 5, the motion of a free-falling motion will be represented using these two basic types of graphs. Representing Free Fall by Position-Time Graphs A position versus time graph for a free-falling object is shown below. Observe that the line on the graph curves. As learned earlier, a curved line on a position versus time graph signifies an accelerated motion. Since a free-falling object is undergoing an acceleration (g = 9.8 m/s/s), it would be expected that its position-time graph would be curved. A further look at the position-time graph reveals that the object starts with a small velocity (slow) and finishes with a large velocity (fast). Since the slope of any position vs. time graph is the velocity of the object (as learned in Lesson 3), the small initial slope indicates a small initial velocity and the large final slope indicates a large final velocity. Finally, the negative slope of the line indicates a negative (i.e., downward) velocity. Representing Free Fall by Velocity-Time Graphs A velocity versus time graph for a free-falling object is shown below. Observe that the line on the graph is a straight, diagonal line. As learned earlier, a diagonal line on a velocity versus time graph signifies an accelerated motion. Since a free-falling object is undergoing an acceleration (g = 9,8 m/s/s, downward), it would be expected that its velocity-time graph would be diagonal. A further look at the velocity-time graph reveals that the object starts with a zero velocity (as read from the graph) and finishes with a large, negative velocity; that is, the object is moving in the negative direction and speeding up. An object that is moving in the negative direction and speeding up is said to have a negative acceleration (if necessary, review the vector nature of acceleration). Since the slope of any velocity versus time graph is the acceleration of the object (as learned in Lesson 4), the constant, negative slope indicates a constant, negative acceleration. This analysis of the slope on the graph is consistent with the motion of a free-falling object - an object moving with a constant acceleration of 9.8 m/s/s in the downward direction. The Kinematic Equations The goal of this first unit has been to investigate the variety of means by which the motion of objects can be described. The variety of representations that we have investigated includes verbal representations, pictorial representations, numerical representations, and graphical representations (position-time graphs and velocity-time graphs). In Lesson 6, we will investigate the use of equations to describe and represent the motion of objects. These equations are known as kinematic equations. There are a variety of quantities associated with the motion of objects - displacement (and distance), velocity (and speed), acceleration, and time. Knowledge of each of these quantities provides descriptive information about an object's motion. For example, if a car is known to move with a constant velocity of 22.0 m/s, North for 12.0 seconds for a northward displacement of 264 meters, then the motion of the car is fully described. And if a second car is known to accelerate from a rest position with an eastward acceleration of 3.0 m/s2 for a time of 8.0 seconds, providing a final velocity of 24 m/s, East and an eastward displacement of 96 meters, then the motion of this car is fully described. These two statements provide a complete description of the motion of an object. However, such completeness is not always known. It is often the case that only a few parameters of an object's motion are known, while the rest are unknown. For example as you approach the stoplight, you might know that your car has a velocity of 22 m/s, East and is capable of a skidding acceleration of 8.0 m/s2, West. However you do not know the displacement that your car would experience if you were to slam on your brakes and skid to a stop; and you do not know the time required to skid to a stop. In such an instance as this, the unknown parameters can be determined using physics principles and mathematical equations (the kinematic equations). The BIG 4 The kinematic equations are a set of four equations that can be utilized to predict unknown information about an object's motion if other information is known. The equations can be utilized for any motion that can be described as being either a constant velocity motion (an acceleration of 0 m/s/s) or a constant acceleration motion. They can never be used over any time period during which the acceleration is changing. Each of the kinematic equations include four variables. If the values of three of the four variables are known, then the value of the fourth variable can be calculated. In this manner, the kinematic equations provide a useful means of predicting information about an object's motion if other information is known. For example, if the acceleration value and the initial and final velocity values of a skidding car is known, then the displacement of the car and the time can be predicted using the kinematic equations. Lesson 6 of this unit will focus upon the use of the kinematic equations to predict the numerical values of unknown quantities for an object's motion. The four kinematic equations that describe an object's motion are: There are a variety of symbols used in the above equations. Each symbol has its own specific meaning. The symbol d stands for the displacement of the object. The symbol t stands for the time for which the object moved. The symbol a stands for the acceleration of the object. And the symbol v stands for the velocity of the object; a subscript of i after the v (as in vi) indicates that the velocity value is the initial velocity value and a subscript of f (as in vf) indicates that the velocity value is the final velocity value. Each of these four equations appropriately describes the mathematical relationship between the parameters of an object's motion. As such, they can be used to predict unknown information about an object's motion if other information is known. In the next part of Lesson 6 we will investigate the process of doing this. Kinematic Equations and Problem-Solving The four kinematic equations that describe the mathematical relationship between the parameters that describe an object's motion were introduced in the previous part of Lesson 6. The four kinematic equations are: In the above equations, the symbol d stands for the displacement of the object. The symbol t stands for the time for which the object moved. The symbol a stand for the acceleration of the object. And the symbol v stands for the instantaneous velocity of the object; a subscript of i after the v (as in vi) indicates that the velocity value is the initial velocity value and a subscript of f (as in vf) indicates that the velocity value is the final velocity value. Problem-Solving Strategy In this part of Lesson 6 we will investigate the process of using the equations to determine unknown information about an object's motion. The process involves the use of a problem-solving strategy that will be used throughout the course. The strategy involves the following steps: 1. Construct an informative diagram of the physical situation. 