Cracking the sat 2013 pdf

This allows you to come back to time-consuming questions if you have time at the end of the test. How Should I Prepare for the Test? The test is offered in May and June, so you can take it near the end of the school year while the material is still fresh. This book contains hundreds of practice questions that review all of the content areas covered on the test. Each chapter except the first is followed by sample multiple-choice questions. One of the most important aspects of this book is that answers and explanations are provided for every example and question.

In addition, two full-length practice tests are provided. These are designed to simulate a real SAT Physics Subject Test and will give you additional practice for the real thing. Again, a complete solution is provided for every question in both of these sample tests. Practice test questions are also available directly from the College Board on its website, www. Good luck! Chapter 1 Math Review The few questions on the SAT Physics Subject Test that require you to know mathematics are straightforward and actually need little math beyond some algebra and maybe a little trig.

The material in this chapter is pretty clear-cut, so you should know this stuff backward and forward for the test. For example, the speed of light through empty space is approximately ,, meters per second. As the two examples above show, when a very large number is written in scientific notation, the value of n is a large positive integer, and when a very small number is written in scientific notation, n is a negative integer with a large magnitude.

Take a look at the following right triangle, ABC. The right angle is at C, and the lengths of the sides are labeled a, b, and c. Pythagoras was actually a cult leader around B. Some rules of his number-worshipping group included prohibitions against eating beans and wearing wool. Now for the trig functions. The number of distinct angles is what goes under the root sign.

This is one of the most common uses of trig for the physics in this book. A quantity that does not involve direction is a scalar. For example, 55 miles per hour is a scalar quantity, while 55 miles per hour, to the north is a vector quantity. Speed and distance are scalar quantities. Other examples of scalars include: mass, work, energy, power, temperature, and electric charge. Distance Distance is a scalar quantity.

It refers to the amount of ground an object has covered. The scalars of distance and speed are paired with the vectors of displacement and velocity, respectively.

In this book we will show all vector quantities in bold. For example, A would be the scalar quantity, and A the vector quantity. Graphically, a vector is represented as an arrow whose length represents the magnitude and whose direction represents, well, the direction.

Displacement which is net distance [magnitude] traveled plus direction is the prototypical example of a vector: Displacement Displacement is a vector quantity. Vector Addition Geometric The figure above illustrates how vectors are added to each other geometrically.

Place the tail the initial point of one vector at the tip of the other vector, then connect the exposed tail to the exposed tip. The vector formed is the sum of the first two. Add the following two vectors. Scalars scale a vector in the sense that they alter the magnitude but not the direction. If the original vector is A and the scalar is 4, then the scalar multiple 4A. Simply put, it has a magnitude that is four times greater than the original vector.

Note that, unlike vector addition, vector subtraction is not commutative. For the two vectors A and B, find the vector A — B. Components of Vectors So as you can see, a vector can be defined as the sum of two or more vectors.

Perpendicular vectors that are added together to make up a vector are called its components. The vectors B and C, below, are called the vector components of A. Two-dimensional vectors, that is, vectors that lie flat in a plane, can be written as the sum of a horizontal vector and a vertical vector. For example, in the following diagram, the vector A is equal to the horizontal vector B plus the vertical vector C.

The three arrows of the known vector and its component vectors create a right triangle. Setting up the components of the vectors in this way makes it much easier to add and subtract vectors and it allows you to use the Pythagorean theorem instead of some tricky trig. Ax and Ay are called the scalar components of A. A vector can be expressed in terms of its components using the unit vectors i and j.

Vector Operations Using Components Using perpendicular components makes the vector operations of addition, subtraction, and scalar multiplication pretty straightforward. Add the components along the x-axis to form the x-component of the resultant vector, and then add the components along the y-axis to form the y-component of the resultant vector. You can use the values for Cx and Cy along with the Pythagorean theorem to determine the magnitude and direction of the resultant vector. Vector Subtraction To subtract vector B from vector A, use the same procedure.

Resolve each vector into perpendicular components and subtract them in the indicated order. Or decrease it, if you multiply by a fraction. Multiply each component by a given number. Therefore, the x-component of the sum is — 2 and the y- component is — 1. The x-component is 6 and the y-component is —5. Magnitude of a Vector Magnitude is a scalar number indicating the length of a vector.

