By using our website you agree to our use of cookies. Dispatched from the UK in 3 business days When will my order arrive? Home Contact us Help Free delivery worldwide. Free delivery worldwide. Bestselling Series. Harry Potter. Popular Features. New Releases. What can be concluded about the net displacement? It is zero. It is positive except for one point, where it is zero. It is negative, then zero, then positive. It is always positive? For questions , consider the following figure representing the velocity of an object in Which best represents the graph of one dimension.

D Consider also the following graphs: Which best represents the graph of acceleration versus time? Which best represents the graph of Which best represents the graph of displacement versus time? Which best represents the graph of Passage 1 acceleration versus time? A man is driving out of his driveway by backing A. He realizes he has forgotten his lunch, so he B. B pulls back into the driveway.

Car experts agree C. C that the best way to do this is to press on the D. D brake until the car comes to a complete stop, shift from reverse into first gear, then accelerate What can be said about the net velocity forward. The driver, however, shifts into first gear while A. It is positive. This causes C. It is negative.

The following D. It is positive, except for one point. After it is stopped for a while, it 1. Consider also the following graphs: 2. What is the value of his initial velocity? What is the value of his average velocity? Which best represents the graph of velocity B. Which of the following is evidence that the In the following questions, consider a ball acceleration is uniform?

## The MCAT Physics Book

The displacement x is always Consider air resistance negligible unless noted nonnegative. The velocity is always increasing. How far does the object fall in the time D. What is the magnitude of the acceleration B. Which expression gives the change in D. What is the direction of the acceleration A.

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Which graph best represents velocity versus D. Passage 2 A. It is less. A physics student leans out of the fortieth story B. It is greater. One is 0. It depends on the object. Not only do the two balls hit the ground at 5. This somewhat counterintuitive result is an A. Free fall means that only the force of gravity is acting on an object. A styrofoam ball of the same size as the lead ball takes a longer time to reach the ground. Which is a good explanation for this?

The force of gravity does not act on the styrofoam ball. The force of gravity on the styrofoam ball is less than that on the lead ball. Air resistance is a significant force in this problem.

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There is a gravitational force between the ball and the building. Most people think the above statement is a law of nature. Some very intelligent thinkers thought it was a law of nature, including Aristotle ancient Greek, no intellectual lightweight and more recently Descartes famous philosopher. Because it is common sense right? But sometimes closer scrutiny conflicts with common sense, and when that happens we have to change our thinking, to retune our intuition, so that what once seemed wrong now seems right. That can be difficult, but that's physics. Galileo discovered this law, although it's generally called Newton's first law of motion.

What does it mean for the forces to be balanced? Before we answer that question, let's look at a few cases. In the following figures Figures af we denote the motion of an object by "motion marks", so that. Case a. There are no forces. In this case think of a rock in deep space moving along.

The velocity vector is constant, meaning the rock continues traveling at constant speed to the right indefinitely. Case b. There are two opposed forces, equal in magnitude, perpendicular to the motion. In this case think of a marble rolling along a smooth level floor no friction.

Gravity pulls down, but the floor pushes up. The velocity vector is constant. Figure b Case c. This scenario is a nonexample, in which the right force is larger than the left force hence unbalanced. The object will speed up. Figure c Case d. This scenario is also a nonexample with the left force larger than the right force. The object will slow down. Figure d Case e.

Two opposed forces, left and right, are equal in magnitude. The case is between cases c and d. The object has constant velocity, that is, it will keep its speed indefinitely. Think about this one for a while. This stumps many people. Figure e Case f. The forces in all three directions are balanced. The object's velocity vector is constant. The forces are balanced if the vector sum of all the forces on the object is zero. The vector Fnet is the total force on the object. Example: A woman kicks a soccer ball, and it rolls for a while at constant speed, then another woman stops it.

Draw a diagram showing all the forces on the ball at the three times: kicking, rolling, and stopping. Solution: Part a: The ball is kicked see Figure The vector Fgrav is the force of gravity, and Fkick is the force of the foot on the ball. The symbol N stands for "normal", a physics word meaning perpendicular to the ground. It is force the ground exerts on the ball. Laws of Motion. Part b: The ball rolls along.

It has only two forces acting on it Figure The ball does not remember or care what started it rolling. According to the first law, the balanced forces guarantee it will keep rolling indefinitely at constant speed. Figure Part c: The ball is stopped. Now there is a force of a foot on the ball as well Figure Figure Over the next several chapters there will be many problems to test your intuition on the first law.