2. Identify and list the given information in variable form. 3. Identify and list the unknown information in variable form. 4. Identify and list the equation that will be used to determine unknown information from known information. 5. Substitute known values into the equation and use appropriate algebraic steps to solve for the unknown information. 6. Check your answer to ensure that it is reasonable and mathematically correct. The use of this problem-solving strategy in the solution of the following problem is modeled in Examples A and B below. Example Problem A . Ima Hurryin is approaching a stoplight moving with a velocity of +30.0 m/s. The light turns yellow, and Ima applies the brakes and skids to a stop. If Ima's acceleration is -8.00 m/s2, then determine the displacement of the car during the skidding process. (Note that the direction of the velocity and the acceleration vectors are denoted by a + and a - sign.) The solution to this problem begins by the construction of an informative diagram of the physical situation. This is shown below. The second step involves the identification and listing of known information in variable form. Note that the vf value can be inferred to be 0 m/s since Ima's car comes to a stop. The initial velocity (vi) of the car is +30.0 m/s since this is the velocity at the beginning of the motion (the skidding motion). And the acceleration (a) of the car is given as - 8.00 m/s2. (Always pay careful attention to the + and - signs for the given quantities.) The next step of the strategy involves the listing of the unknown (or desired) information in variable form. In this case, the problem requests information about the displacement of the car. So d is the unknown quantity. The results of the first three steps are shown in the table below. Diagram: Given: Find: vi = +30.0 m/s vf = 0 m/s a = - 8.00 m/s2 d = ?? The next step of the strategy involves identifying a kinematic equation that would allow you to determine the unknown quantity. There are four kinematic equations to choose from. In general, you will always choose the equation that contains the three known and the one unknown variable. In this specific case, the three known variables and the one unknown variable are vf, vi, a, and d. Thus, you will look for an equation that has these four variables listed in it. An inspection of the four equations above reveals that the equation on the top right contains all four variables. vf2 = vi2 + 2 ⢠a ⢠d Once the equation is identified and written down, the next step of the strategy involves substituting known values into the equation and using proper algebraic steps to solve for the unknown information. This step is shown below. (0 m/s)2 = (30.0 m/s)2 + 2 ⢠(-8.00 m/s2) ⢠d 0 m2/s2 = 900 m2/s2 + (-16.0 m/s2) ⢠d (16.0 m/s2) ⢠d = 900 m2/s2 - 0 m2/s2 (16.0 m/s2)*d = 900 m2/s2 d = (900 m2/s2)/ (16.0 m/s2) d = (900 m2/s2)/ (16.0 m/s2) d = 56.3 m The solution above reveals that the car will skid a distance of 56.3 meters. (Note that this value is rounded to the third digit.) The last step of the problem-solving strategy involves checking the answer to assure that it is both reasonable and accurate. The value seems reasonable enough. It takes a car a considerable distance to skid from 30.0 m/s (approximately 65 mi/hr) to a stop. The calculated distance is approximately one-half a football field, making this a very reasonable skidding distance. Checking for accuracy involves substituting the calculated value back into the equation for displacement and insuring that the left side of the equation is equal to the right side of the equation. Indeed it is! Example Problem B Ben Rushin is waiting at a stoplight. When it finally turns green, Ben accelerated from rest at a rate of a 6.00 m/s2 for a time of 4.10 seconds. Determine the displacement of Ben's car during this time period. Once more, the solution to this problem begins by the construction of an informative diagram of the physical situation. This is shown below. The second step of the strategy involves the identification and listing of known information in variable form. Note that the vi value can be inferred to be 0 m/s since Ben's car is initially at rest. The acceleration (a) of the car is 6.00 m/s2. And the time (t) is given as 4.10 s. The next step of the strategy involves the listing of the unknown (or desired) information in variable form. In this case, the problem requests information about the displacement of the car. So d is the unknown information. The results of the first three steps are shown in the table below. Diagram: Given: Find: vi = 0 m/s t = 4.10 s a = 6.00 m/s2 d = ?? The next step of the strategy involves identifying a kinematic equation that would allow you to determine the unknown quantity. There are four kinematic equations to choose from. Again, you will always search for an equation that contains the three known variables and the one unknown variable. In this specific case, the three known variables and the one unknown variable are t, vi, a, and d. An inspection of the four equations above reveals that the equation on the top left contains all four variables. d = vi ⢠t + ½ ⢠a ⢠t2 Once the equation is identified and written down, the next step of the strategy involves substituting known values into the equation and using proper algebraic steps to solve for the unknown information. This step is shown below. d = (0 m/s) ⢠(4.1 s) + ½ ⢠(6.00 m/s2) ⢠(4.10 s)2 d = (0 m) + ½ ⢠(6.00 m/s2) ⢠(16.81 s2) d = 0 m + 50.43 m d = 50.4 m The solution above reveals that the car will travel a distance of 50.4 meters. (Note that this value is rounded to the third digit.) The last step of the problem-solving strategy involves checking the answer to assure that it is both reasonable and accurate. The value seems reasonable enough. A car with an acceleration of 6.00 m/s/s will reach a speed of approximately 24 m/s (approximately 50 mi/hr) in 4.10 s. The distance over which such a car would be displaced during this time period would be approximately one-half a football field, making this a very reasonable distance. Checking for accuracy involves substituting the calculated value back into the equation for displacement and insuring that the left side of the equation is equal to the right side of the equation. Indeed, it is! The two example problems above illustrate how the kinematic equations can be combined with a simple problem-solving strategy to predict unknown motion parameters for a moving object. Provided that three motion parameters are known, any of the remaining values can be determined. In the next part of Lesson 6, we will see how this strategy can be applied to free fall situations. Or if interested, you can