Use the Pythagorean theorem! You can use components Cx and Cy to find the magnitude of the new vector C. In general, any vector in the plane can be written in terms of two perpendicular component vectors.

Add vectors by connecting vector arrows tip to tail and connecting the exposed tail to the exposed tip. The vector formed is the sum of the other vectors. You can also add or subtract vectors by adding or subtracting their components. Multiplying a vector by a positive scalar creates a vector in the same direction. Multiplying a vector by a negative scalar creates a vector in the opposite direction.

To find the magnitude length of a vector, you cannot simply add the lengths of the other two vectors. Resolve the vectors into horizontal and vertical components and use the Pythagorean theorem. Chapter 2 Kinematics Kinematics in many ways is the heart and soul of physics and, not surprisingly, a big deal on the SAT Physics Test. In this chapter, we will explicitly define these terms and investigate how they relate to one another.

Additionally, we will go beyond one-dimensional motion and delve into two-dimensional motion, that is, the world of projectile motion. Displacement: A Strange Trip The insect on the table below crawls 1 meter north, 2 meters east, 1 meter south, and finally 2 meters west. Even though the insect has crawled a total distance of 6 meters, its displacement is 0 meters. Displacement is a vector quantity, and must incorporate net direction. The 1 meter north is canceled by the 1 meter south, and the 2 meters east is canceled by the 2 meters west.

Displacement is a net change, so it may differ in magnitude from total distance traveled though if the path is all in one direction, it will not. A rock is thrown straight upward from the edge of a 30 m cliff, rising 10 m then falling all the way down to the base of the cliff. Since the rock started on the edge of the cliff and ended up on the ground 30 m below, its displacement is 30 m downward. In a track-and-field event, an athlete runs exactly once around an oval track, a total distance of m.

The total distance covered is m, but the net distance—the displacement—is 0. Distance vs. Displacement Note that distance is not the magnitude of the displacement unless the object has moved in a straight line. What if the car changes its speed as it drives say, it stops at a traffic light? We can look at a quantity that gives us information about the entire trip. By definition, average speed is the ratio of the total distance traveled to the time required to cover that distance.

You could be driving north, south, east, or west, the speedometer would make no distinction: 55 miles per hour, north and 55 miles per hour, east register the same on the speedometer as 55 miles per hour.

Speed is a scalar quantity. However, we also need to include direction in our descriptions of motion. We just learned about displacement, which takes both distance net distance and direction traveled into account. The Skinny on Velocity Since velocity is defined as the change in position per second, we can say the following for motion along the x- or y-axis : If v is positive, then the displacement is positive: The object is traveling in a positive direction.

If v is negative, then the displacement is negative: The object is traveling in a negative direction. Notice the distinction between speed and velocity. However, in physics, speed and velocity are technical terms with different definitions.

Speed has no direction and is always taken as a positive. Velocity is speed and direction. The magnitude of the average velocity is not called the average speed. Average speed is the total distance traveled divided by the elapsed time. Average velocity is the net distance traveled divided by the elapsed time. Average Velocity vs. Average Speed Average speed is not the magnitude of the average velocity unless the object has moved in a straight line.

Assume that the runner in sample question 3 completes the race in 1 minute and 20 seconds. Find her average speed and the magnitude of her average velocity. Is it possible to move with constant speed but not constant velocity? Is it possible to move with constant velocity but not constant speed? The answer to the second question is no. Velocity means speed and direction; if the velocity is constant, then that means both speed and direction are constant.

In all of these cases, the velocity changes. To describe this change in velocity, we need a new term: acceleration. A car is traveling in a straight line along a highway at a constant speed of 80 miles per hour for 10 seconds. Find its acceleration. Find its average acceleration. The negative sign means that the direction of the acceleration is opposite the direction of the velocity: The car is slowing down.

If an object has negative velocity, then a positive acceleration means it is slowing down and a negative acceleration means it is speeding up. This can be confusing. Just remember that if velocity and acceleration point in the same direction, the object is speeding up and if they point in opposite directions, it is slowing down.

Note: If velocity and acceleration are perpendicular, the object is turning with constant speed. The Skinny on Acceleration Since acceleration is defined as the change in velocity per change in time, we can say the following: If a is in the same direction as v, then the object is speeding up. If a is in the opposite direction as v, then the object is slowing down. This means that, for example, positive acceleration does not necessarily imply that an object is speeding up.