Second Law of Motion So what happens if the forces on an object are not balanced? If the net force on an object is nonzero, then the velocity vector changes. There must be acceleration. In fact the larger the force, the larger the acceleration. On the other hand, if we apply the same push to both a small car and a large car Figure , the small car will have the larger acceleration. Equation 3a , for example, states that the sum of all the horizontal forces is mass times the horizontal acceleration.

We will discuss breaking vectors into vertical and horizontal components in Section 4. Finally, we are able to make the connection between the units for force 1968 and for mass [kg], introduced in Chapter 1. Assume no friction. Example 2: A rocket provides a constant force to wagon A that rolls without friction. It starts from rest and after time t attains velocity v. A similar rocket providing the same force is attached to wagon B, which has five times the mass of A Figure How much time does it take wagon B to go from rest to velocity v?

Solution: This one looks difficult, but if we write down the relevant equations, it is not so hard. The answer is 5t. The third law of motion is not so much a law about motion as it is a rule of thumb about pairs of forces. It is usually stated thus:. Example 3: A basketball player jumps up. While he is in the air, he pushes the basketball horizontally. Draw all the forces while he is pushing the ball. Ignore the tiny gravitational force between the player and the ball. Solution: See Figure Notice that the magnitude of the force of the player on the ball is the same as that of the ball on the player.

But the player moves hardly at all, while the ball springs toward another player.

## The MCAT Physics Book

Why is the basketball affected more than the player? Hint: Look at equation 1. Force Diagrams Already in this chapter we have seen a number of force diagrams. In this section we discuss some rules for drawing force diagrams. There are two types of force diagrams: 1. In most problems we will want the second type, but it is important to know how to draw both, and knowing diagrams of the first type will help with the second type.

To draw the first type of diagram, we ask four questions: 1. What gravitational forces are important? What things are touching? These give contact forces. Does the problem mention any specific forces? Do the net forces in the diagram conform to expectation? For each force we draw an arrow whose tail lies on the object on which the force acts. This may seem unnatural at first, but it makes things easier in the end. For some examples, look at the diagrams we drew in Section C.

Example 1: A girl jumps horizontally from a boat in the water. Draw all the forces on the boat, the girl, and the Earth. Ignore the tiny gravitational force between the girl and the boat, and ignore the drag force of the water on the boat. Solution: First we add the gravitational forces in pairs Figure Figure Then we add the forces due to the boat and girl touching Fbg and Fgb and the contact force between the Earth and the bat Neb and NbE. Figure The net forces on the boat indicate that it accelerates backwards, which seems right.

The net force on the girl indicates she would accelerate forward and down, which seems right. It is difficult to tell what is going on with the Earth. Example 2: A vase sits on a table, which sits on the Earth. List all pairs of forces. Do this example on your own before you look at the solution. Drawing a diagram of the second type is easier, but you have to be careful not to leave out any forces nor to add any ghost forces.

Example 3: A roller skate is rolling frictionlessly on level ground to the left. Draw all the forces on the roller skate. Try doing this problem before looking at the solution.

Solution: Gravity is pulling down question 1. And the ground is touching the skate, pushing up question 2. There is no friction, nor any other forces, so the force diagram is Figure If so, you have not yet tuned your intuition about the first law of motion. Just because the skate is going to the left does not mean there is a force to the left. Only if the skate were speeding up to the left would we be forced to conclude that there was a force to the left.

In this chapter we studied Newtons laws of motion.

In a sense, the first law of motion is the most subtle. If an object is moving at a constant velocity, then the forces on the object add to zero, and if the vector sum of the force vectors for an object is zero, then the object moves at constant velocity. Constant velocity means constant speed in a straight path. No force is required to keep an object moving. The second law of motion concerns objects whose force vectors sum is not zero: The acceleration of such an object is in the same direction as the total force, proportional to its magnitude and inversely proportional to the objects mass.

Do you see why we use equations? The third law states that forces come in pairs: If object 1 pushes object 2, then object 2 pushes object 1 in the opposite direction. Pay especial attention to Section D on force diagrams. In solving problems, we are always interested in the forces on an object at a given instant in time. These include gravity, usually, and forces due to things touching the object at that moment.

No other forces need to be included. In particular, do not include a force in a direction just because the object in moving in that direction. Chapter 3 Problems Section B 5. Section A What is the magnitude of the net force in the 1. Consider a paratrooper who has jumped from three cases? After an initial accelerating plunge, he begins to fall at a constant speed in a straight vertical plunge at terminal velocity. During the latter portion of his fall, are the forces on the paratrooper balanced?