try some practice problems and check your answer against the given solutions. Kinematic Equations and Free Fall As mentioned in Lesson 5, a free-falling object is an object that is falling under the sole influence of gravity. That is to say that any object that is moving and being acted upon only be the force of gravity is said to be "in a state of free fall." Such an object will experience a downward acceleration of 9.8 m/s/s. Whether the object is falling downward or rising upward towards its peak, if it is under the sole influence of gravity, then its acceleration value is 9.8 m/s/s. Like any moving object, the motion of an object in free fall can be described by four kinematic equations. The kinematic equations that describe any object's motion are: The symbols in the above equation have a specific meaning: the symbol d stands for the displacement; the symbol t stands for the time; the symbol a stands for the acceleration of the object; the symbol vi stands for the initial velocity value; and the symbol vf stands for the final velocity. Applying Free Fall Concepts to Problem-Solving There are a few conceptual characteristics of free fall motion that will be of value when using the equations to analyze free fall motion. These concepts are described as follows: ⢠An object in free fall experiences an acceleration of -9.8 m/s/s. (The - sign indicates a downward acceleration.) Whether explicitly stated or not, the value of the acceleration in the kinematic equations is -9.8 m/s/s for any freely falling object. ⢠If an object is merely dropped (as opposed to being thrown) from an elevated height, then the initial velocity of the object is 0 m/s. ⢠If an object is projected upwards in a perfectly vertical direction, then it will slow down as it rises upward. The instant at which it reaches the peak of its trajectory, its velocity is 0 m/s. This value can be used as one of the motion parameters in the kinematic equations; for example, the final velocity (vf) after traveling to the peak would be assigned a value of 0 m/s. ⢠If an object is projected upwards in a perfectly vertical direction, then the velocity at which it is projected is equal in magnitude and opposite in sign to the velocity that it has when it returns to the same height. That is, a ball projected vertically with an upward velocity of +30 m/s will have a downward velocity of -30 m/s when it returns to the same height. These four principles and the four kinematic equations can be combined to solve problems involving the motion of free-falling objects. The two examples below illustrate application of free fall principles to kinematic problem-solving. In each example, the problem solving strategy that was introduced earlier in this lesson will be utilized. Example Problem A Luke Autbeloe drops a pile of roof shingles from the top of a roof located 8.52 meters above the ground. Determine the time required for the shingles to reach the ground. The solution to this problem begins by the construction of an informative diagram of the physical situation. This is shown below. The second step involves the identification and listing of known information in variable form. You might note that in the statement of the problem, there is only one piece of numerical information explicitly stated: 8.52 meters. The displacement (d) of the shingles is -8.52 m. (The - sign indicates that the displacement is downward). The remaining information must be extracted from the problem statement based upon your understanding of the above principles. For example, the vi value can be inferred to be 0 m/s since the shingles are dropped (released from rest; see note above). And the acceleration (a) of the shingles can be inferred to be -9.8 m/s2 since the shingles are free-falling (see note above). (Always pay careful attention to the + and - signs for the given quantities.) The next step of the solution involves the listing of the unknown (or desired) information in variable form. In this case, the problem requests information about the time of fall. So t is the unknown quantity. The results of the first three steps are shown in the table below. Diagram: Given: Find: vi = 0.0 m/s d = -8.52 m a = - 9.8 m/s2 t = ?? The next step involves identifying a kinematic equation that allows you to determine the unknown quantity. There are four kinematic equations to choose from. In general, you will always choose the equation that contains the three known and the one unknown variable. In this specific case, the three known variables and the one unknown variable are d, vi, a, and t. Thus, you will look for an equation that has these four variables listed in it. An inspection of the four equations above reveals that the equation on the top left contains all four variables. d = vi ⢠t + ½ ⢠a ⢠t2 Once the equation is identified and written down, the next step involves substituting known values into the equation and using proper algebraic steps to solve for the unknown information. This step is shown below. -8.52 m = (0 m/s) ⢠(t) + ½ ⢠(-9.8 m/s2) ⢠(t)2 -8.52 m = (0 m) *(t) + (-4.9 m/s2) ⢠(t)2 -8.52 m = (-4.9 m/s2) ⢠(t)2 (-8.52 m)/(-4.9 m/s2) = t2 1.739 s2 = t2 t = 1.32 s The solution above reveals that the shingles will fall for a time of 1.32 seconds before hitting the ground. (Note that this value is rounded to the third digit.) The last step of the problem-solving strategy involves checking the answer to assure that it is both reasonable and accurate. The value seems reasonable enough. The shingles are falling a distance of approximately 10 yards (1 meter is pretty close to 1 yard); it seems that an answer between 1 and 2 seconds would be highly reasonable. The calculated time easily falls within this range of reasonability. Checking for accuracy involves substituting the calculated value back into the equation for time and insuring that the left side of the equation is equal to the right side of the equation. Indeed it is! Example Problem B Rex Things throws his mother's crystal vase vertically upwards with an initial velocity of 26.2 m/s. Determine the height to which the vase will rise above its initial height. Once more, the solution to this problem begins by the construction of an informative diagram of the physical situation. This is shown below. The second step involves the identification and listing of known information in variable form. You might note that in the statement of the problem, there is only one piece of numerical information explicitly stated: 26.2 m/s. The initial velocity (vi) of the vase is +26.2 m/s. (The + sign indicates that the initial velocity is an upwards velocity). The remaining information must be extracted from the problem statement based upon your understanding of the above principles. Note that the vf value can be inferred to be 0 m/s since the final state of the vase is the peak of its trajectory (see note above). The acceleration (a) of the vase is -9.8 m/s2 (see note above). The next step