If the velocity is negative, positive acceleration means that the velocity is becoming less negative slowing down. We will discuss this further in Chapter 3. In these cases, there are only two possible directions of motion— one is positive, and the opposite direction is negative. With straight-line motion, we can show direction simply by attaching a plus or minus sign to the magnitude of the quantity; therefore we will drop the standard vector notation.

Keep in mind that all of the quantities in the Big Five except t are vector quantities that is, they can be positive or negative. Acceleration is a change in velocity, from an initial velocity vi or v0 to a final velocity vf or simply v—with no subscript.

These five quantities are related by a group of five equations that we call the Big Five. This is true because the acceleration is constant. Each of the Big Five equations is missing one of the five kinematic quantities. How far did it travel during this time? How far does the car travel during this time? Since t is missing, we use Big Five 5. Those Pesky Signs Make sure you are clear which direction is positive.

This makes sense, because the object moves downward and the acceleration it experiences is due to gravity, which also points downward.

The two most popular graphs in kinematics are position-versus-time graphs and velocity-versus-time graphs. Position vs.

For a straight line, the slope is constant. Thus, average velocity and velocity are equal. Therefore: The slope of a position-versus-time graph gives the velocity. The fact that v is negative also agrees with the observation that the slope of a line that falls to the right is negative. The average speed is the total distance traveled by the object divided by the change in time. In this case, notice that the object traveled 10 m in the first 2 s, then 15 m backward in the next 1.

Slope The slope of a line that goes up to the right is positive, the slope of a line that goes down to the right is negative, and the slope of a flat horizontal line is zero. Also, remember that if any portion of a Position vs. Velocity vs. What can we ask about this motion? Therefore The slope of a velocity-versus-time graph gives the acceleration.

Time Graphs: How Far? We can ask another question when we see a velocity-versus-time graph: How far did the object travel during a particular time interval? Displacement vs. Distance If we wish to find the distance traveled using a velocity vs.

Questions The velocity of an object as a function of time is given by the following graph: How would you answer this same question if the graph shown were a position-versus-time graph? The acceleration is equal to the slope of the velocity-versus-time graph. Although this graph is not composed of straight lines, the concept of slope still applies; at each point, the slope of the curve is the slope of the tangent line to the curve. The slope is essentially zero at points A and D where the curve is flat , small and positive at B, and small and negative at E.

If the graph shown were a position-versus-time graph, then the slope would be equal to the velocity. The slope of the given graph starts at zero around point A , slowly increases to a small positive value at B, continues to slowly increase to a large positive value at C, and then, at around point D, quickly decreases to zero.

Of the points designated on the graph, point D is the location of the greatest slope change, which means that this is the point of the greatest velocity change. Therefore, this is the point at which the magnitude of the acceleration is greatest.

With these effects ignored, an object can fall freely, that is, it can fall experiencing only acceleration due to gravity. Near the surface of the earth, the gravitational acceleration has a constant magnitude of about 9.

And, of course, the gravitational acceleration vector, g, points downward. Hammers and Feathers At a given location on the earth and in the absence of air resistance, all objects fall with the same uniform acceleration. Thus, two objects of different sizes and weights, such as hammers and feathers, dropped from the same height will hit the ground at the same time. A rock is dropped from an meter cliff. How long does it take to reach the ground? How fast will it be falling 2 seconds later?

Since s is missing, we use Big Five 4. Since v is missing, we use Big Five 2. If we launch an object at an angle other than straight upward, and consider only the effect of acceleration due to gravity, then the object will travel along a parabolic trajectory.

To simplify the analysis of parabolic motion, we analyze the horizontal and vertical motions separately, using the Big Five. This is the key to doing projectile motion problems. Calling down the negative direction, we have The Skinny on Projectile Motion The perpendicular components of motion horizontal and vertical are independent of each other.

Work them out separately. Horizontal A projectile launched with horizontal velocity v0x maintains that velocity. There are no accelerations in the horizontal force, so the x-velocity is constant. The angle of launch determines the relationship of v0y and v0x. How far will it drop in 4 seconds? Free Fall vs. Horizontal Projection The time it takes an object dropped from rest to fall a certain distance is the same as if it were projected horizontally with any speed. Also, notice that the information given about v0x is irrelevant to the question.

A projectile is traveling in a parabolic path for a total of 6 seconds. How does its horizontal velocity 1 s after launch compare to its horizontal velocity 4 s after launch?

No Horizontal Change Once a projectile is launched, its horizontal velocity remains constant during the entire flight. How many seconds will it be in the air?

How far will it travel horizontally? Now, using the first horizontal-motion equation, we can calculate the horizontal displacement after 6 seconds.

Chapter 2 Review Questions See Chapter 17 for solutions. True statements about this motion include which of the following? The displacement is zero. The average speed is zero. The acceleration is zero. Which of the following must always be true?

A baseball is thrown straight upward. A 0 B g, downward C g, downward D g, upward E g, upward 5. How high was the cliff? Calculate its total flight time, assuming that air resistance is negligible. Ignore air resistance.

A The acceleration vector points opposite to the velocity vector on the way up and in the same direction as the velocity vector on the way down. B The speed at the top of the trajectory is zero. D The horizontal speed decreases on the way up and increases on the way down. E The vertical speed decreases on the way up and increases on the way down. It is the net distance traveled. Distance is the length of the particular path chosen a scalar.

Speed is a scalar quantity and is always taken as a positive. For cases in which acceleration is uniform, use the Big Five equations to find the missing variable that represents acceleration, displacement, initial velocity, final velocity, or elapsed time. Memorize the chart on this page.

The two most popular graphs in kinematics are the position-versus-time graph and the velocity-versus-time graph. The slope of a position-versus-time graph gives the velocity, while the slope of a velocity-versus-time graph gives the acceleration. Gravitational acceleration has a constant magnitude of about 9.

Projectile motion is the parabolic path caused by the pull of gravity on an object moving near the surface of the earth. Now we will learn why things move the way they do; this is the subject of dynamics. An interaction between two bodies, a push or a pull, is called a force. You see examples of forces every day.

If you lift a book, you exert an upward force created by your muscles on it. When a skydiver is falling through the air, the earth is exerting a downward pull called gravitational force, and the air exerts an upward force called air resistance. When you stand on the floor, the floor provides an upward, supporting force called the normal force.

If you slide a book across a table, the table exerts a frictional force against the book, so the book slows down and then stops. Static cling provides a directly observable example of the electrostatic force. If the object is at rest, then it will stay at rest, and if it is moving, then it will continue to move at a constant speed in a straight line. The Skinny on the First Law Mass is a measure of inertia; the more mass an object has the more the object resists changing its velocity.

Since a bowling ball has more mass, it has more inertia. Basically, no force means no change in velocity. This property of objects—their natural resistance to changes in their state of motion—is called inertia.

In fact, the first law is often referred to as the law of inertia. The mass of an object is directly related to its weight: The heavier an object is, the more mass it has. Two identical boxes, one empty and one full, have different masses. Mass is measured in kilograms kg.

Note: An object whose mass is 1 kg weighs about 2. It takes twice as much force to produce the same acceleration of a 2 kg object than of a 1 kg object. The Skinny on the Second Law This law defines force. The second law relates the acceleration an object of a certain mass experiences when a force is applied to it. The larger the force on the object, the larger its acceleration. The wagon pulled by your joint force has a greater acceleration.

Fnet is the sum of all the forces acting on an object. Beware, there can be forces acting on an object without causing a net acceleration. Forces are represented by vectors; they have magnitude and direction. If several different forces act on an object simultaneously, then the net force, Fnet, is the vector sum of all these forces. The phrase resultant force is also used to mean net force. Force vs. A medium-size apple weighs about 1 N. The relationship between the direction of net force and velocity is the same as the relationship between acceleration and velocity.

Forward forces speed up objects, backward forces slow down objects, and forces perpendicular to the velocity are responsible for turning. An object feels two forces: one of magnitude 8 N pulling to the left and one of magnitude 20 N pulling to the right.

The Skinny on the Third Law Two objects must interact for a force to exist. When both objects interact, each body experiences a force due to the other interacting body. F1 and F2 are the same magnitude but have opposite directions. A woman riding a bicycle collides head-on with a parked school bus. Which object feels greater force? What is different is the effect of the force. If we let G be the universal gravitational constant, which is equal to 6.