involves the listing of the unknown (or desired) information in variable form. In this case, the problem requests information about the displacement of the vase (the height to which it rises above its starting height). So d is the unknown information. The results of the first three steps are shown in the table below. Diagram: Given: Find: vi = 26.2 m/s vf = 0 m/s a = -9.8 m/s2 d = ?? The next step involves identifying a kinematic equation that would allow you to determine the unknown quantity. There are four kinematic equations to choose from. Again, you will always search for an equation that contains the three known variables and the one unknown variable. In this specific case, the three known variables and the one unknown variable are vi, vf, a, and d. An inspection of the four equations above reveals that the equation on the top right contains all four variables. vf2 = vi2 + 2 ⢠a ⢠d Once the equation is identified and written down, the next step involves substituting known values into the equation and using proper algebraic steps to solve for the unknown information. This step is shown below. (0 m/s)2 = (26.2 m/s)2 + 2 â˘(-9.8m/s2) â˘d 0 m2/s2 = 686.44 m2/s2 + (-19.6 m/s2) â˘d (-19.6 m/s2) ⢠d = 0 m2/s2 -686.44 m2/s2 (-19.6 m/s2) ⢠d = -686.44 m2/s2 d = (-686.44 m2/s2)/ (-19.6 m/s2) d = 35.0 m The solution above reveals that the vase will travel upwards for a displacement of 35.0 meters before reaching its peak. (Note that this value is rounded to the third digit.) The last step of the problem-solving strategy involves checking the answer to assure that it is both reasonable and accurate. The value seems reasonable enough. The vase is thrown with a speed of approximately 50 mi/hr (merely approximate 1 m/s to be equivalent to 2 mi/hr). Such a throw will never make it further than one football field in height (approximately 100 m), yet will surely make it past the 10-yard line (approximately 10 meters). The calculated answer certainly falls within this range of reasonability. Checking for accuracy involves substituting the calculated value back into the equation for displacement and insuring that the left side of the equation is equal to the right side of the equation. Indeed, it is! Kinematic equations provide a useful means of determining the value of an unknown motion parameter if three motion parameters are known. In the case of a free-fall motion, the acceleration is often known. And in many cases, another motion parameter can be inferred through a solid knowledge of some basic kinematic principles.What is an earthquake? Would you be surprised to learn that several million earthquakes happen every year? Seriously. Most are so small in magnitude or size that we cannot even feel them. In fact, only 20 earthquakes are efficiently reported each year in the United States Geological Survey. Wow! That is a huge difference! The Earth has four major layers. Inner core, outer core, mantle, and crust. Think of the crust and top of the mantle like the skin of the earth. This skin is made up of different pieces of rock called tectonic plates. There are about 15 major slabs that join together, kind of like a puzzle. The edges around the tectonic plates are called plate boundaries. These massive pieces of rock slide back and forth under the Earth's surface, bumping up against each other and creating a lot of tension. This tension and movement create faults, which are basically huge cracks in the rock. When the faults get stuck, they build up pressure. And when they get unstuck, you guessed it, an earthquake. So basically, an earthquake is caused by the shifting and sliding of tectonic plates on the Earth's upper mantle and crust. There are three ways that tectonic plates shift or slide. They are subduction, lateral sliding, and spreading. Subduction happens when plates crash into each other. This can cause one plate to slide under another and be destroyed. Or the edges of the plate may rise up and form mountains. Lateral sliding means that the plates slide alongside each other, which can create lots of friction. And like you might have guessed, spreading happens when plates move apart from each other. When they do, melted rock between the plates rises and cools, forming new crust. Here's an interesting fact. Nearly 90% of all earthquakes begin in the Pacific Ocean, in an area called the Ring of Fire. It's called the Ring of Fire because along with earthquakes, it's filled with many active volcanoes. More than 450! Earthquakes can be powerful enough to change the surface of the earth and can do a lot of damage. And sometimes earthquakes can even cause other natural disasters, like avalanches, landslides, and tsunamis. Pretty wild, right? The epicenter is the location of an earthquake on the Earth's surface. The closer you are to the epicenter, the more of the earthquake you will feel. Earthquakes lose intensity as they travel away from the epicenter. Scientists measure the intensity of an earthquake using a special device called a seismograph. Seismometers detect and measure the vibrations given off by an earthquake. Magnitude is the number given to record the size of an earthquake. For example, a magnitude 5.5 is considered moderate. Above 8.0 is considered a major earthquake and we see one every year or two. Earthquakes measured at 2.5 or less are usually not felt, but can be recorded. And believe it or not, there are millions that happen each year. You can make a model of a seismograph at home, and we are going to show you how. It's activity time! You can print off directions for this one on our website at learnbright.org. You'll need a cardboard box, string, a plastic cup, a marker, small heavy objects, a long strip of paper, and a friend because this is an activity for at least two people. Now comes the fun part. One friend shakes the box, alternating between hard and soft and slow and fast, while the other friend is pulling the strip of paper through the bottom. Watch the marker as it records the movement. This is exactly what a seismograph does during an earthquake. So, in a way, we have not only created our own seismograph, but our own earthquake as well. Now, we can analyze the data just like scientists. Can you tell how hard the box was shaking based on the line? Can you tell when it was barely shaking at all? You are on your way to becoming a seismologist. A seismologist is a person that studies earthquakes. It's pretty cool to watch the process, but it's even more exciting to do it yourself. You can head on over to our website to get detailed instructions for this activity. Just download the lesson plan and as always have fun! Hope you had fun learning with us! Visit us at learnbright.org for thousands of Hope you had fun learning with us! Visit us at learnbright.org for thousands of free resources and turnkey solutions for teachers and homeschoolers.Cohesion and Adhesion Water molecules stick to each other as a result of hydrogen