Therefore, r is the distance between the centers of mass of the two objects. For objects with uniform density, this is merely the distance from center to center. The force of gravity is very small unless at least one of the objects is large, like a planet or moon. How does the acceleration of the Sun due to Mars compare to the acceleration of Mars due to the Sun?

So, which exerts a greater gravitational force on the earth: the Moon or the Sun? An artificial satellite of mass m travels at a constant speed in a circular orbit of radius R around the earth mass M. What is the speed of the satellite? A communications satellite of mass m is orbiting the earth at constant speed in a circular orbit of radius R. WEIGHT For this test, remember that although they are used interchangeably in everyday life, mass and weight are not the same thing; there is a clear distinction between them in physics.

The weight of an object is the gravitational force exerted on it by Earth or by whatever planet on which it happens to be. What acceleration would gravitational force impose on an object? The gravitational acceleration, of course! Notice that mass and weight are proportional but not identical. Furthermore, mass is measured in kilograms, while weight is measured in newtons.

Remember that G is a universal constant equal to 6. What is the mass of an object that weighs N? A person weighs pounds. Given that a pound is a unit of weight equal to 4. A book whose mass is 2 kg rests on a table. Find the magnitude of the force exerted by the table on the book. Since the book is at rest on the table, its acceleration is zero, so the net force on the book must be zero.

A can of paint with a mass of 6 kg hangs from a rope. Represent the object of interest the can of paint as a heavy dot, and draw the forces that act on the object as arrows connected to the dot. This is called a free- body or force diagram. We have the tension force in the rope, FT also symbolized merely by T , which is upward, and the weight, Fw, which is downward. Calling up the positive direction, the net force is FT — Fw.

In the diagram above, FT would need to have the same magnitude as Fw in order for the can to be moving at a constant velocity. In physics, the word normal means perpendicular. The normal force is what prevents objects from falling through tabletops or you from falling through the floor. If you use the latter notation, be careful not to confuse it with N, the abbreviation for the newton.

Find the magnitude of the normal force exerted by the table on the book. Normal vs. Weight The normal is not always equal to mg. It is whatever needs to be in a given problem to make sure the object does not break through the surface.

Since the book is at rest on the table, its acceleration is zero, so the net force on the book must equal zero. Also note that weight and the normal force are not an action-reaction pair, even though they are equal. The forces in an action-reaction pair work on different objects e. Friction, like the normal force, arises from electrical interactions between atoms that make up the object and those that make up the surface. If you attempt to push a heavy crate across a floor, at first you meet with resistance, but then you push hard enough to get the crate moving.

The force that acted on the crate to cancel out your initial pushes was static friction, and the force that acts on the crate as it slides across the floor is kinetic friction. The strength of the friction force depends, in general, on two things: the nature of the surfaces and the strength of the normal force. The greater this number is, the stronger the friction force will be. For example, the coefficient of friction between rubber-soled shoes and a wooden floor is 0.

This is because static friction can vary, counteracting weaker forces that are less than the minimum force required to move an object. Then, the maximum force that static friction can exert is 0. The net force on a stationary object must be zero. Static friction can take on all values, up to a certain maximum, and you must overcome the maximum static friction force to get the object to slide. Kinetic vs. The person pushes on the floor in the backward direction.

Static friction prevents it from moving backward, and so therefore must be forward. For similar reasons, objects that are rolling without slipping— rolling normally, not skidding—roll because of static friction. Questions A crate of mass 20 kg is sliding across a wooden floor.

The coefficient of kinetic friction between the crate and the floor is 0. Determine the magnitude of the friction force acting on the crate. If the crate is being pulled by a force of 90 N parallel to the floor , find the acceleration of the crate. A crate of mass kg rests on the floor. The coefficient of static friction is 0. In the case of two single masses m1 and m2 that are attached to a pulley and cord, the downward forces are due to the weight mass and gravity exerted on it of the masses.

The upward forces are due to the tension T in the cord. In the diagram above, assume that the tabletop is frictionless. Notice that there are two unknowns, FT and a, but we can eliminate FT by adding the two equations, and then we can solve for a. A quicker way of solving for the acceleration is to treat the entire system blocks plus string as one object. Since we are only concerned with forces acting on the object, we can ignore tension.

The string is part of the object. Then we need only consider forces acting in the direction of motion Mg and forces opposite the direction of motion none. What is the acceleration of the blocks? Notice that the only difference between these diagrams and the ones in the previous example is the inclusion of friction, Ff, that acts on the block on the table. As before, we have two equations that contain two unknowns a and FT. In the previous example, calculate the magnitude of the tension in the cord.

Find the acceleration of this block. Which Component? A person standing on a horizontal floor feels two forces: the downward pull of gravity and the upward supporting force from the floor.

A person who weighs N steps onto a scale that is on the floor of an elevator car. A frictionless inclined plane of length 20 m has a maximum vertical height of 5 m. If an object of mass 2 kg is placed on the plane, which of the following best approximates the net force it feels?

A 20 N block is being pushed across a horizontal table by an 18 N force. If the coefficient of kinetic friction between the block and the table is 0. The coefficient of static friction between a box and a ramp is 0. If the box is placed at rest on the ramp, the box will A accelerate down the ramp B accelerate briefly down the ramp but then slow down and stop C move with constant velocity down the ramp D not move E Cannot be determined from the information given 6.

Assuming a frictionless, massless pulley, determine the acceleration of the blocks once they are released from rest. A block of mass m is at rest on a frictionless, horizontal table placed in a laboratory on the surface of the earth. An identical block is at rest on a frictionless, horizontal table placed on the surface of the moon.

Let F be the net force necessary to give the earth-bound block an acceleration of a across the table. Given that gmoon is one sixth of gearth, the force necessary to give the moon-bound block the same acceleration a across the table is A B C D F E 6F 9. A crate of mass kg is at rest on a horizontal floor.

The coefficient of static friction between the crate and the floor is 0. A force F of magnitude N is then applied to the crate, parallel to the floor. Which of the following is true? A The crate will accelerate across the floor at 0. C The crate will slide across the floor at a constant speed of 0.

D The crate will not move. E None of the above Two crates are stacked on top of each other on a horizontal floor; crate 1 is on the bottom, and crate 2 is on the top.

Both crates have the same mass. If the distance between two point particles is doubled, then the gravitational force between them A decreases by a factor of 4 B decreases by a factor of 2 C increases by a factor of 2 D increases by a factor of 4 E Cannot be determined without knowing the masses At the surface of the earth, an object of mass m has weight w.

A moon of mass m orbits a planet of mass m. Let the strength of the gravitational force exerted by the planet on the moon be denoted by F1, and let the strength of the gravitational force exerted by the moon on the planet be F2. What is the value of g on the surface of Pluto? No force means no change in velocity. The forces are equal in magnitude, opposite in direction, and act on different bodies.

The weight of an object is the gravitational pull exerted on it by the planet on which the object exists. Friction is the component of the contact force that is parallel to the surface when an object is in contact with the surface. Kinetic sliding friction occurs when there is relative motion the object is actually sliding across the floor. Static friction occurs when there is no relative motion the object is still or is rolling without slipping.

Pulleys change the direction of the tension force in the cords that slide over them. An inclined plane is a ramp. Loosely speaking, energy is a quantity which gives an object or system the ability to accomplish something what we will define as work.

There are different forms of energy partly because there are different kinds of forces. Energy can come into a system or leave it via various interactions that produce changes. For the SAT Physics Subject Test, you should think of force as the agent of change, energy as the measure of change, and work as the way of transferring energy from one system to another.

And one of the most important laws in physics—the law of conservation of energy, equivalent to the first law of thermodynamics—says that the total amount of energy in a given process will stay constant—that is, it will be conserved. For example, electrical energy can be converted into light and heat this is how a light bulb works , but the amount of electrical energy coming in to the lightbulb equals the total amount of light and heat given off.

Energy cannot be created or destroyed; it can only be transferred from one system to another or transformed from one form to another. WORK When you lift a book from the floor, you exert a force on it over a distance, and when you push a crate across a floor, you also exert a force on it over a distance.

The application of force over a distance and the resulting change in energy of the system give rise to the concept of work. When you hold a book in your hand, you exert a force normal force on the book, but since the book is at rest, the force does not act through a distance, so you do no work on the book.

In short, if a constant force F acts over a distance d, and F is parallel to d, then the work done by F is the product of force and distance. Work is a scalar quantity. You slowly lift a book of mass 2 kg at constant velocity a distance of 3 m. How much work did you do on the book? So the work done is 60 J. The tension in the rope is N and the crate slides a distance of 10 m. How much work is done on the crate by the worker? In question 2, assume that the coefficient of kinetic friction between the crate and the floor is 0.