bond- ing. An attractive force that holds molecules of a single substance together is known as cohesion. Cohesion due to hydrogen bonding between water molecules contributes to the upward movement of water from plant roots to their leaves. Related to cohesion is the surface tension of water. The cohe- sive forces in water resulting from hydrogen bonds cause the mol- ecules at the surface of water to be pulled downward into the liquid. As a result, water acts as if it has a thin âskinâ on its sur- face. You can observe waterâs surface tension by slightly overfill- ing a drinking glass with water. The water will appear to bulge above the rim of the glass. Surface tension also enables small crea- tures such as spiders and water-striders to run on water without breaking the surface. Adhesion is the attractive force between two particles of differ- ent substances, such as water molecules and glass molecules. A related property is capillarity (KAP-uh-LER-i-tee), which is the attrac- tion between molecules that results in the rise of the surface of a liquid when in contact with a solid. Together, the forces of adhe- sion, cohesion, and capillarity help water rise through narrow tubes against the force of gravity. Figure 2-11 shows cohesion and adhesion in the water-conducting tubes in the stem of a flower. Temperature Moderation Water has a high heat capacity, which means that water can absorb or release relatively large amounts of energy in the form of heat with only a slight change in temperature. This property of water is related to hydrogen bonding. Energy must be absorbed to break hydrogen bonds, and energy is released as heat when hydrogen bonds form. The energy that water initially absorbs breaks hydro- gen bonds between molecules. Only after these hydrogen bonds are broken does the energy begin to increase the motion of the water molecules, which raises the temperature of the water. When the temperature of water drops, hydrogen bonds reform, which releases a large amount of energy in the form of heat. Therefore, during a hot summer day, water can absorb a large quantity of energy from the sun and can cool the air without a large increase in the waterâs temperature. At night, the gradually cooling water warms the air. In this way, the Earthâs oceans stabilize global temperatures enough to allow life to exist. Waterâs high heat capac- ity also allows organisms to keep cells at an even temperature despite temperature changes in the environment. As a liquid evaporates, the surface of the liquid that remains behind cools down. A relatively large amount of energy is absorbed by water during evaporation, which significantly cools the surface of the remaining liquid. Evaporative cooling prevents organisms that live on land from overheating. For example, the evaporation of sweat from a personâs skin releases body heat and prevents over- heating on a hot day or during strenuous activity. Adhesion Cohesion Hydrogen bonds Cohesion, adhesion, and capillarity contribute to the upward movement of water from the roots of plants. FIGURE 2â11 www.scilinks.org Topic: Hydrogen Bonding Keyword: HM60777 mb06se_cols03.qxd 5/18/07 10:47 AM Page 41 42 CHAPTER 2 Density of Ice Unlike most solids, which are denser than their liquids, solid water is less dense than liquid water. This property is due to the shape of the water molecule and hydrogen bonding. The angle between the hydrogen atoms is quite wide. So, when water forms solid ice, the angles in the molecules cause ice crystals to have large amounts of open space, as shown in Figure 2-12. This open space lattice structure causes ice to have a low density. Because ice floats on water, bodies of water such as ponds and lakes freeze from the top down and not the bottom up. Ice insulates the water below from the cold air, which allows fish and other aquatic crea- tures to survive under the icy surface. âOn this night, we share a roof protecting us from fleets of inequity. Our unification promises a better tomorrow. Those larger than myself, sitting on their marble thrones, sipping blood from cups composed of human skin and singing songs of so-called virtue, grow weaker each moment. Their caravans are revolting. There is hope yet. There is progress! Though tonight may mark a countdown, it is still a celebration. Look at all we have done, not just for Trials but for Palatium Infra as a whole. In four years, when Iâm no longer Sovereignty, the Spoiled Purity and his people will continue to strive. So drink! Smoke! Crush up those exotic plants and snort them! We will not falter, weaken, or wane. Our influence is expanding, and somebody new opens their eyes every day. Even the Silbys of Aculeus have reached alarming potentials despite their embittered minds. So long as you relish in tonight, dance, and pray to your âdeadâ Gods, our revolution shall rise beyond the bounds of class, and when Iâm only a commoner, we shall rise again beyond our brainwashed adversaries! Cheers, my people. Cheers!â Followers raised their cups. Some clinked theirs together. Others stood still and screamed breathlessly in agreement. I smiled with courtesy, then stepped off my platform. My voice still rang across the cellar. Speeches before were grander. Those displays were supposed to be emptying, and yet this one left me bloated, swollen tight. I watched as they popped the corks of their bottles and chanted in the name of Purity. Maybe the quality of my words wasnât what mattered to them anyway, so long as I screamed loud enough. Thereâs no merit in attacking your people, a voice corrected me. âThatâs right,â I said aloud. âKnox, my-my Sovereign!â squealed a nearby devotee, jittering as he stuffed his face with catered pastries. He was one Iâd never seen before or had failed to remember. âLook what Iâve found! Itâs wine, and not the shoddy Infran kind, either. Earth-made with good fruit! I donât know how anyone managed to get their hands on this. Maybe some space travel mischief.â He giggled and held up a small glass bottle. âHow neat.â âI want you to have it, Sir.â I nodded my head. âYes, of course. Thank you.â Backing off into the midst of rowdy disciples, I clutched the bottle. What a waste of grapes. It could have been jam instead. Earthly food had a superior taste, ripe with delicate intricacies and nostalgia, but Palatium Infra had mastered the art of alcohol. Why waste your time with a drunkenness so sad and sickening? The booze of trash. Not many more followers approached me. The barren peroration must have upset them. My hands itched to submerge into my suit pockets, and my legs stood suddenly numb, wobbling. Four more years until Iâm nothing. But tonight, you are nothing. âShut up,â I told myself. Tightly packed together in the corner of the dwelling sat the Sibyls. A mound of writhing fabric and tones of skin made up their unified silhouette. I snapped the strap of the nearest gown, balancing on my hands and knees, waving the bottle before them. In their almost rodent nature, narrow noses prodded my way. Their dresses wrinkled and fell to their ankles. Knees dropped, and eyes widened. Many grumbled at me like hungry she-beasts. Those newer ones with faded curtains for hair, sunken eyes, and dirtied nails looked, hid their face, then sobbed. I imagined them in a pack together, fighting wildly against the Spoiled Purity in their rat decorumâbiting down with square teeth laced with rabies. âIâve got you all something,â I said. âGo back off to your pedestal and yap some more. We donât want it.â A woman rose from the pile and spat. âYou donât even know what it is yet. It's Earth hooch, or more likely a near-flawless replica. I figured you girls would also like a chance to enjoy yourselves tonight.â âYour playmates have been harassing us since the moment you hung the banners and opened the cellar door.â The youngest, with a striking cyan mop upon her head, uncoiled from the mass. What was she now? 20, 21? We celebrated a birthday recently, I thought as she spun around me. âI remember something about a promise. Multiple promises, actually. Are you trying to bribe us into just shutting up and taking it? Because if another sticky, 40-year-old, Earth-born virgin gropes my shoulder, Iâm going to have an aneurysm!â the girl continued. âWhy not an Infran follower? Do you like it when they touch you?â I returned her accusing tone. âIâm sorry, sweet prophets, that you feel Iâve neglected my duties. Iâll keep a better eye out. Remember, you can always just holler if somebody is bothering you. And Anwen, friend, if Iâve ever tried to bribe you with anything, it was certainly the hair dye. I mean, look at you! Such handsomeness!â I exclaimed. The other Siblys began to encircle her, uttering compliments or even announcements of their envy. Anwen disappeared in a wink with flushed cheeks back into the mound. âIâll just leave this here.â Smiling, I set down the bottle. ** â141, 143. . .â I counted each step as I trekked the staircase. There was no doubt I lost track somewhere. The ledges kept spawning under my feet, infinitely multiplying until I wasnât moving at allâswallowing me up in a whirlpool of stone. My tie still hung around my neck, and my blazer remained tied around my hips as a skirt. Streaks of red dribbled off from the cavity in my chest. It was a gorgeous marking, sensual to my fingertips as I traced its edges. Purity, oh, Purity. Purity and his wings of burnt skin. Purity and his many faces. Purity the spoiled. Purity the mutilated. The Silbys did not bother waiting for me. On bare feet, they stormed up the stairs to their room. A trail of red, though in paint unlike mine, streamed after them. None looked remotely near me as they squeaked and gossiped intangibly. I saved them, those Infran broads, enlightened them. As much as they liked to deny it, spit at me, and bask in the thought of their victimhood, in this home, they stood empowered. Youâve done well, my thoughts affirmed, though in the manner of an insincere commentator rather than a hype man. Teeth grace in tile violin goes laundry paper when. It dissolved into an intruding drivel. I rubbed my head and sniveled. âDo you need help, Knox?â called a Silby. Fattened by my coddling, her shadow fell upon me from the doorway steps ahead. I attempted counting again. There mustâve been at least another hundred between me and her. âIâm hallucinating some,â I said, breathing deeply to suppress a burp as I struggled to recall her name. Two syllables. Typically Latin, though sometimes English. Drops of slobber leaked from my mouth. âIâm hallucinating some, Tybal. Do you like your name, Tybal? I would have named you something better. Ty-Tyballinia. No, weâd have to eliminate the âballâ aspect. It sounds too crude.â âOne foot in front of the other,â she said. So I walked. Mess greeted me at the doorway. Dirtied culinary obscured the dark wooden countertops, and the sink lay running. I approached the kitchen table, sat, and set my face down upon its cool wooden surface. Assaulting my nose was the smell of neglected flowers, like soil mixed with the kind of sweet cough medicine that would have left me gagging as a child. Open windows whispered songs of the twilight hour through the vessels of busy trolleys and shooting guns. My mouth strained to vomit, but there was nothing in my stomach to regurgitate except the petals of Stultoâs bloom, which came out effortlessly in little sputters. Teetering, I stood up and brushed disgorged plant parts off the tabletop. âLove,â I said as I slogged up yet another staircase. âAre you awake?â She said sheâd wait. Somebodyâs gotten her. No, she always misses movie night. That sleepyhead, I assured myself. There was a stirring amidst the manorâs cloak of dusk. Portraits of myself, my wife, and my daughter turned to face me as the hallway lights flickered, escaping their quartz frames to penetrate my ears with nonsense. The taxidermied heads of Infran creatures bared their teeth. I stopped to stare at my favorite, an adabactor with daunting spiked tusks poking out from its forehead. Its nose remained black and sharp, and its eyes wide with malice. âWhere is my Spes, Adaba-boy? Is she sleepy?â Thereâs someone in the house. The sounds of the stirring rose along with my blood pressure. Footsteps orbited around me, drawing near and far and then near again, little dancers in the dark. The carpet immersed me in its mass of purples and blues, leaving my skin stained indigo and my vision abstracted. I toiled to reach the master bedroom across the aisle as it stretched out to me with bright lights and celestial howling, like a dove struggling in a pool of oil. Never again with Stultoâs bloom. Never again on what was already a bad night. My hand brushed the doorknob, and the high abruptly faded into only a persistent hum-buzz twirling around my brain. The portraits returned to their typical depressionâSpes posing with her ax, Ariâs school photo, and myself in the cap I wore when addressing the military with the Verbis emblem embroidered in its center. All lifeless shots. Who were they for when they captured not the subjectâs essence but only some fragment of their identity? They used to feel personal, not advertisements of some supposed characters. Servants, babysitters, and likewise civilian guests, I reminded myself, mustnât forget whose home theyâre in. Yet my body moved independently, taking Ariâs from its hook and laying it backward against the wall to hide her distant grin and tamed posture. It was time for new pictures. Sweet ones, real ones; time was ticking. I approached my own when the stirring began again. Groans and squeals erupted from the vents as if someone had set a pen of pigs loose in my crawlspace. No, not the crawlspace, my bedroom door. I turned the ruby knob. Underneath a blanket wrestled my two squealing piglets, their skins melting together beneath the layer of duvet. Fishnet leggings and manicured nails outstretched and scraped at the sheet beneath them. One raised its head, a salmon-colored man with sweat running down his forehead. Through the crack in the door, we met eyes, his Infran Dr. Sesuss nose flaring its narrow nostrils. No mark of the Spoiled Purity existed carved onto his naked body. My chest felt tight. I stepped back. I was suffocating. Spes emerged from the linens, her hair flowing down her back and her dark skin glistening in front of the bedroom window. She giggled and held the man, the blanket falling and revealing inches of her body I had not seen in months. âDarling,â whispered the rosy-faced man, âlook.