In other words, if a force helps the motion, the work done by the force is positive, but if the force opposes the motion, then the work done by the force is negative.

How much work is done by gravity? How much work is done by the normal force? How much work is done by friction? What is the total work done? Since the normal force is perpendicular to the motion, the work done by this force is zero. The work done on the object has transferred energy to it, in the amount mv2. The energy an object possesses by virtue of its motion is therefore defined as mv2 and is called kinetic energy.

How much work would it take to stop an object that has 30 J of kinetic energy? Kinematics vs. An object initially has 10 J of kinetic energy. Two forces act on it, one performing 40 J of work and the other friction performing —20 J. What is the final kinetic energy of this object? If the force of the cue on the ball was 25 N, over what distance did this force act? For example, a ball at the edge of a tabletop has energy that could be transformed into kinetic energy if it falls off. Both of these examples illustrate the concept of potential energy symbolized as U or PE , the energy an object or a system has by virtue of its position.

In each case, work was done on the object to put it in the given position the ball was lifted to the tabletop, the arrow was pulled back , and since work is the means of transferring energy, these things have stored energy that can be retrieved, as kinetic energy.

When an object falls, gravity does positive work, thereby giving the object kinetic energy. This energy is called potential energy. Because there are different types of forces, there are different types of potential energy.

This energy would be converted to kinetic energy as gravity pulled the ball down to the floor. How much work did gravity do as the ball was lifted from the floor to the table? That energy is now stored, and if someone gave the ball a push to send it over the edge, by the time the ball reached the floor it would acquire a kinetic energy of 30 J.

The ball could be lifted straight upward or on some curvy path—it would make no difference. Gravity is said to be a conservative force because of this property. For example, consider a passenger in an airplane reading a book. However, to someone on the ground looking up, the floor of the plane may be, say, 9, m above the ground. What is her gravitational potential energy relative to the ground? In that case, the variation in g was negligible, so g was thought of as a constant.

Consider an object of mass m at a distance r1 from the center of the earth or any spherical body moving by some means to a position r2. How much work did the gravitational force perform during this displacement? The answer is given by the equation.

A satellite of mass m is in a circular orbit of radius R around the earth radius rE, mass M. What is its total mechanical energy where Ugrav is considered zero as R approaches infinity? You can calculate the kinetic energy, since you know that the centripetal force on the satellite is provided by the gravitational attraction of the earth.

Assuming that no nonconservative forces friction, for example act on an object or a system as it undergoes some change, mechanical energy is conserved. A ball of mass 2 kg is gently pushed off the edge of a tabletop that is 1. Find the speed of the ball as it strikes the floor. This is the basic idea behind conservation of mechanical energy: One form of energy decreases while the other increases.

If the surface of the ramp is very smooth essentially frictionless , how high up the ramp will the box go? What distance along the ramp will it slide? Wile E. On the way down, the force of air resistance has an average strength of 40 N. This is called escape speed. Suppose you and I each do 1, J of work, but I do the work in 2 minutes while you do it in 1 minute. We both did the same amount of work, but you were quicker; you were more powerful. If he moves the crate this distance in 20 s, what is his power output during this time?

Chapter 4 Review Questions See Chapter 17 for solutions. A force F of strength 20 N acts on an object of mass 3 kg as it moves a distance of 4 m. How much work was done on the object during this time? A box of mass m slides down a frictionless inclined plane of length L and vertical height h.

What is the change in its gravitational potential energy? An object of mass m is traveling at constant speed v in a circular path of radius r. How much work is done by the centripetal force during one half of a revolution? While a person lifts a book of mass 2 kg from the floor to a tabletop, 1. A block of mass 3 kg slides down a frictionless inclined plane of length 6 m and height 4 m.

If the block is released from rest at the top of the incline, what is its speed at the bottom? A block of mass 3 kg slides down an inclined plane of length 6 m and height 4 m. If the force of friction on the block is a constant 16 N as it slides from rest at the top of the incline, what is its speed at the bottom? As a rock of mass 4 kg drops from the edge of a meter-high cliff, it experiences air resistance, whose average strength during the descent is 20 N. At what speed will the rock hit the ground?