â He was unfathomably ugly and grotesquely young, with beady, lifeless pupils that dilated when he faced me. The excess flesh on his face sagged while he bit down on his thin lips. My wife faced me, gasped, and strained to cover herself. Suddenly, I was a stranger. A small child who had walked into his parents having sex. I unfurled the door completely. âGet out of my house,â I said. The man stayed in place. âGet out of my house,â I repeated. âKnox,â Spes began. Tears ran down her round cheeks. âShut up!â I turned to the man, picking up a marble trophy from on top of my dresser. âGet out of my house! Iâll kill you!â âKnox!â Spes sobbed. âGod damn it! I hate you! You barely look at me. Every day, thereâs less passion. God, God, God, I donât want to fuck a dead man!â she screamed, âYou get out! Get! Get!â My hands wrapped tighter around the statue. That pig of a man was attached to her at the side, his face equipped with a scowl that challenged mine. He thought I was weak; frail like a decaying dementia-ridden senior. I imagined his skull bashed in, his scowl gone, and the feist and confidence in his face beaten into numbness. A new portrait was in order of such brutality, him as a splintered slab of wood, rashed and beaten, a carcass licking my boot. The churning in my brain had come back. Every wall shook. Clock faces came to life and rang in alarm. Indescribable noises caressed my eardrum before breaking into sorrowful weeps. Was it my own? I stared at Spes in motionless frenzy, clenched my teeth, and screamed like a siren. Passionless. What a lie! An excuse, more like. One that erased all my ventures, reducing me to a nobody. But I was not a nobody. I thought of my sect, my campaigns, my endurance through the political brutality of my empty hive-mind worldâeven my collection of literature, maps, and artifacts. I thought of daring nights alone with Spes when we were young, ravaging each other, two sardonic eggheads suddenly overcome with desire. The veins in my neck throbbed as I gasped for air. It was all I had. I threw the figurine at the manâs head. Eye shut, I heard the thud. A million singing voices of victory flooded out of the cracks in the floorboard. Proving myself a man to the woman I loved in a display of fervent violence was passion. I strained my ears for his cries, though I did not look yet. There had to be a pause, a moment of relief, where I stood tall as a skyscraper and seemingly fought to stay contained in front of my wife and her wounded, quivering paramour. Frantic footsteps rushed off the bed and past my side. I turned and grappled against myself to seize my wifeâs shoulder. âSpes!â My eyelids lifted. Escaping was the man with that same numb expression in which I had imagined him. âYouâre insane,â he said. I swiveled back towards the bed. With her curly locks flowing over her breasts and her limbs bent at her sides, Spes sat limp pressed against the headboard, her forehead bludgeoned and the statue resting on her stomach. Lips pursed and sweet, my Renaissance beauty reclined there in the guise of a squashed bug. But she was not dead. The desk ornament I flung was only the size of my shoe. Spes, that dramatist, may have been slightly hurt but was far from dead. She only wanted me to think she was to observe me at my most distraught, like a leech feeding on misery. âGet up.â Staggering toward the bed, I said. âYou wanted passion? I showed you passion. âShoved it right into your head. Of course, we both know who that gesture was meant for. . .â I fumbled to find my wit. Cold skin met my hands as I stroked her face, unable to resist checking her pulse, even though she was not dead. âI love you, Spes,â I said. Rain pelted against a nearby window. âSpes, please. Please.â No vibration answered my plea. I lifted my hand, sitting next to her now. Tears did not come. There was not any blood on the trophy, but when I picked it up, it felt to be now only a cruel instrument. It depicted a younger me in white marble, with my glasses and collared shirt being the only things painted. Both were in pink. It was a favorable color. I scrambled from the bed to vomit pure digestive bile on the rug. My stomach heaved. I ran my nails along every piece of myself I saw, a dog chasing my tail. As I slammed myself against walls and convulsed, my own heart grew ever louder in my chest. âDad? I heardââ Ariâs slippered feet hammered across the floor. âMom? Mom?â I kept my eyes on the storm. Silence fell. âShe-She isnâtâyourâ.â Gasps interrupted every syllable she spoke. âYouâre a murderer. Bad. Like they said,â she breathed, â You beat her!â The words became mush, alphabet soup. Ari ran back down the hall. âMy-My mom is dead. . . .Yes. . . Manor of the Trials Sovereignty. . .Ari Sorkin. . . Iâm afraid heâs going to hurt me,â she said, presumably over the phone. It was all too fast. I crawled onto the windowsill, opened the glass, and let myself plummet into the alley below. Gusts of wind howled. The lack of motion or sensation informed me I had passed and again lived. Another Palatium Infra, another strange planet in which the celestial endowed rotting men with the opportunity to inhabit. Was this it? Was it all just an impossible limbo of galactic traveling? My surroundings were overwhelmingly gray, an abyss of clouds. Perhaps I had now met the real coming world, and my family and old friends lived here, ready to rush to my sides, lift me up, and jump for joy. Spes would be there. She would be enraged, but at least sheâd be there. You are a bad man. You are a bad man. My eyelashes fluttered. There was a tugging sensation in my leg. The fog was wavering along with my ascendance. âNo,â I yearned, trying to grip the clouds and stick them in place. âStay with me.â But the peace was fleeting. I felt the cement under me and the moist garments clinging to my figure. My leg burned. Carefully, I craned my neck, only to observe the promenade as my surroundings. The most underwhelming of filth and danger, individually Infran. Forever my coming world. What a fool I was, having forgotten my blessing. Those idiot Gods could not tell the difference between assassination and self-infliction; a faulty insurance plan. The urge to cry at last set over me, and so I sat and wailed hot salvia into my palm, shielding my mouth to muffle the noise. Thunder echoed my hushed howling. Raindrops turned to pebbles. Under the ambiance of the stormy night, I could have sworn I heard troops stomping, guns cocking, and the chanting of my name. They had all been waiting for this. Billboards came to life, and I could only sit and spectate as the scenery flashed red. I inhaled fear and sobriety through runny nostrils. âTrials Sovereign Vsevolod âKnoxâ Sorkin is currently at large for the suspected homicide of Spes Sorkin, breaking the first term of the Sovereignty Charter. We now instruct you to report any sightings of the Earth-born, caucasian, roughly 195 centimeters tall, brown-haired, and brown-eyed man to your local Guard post. One can identify the suspected convict specifically by an occult tattoo of Purityâs Coronet on his lower back. No attempted execution or elongated punishment will take place until our Guards conduct an autopsy proving his guilt, per Lifeâs 1238 commandment. We cannot be sure when or if the Gods will revoke his blessing. Remember, when Gods frown upon strife, opt for a peaceful life. We permit all grieving festivities until Cagidus 4th. Good year!â towering buildings sang out in broadcast, repeating that same convoluted message quicker the instant it ended. Sometimes, the announcer spoke in Latin for the Infran children, other times in Chinese, Hindi, or Spanish to cater to those of irrelevant tongues. You arenât a bad man. You are a stupid boy. Puddles sloshed. Somebody was approaching. I didnât dare waste any remaining energy avoiding the Guards and their prodding blades. How did that phrase go? You dug your grave. Now lie in it. And so I embraced the cement. âKnox?â said the Guard. No, her tone was too sincere, and no authority would proceed in such a manner. There wasnât confirmation on whether or not I was armed, and it wasnât as if she could shoot me first. She was a partygoer, having just left from the cellarâs backdoor. I shooed her away with my hand. She hovered, and I discerned her shadow hesitating over my body. A man could not rot in peace. âCome on, get up! Theyâre after you!â Hands reached around my torso, struggling to handle my weight as they urged me onto my feet. That leg, the burning one, my right, trembled and bent unnaturally upon impact with the ground. The partygoer slung my arm over her shoulder, balancing me. My eyes caught a glimpse of a cyan mop. âAnwen?â I rasped, âhu-who let you out?â Keys jangled in her handsâmy keys. âI escaped,â she said casually, coercing me to walk beside her. âQuicken your pace. I just heard somebody on your front porch. âYou see that compost bin down the alley? Weâre gonna burrow right down into the depth of that. If they open it and uncover us, Iâll be on top, and I can hide you and act like Iâm just a homeless amica trying to take a nap.â With a tightening grip, she led me like livestock to the stinking crate. âI donât understand, Anwen,â I said. âTheyâre going to torture and kill you, stupid. You know theyâve been wanting to, and you just handed the opportunity to them!â âI understand that.â It was becoming increasingly challenging to hide the fragility emerging in my voice. âYou said you were escaping. Why stop and help your captor?â âWhat else could I do? Leave you there?â Attempts to shove my wounded body inside its mass of discarded fruits and vegetables began. She yanked down upon my head and submerged me in the fertilizer sea. The evidence grows indisputable, I thought as I stared at the abruptly humane Infran girl, diving in after me, that I belong here. âDamn me to hell! Iâve killed her! My love is dead!â an uncontrollable cry leaped from my mouth. âShut up! Soon youâll be, too, if you donât quiet down.â The actual noise of the Guards darted past us: disorientated marching, guns clanking against each other, cluttered belts rattling, the Latin squawking. One paused to open the binâs lid, though only rummaged through the surface layer of peat before carrying on. âWhat are they talking about? I struggle with my Latin,â I whispered. âThe search, mainly.â Aggression remained firey in Anwenâs clenched jaw. Though she sat on top of me, there was a monumental distance between our rain-soaked forms. I curled up into a ball, ducked my head between my knees, and dreamt of Spes, ignoring the stench of spoiled food rising from every crevice of my dwelling. The next coming world was due to adopt me again as I forced sleep. I prayed for a canyon of fluffy haze, where I waltzed with pale memories but found nothing but the petrifying stillness of my mind. Killed and ran. Violent as a Guard just to prove a point and watch it backfire. Why would any heaven want to welcome me? I clung to the picture of Spes in my head like it was the last ember of an extinguished flame. âDid you mean to kill her?â Anwen interrogated. âSomeone like you would immutably believe yes.â âAnd who is someone like me? You canât even treat me like a person for a moment, can you?â grating drama decorated her words. âYou know my opinions. I have not seen much of your or your breedâs faces besides that of cruelty and ignorance.â I retorted. âI just saved you! Does that make me cruel and ignorant?â âIt makes you an idiot, which is another word for somebody ignorant.â âAnd why am I an idiot?â She asked. âBecause you helping me does no good. Thank you anyhow. Now, do yourself a favor and scram.â As she bent her leg in anticipation, preparing to strike me on the forehead, I sensed an invisible withdrawal widening the gap between us. âYou never answered my question,â Anwen took me by the end of my tattered tie suddenly and started her game of shepherd and sheep over again, pulling me back up to the crateâs exit. It appeared as a shining light at the end of a maze of rubbish and mold. âNo. Of course not. Spes was my everything,â I sniffled. âI knew it. You couldnât even bring yourself to hit us, let alone murder your wife. The girls and I always figured you were sensitive.â My heart rate quickened. Today was one of humbling and miseryâone to pray a hail spike would fall from the sky as sharp as a needle, pierce into my eyelid, and lobotomize me. I wished I could have merely died or hit my head hard enough not to have to deal with it all. No, I wished I was Anwen with her snarky, careless glow and lack of depth in her eyes. As we emerged from the compost bin together, I fantasized about strangling her until her face turned purple, her weakening spirit no longer categorizing me as âsensitiveâ, but the thought could only remind me of wielding that trophy and the microscopic traces of my wifeâs tender skin tainting it, which turned my guts inside out. âThatâs why I think you could use a little help,â Anwen said, âIt seems like you canât walk, either. Your leg is all twisted up.â She undid one of her trim pigtails and handed me the band. âTake off your tie and put up your hair. âWill make you less recognizable. Then swallow your pride and stick with me.â