An astronaut drops a rock from the top of a crater on the moon. When the rock is halfway down to the bottom of the crater, its speed is what fraction of its final impact speed?

How much power is being expended to maintain this motion? The moon has mass M and radius R. Forward forces do positive work, backward forces do negative work, perpendicular forces do no work. Work done by a variable force is measured by graphing F versus the horizontal, and then finding the area bounded by the graph of F, the x-axis, and vertical lines indicating the beginning and end of the period of force.

Kinetic energy refers to the energy an object possesses by virtue of its motion and equals mv2. Potential energy is the energy an object has by virtue of its position. Work done on an object to put it in a given position is stored in the object that can be retrieved. Nonconservative forces, such as friction, are disregarded, so the initial mechanical energy is equal to the final mechanical energy.

It is the rate at which work is done. In this case, gravitation is a variable force. Chapter 5 Linear Momentum When an object moves, it is necessary to account for both its mass and its velocity. Mass is definitely important. In this chapter, we will discuss linear momentum, impulse, what happens when objects collide, and the center of mass of a system of objects. Instead, he expressed the law in terms of something we refer to nowadays as linear momentum.

Linear momentum is the product of mass and velocity and is symbolized by p. Although the car and truck have the same speed, the truck has more momentum because it has more mass. That Hurts! Since concrete is hard and has no cushion, this makes the impact time of any object striking concrete very short. Forces that exist over a short period of time are called impulsive forces.

A large change in momentum divided by a short time interval makes for a painful landing on a concrete floor. How fast is he falling when he reaches ground level? He lands on a large, air-filled target, coming to rest in 1. What average force does he feel while coming to rest? In this case Time Seconds are represented in questions as s. If you see a quantity that refers to time labeled with ms, it is using milliseconds.

Because impact happens so quickly, a smaller quantity of time is necessary. This force is equivalent to about 27 tons!

Notice how crucial the impact time is: Increasing the slowing-down time reduces the acceleration and the force, ideally enough to prevent injury. This is the purpose of safety devices such as air bags in cars.

A small block is struck by a force F whose strength varies with time according to the following graph: What is the impulse delivered to the block? In fact, given any number of interacting objects, each pair that comes in contact will undergo equal but opposite momentum changes, so the result described for two interacting objects will actually hold for any number of objects, given that the only forces they feel are from each other.

When is Momentum Conserved? Remember that momentum is conserved in an isolated system. This means that if an object collides with a wall, the floor, or any permanently immovable object, momentum is NOT conserved. If the ship is 10 m away, how long will it take her to reach it? The Skinny on Collisions Elastic Collision: In an isolated system, momentum and kinetic energy are conserved. Collisions are classified into two major categories: 1 elastic and 2 inelastic.

A collision is said to be elastic if kinetic energy is conserved. Ordinary collisions are never truly elastic because there is always a change in energy due to energy transferred as heat, deformation of the objects, or the sound of the impact. However, if the objects do not deform very much for example, two billiard balls or a hard glass marble bouncing off a steel plate , then the loss of initial kinetic energy is small enough to be ignored, and the collision can be treated as virtually elastic.

Inelastic collisions, then, are ones in which the total kinetic energy is different after the collision. An extreme example of inelasticism is completely or perfectly or totally inelastic.

In this case, the objects stick together after the collision and move as one afterward. Two balls roll toward each other. The red ball has a mass of 0.

The green ball has a mass of 0. Find the speed of the green ball after the collision. Was the collision elastic? Since the balls roll toward each other, one ball has a positive velocity while the other has a negative velocity. To see whether the collision was elastic, we need to compare the total kinetic energies before and after the collision. Kinetic energy was lost, so the collision was inelastic; this is usually the case with collisions between ordinary size objects.

Most of the lost energy was transferred as heat; the two objects are both slightly warmer as a result of the collision. If the collision is perfectly inelastic, determine the velocity of the composite object after the collision. The objects collide head-on, and immediately after the collision, the speed of block m is 4 times the speed of block M.

What is the speed of block M after the collision? Is the collision elastic? A collision is elastic if the total kinetic energy is conserved.

In the case of two dimensional collisions e. Likewise, the Princeton Review has helped millions succeed on standardized tests, and provides expert advice and instruction to help parents, teachers, students, and schools navigate the complexities of school admission.

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