No, since a force balance exists only if an object is not moving. No, since gravity is not balanced by anything. In case 1, the net force is N; case 2, C. No, since gravity is greater than the drag N; and case 3, N. In case 1, the net force is N; case 2, D. Yes, since he is moving at a constant N; and case 3, N. In case 1, the net force is N; case 2, 50 N; and case 3, N.

There is one force acting on an object. What D. In case 1, the net force is N; case 2, can we definitely conclude from this? The object is speeding up or slowing Use the following information for questions 6 down. The object is going at a constant speed, not necessarily in a straight line. A man is pulling his son in a toy wagon. The C. The object is going at a constant speed in son and the wagon are 60 kg.

For 3 s the man a straight line. None of the above may be definitely uniformly accelerating the wagon from 1. A car's engine has died, and the car is slowing 6. What is the acceleration of the wagon with down as it coasts. What may we conclude the son? There are no forces acting on the car. There are forces acting on the car, but the C. The net force acting on the car is not zero. None of the above may be definitely 7. What is the net force on the wagon and son? An object is moving with uniform motion, that B.

There C. What can D. The net force is in the same direction that the object is moving. Both forces are in a direction perpendicular to the object's motion. The two forces have equal magnitudes but point in opposite directions. None of the above may be definitely concluded. Object A is acted upon by a net force FA to produce an acceleration. What is the acceleration of the tiger? How much distance does the tiger cover in pushing a small ball 0. One pushes those 12 s?

What is the magnitude of the net force on the D. A rocket ship kg is firing two jets at A. The two jets are at right angles, with B. What is D. What are all the forces acting on the tiger? Gravity, down. Gravity, down; and the normal force, up. Gravity, down; the normal force, up, and D. A girl shoves a 4-kg toy cart across the level D. None of the above is correct. It slides to Three men push on a station wagon with a a rest in 5 s. Assuming a constant force net force F, producing an acceleration. If they push the force? A piece of steel of mass 0. Car A starts from rest and accelerates string over the edge of a table.

The string uniformly for a period of time t to travel a passes over a pulley and is connected in distance d. Car B, which has four times the such a way as to maintain a tension force of mass of car A, starts from rest and 6 N see figure. If the magnitudes of the forces accelerating A and B are the same, how long does is take B to travel the same distance d? We allow the piece of steel to fall trailer is 30 N, and the force of air resistance from rest for 5 s. What is the final acceleration of on the trailer is 70 N.

The force of gravity the piece of steel? It is speeding up. It is staying the same speed. It is slowing down. A woman is riding in an elevator which is D. It is speeding up or staying the same going up at constant speed. The force of the speed. A car is accelerating from rest at an B. The horizontal force of the wheels on the gravity on her that can be determined by the road.

The vertical force of the wheels on the road. On September 12, , astronauts C. The horizontal force of the road on the conducted an experiment using the second wheels. A Gemini spacecraft D. The normal force of the road on the car. The thrusters were fired to provide a force of N for 7. The change in velocity of the spacecraft and rocket case was found to be 0.

What was the mass of the rocket case? Why is the force vector A equal in magnitude to the force vector C? An antique stove is sitting on the ground. See A. The first law of motion states that objects figure Assume for this problem that the Earth is which are motionless have balanced forces. The first law of motion states that an object in motion will remain in motion unless acted upon by an unbalanced force. The second law of motion states that a force on an object and acceleration of the object are proportional. The third law of motion states that forces come in equal and opposite pairs.

A car's engine has died, and the car is slowing down as it coasts. What forces are acting on the car? Which arrow represents the gravitational B. Gravity, down; and the road's force, up. Gravity, down; the road's force, up; and friction, backwards. Gravity, down; the road's force, up; B. B friction, backwards; and a forward force. An arrow is shot into the air. When the arrow is in the air, what forces are acting on Which arrow represents the force paired the arrow? There is the force of gravity. There is the force of gravity and an upward normal force.

There is the force of gravity and a B. B forward force. The planet Mars is traveling around the Sun. What forces are acting on Mars? Why is the force vector A equal in magnitude to the force vector B? The first law of motion states that an C. There is the force of gravity and a object which is motionless has balanced forward force. There is the force of gravity, a forward B. The first law of motion states that an force, and an outward force. The second law of motion states that force and acceleration are proportional.

Passage 1 3. What are the forces on the mass m? We perform an experiment which involves two masses m and M connected by a string which we A. The force of gravity. Mass m hangs over B. The force of gravity and the tension of the the edge of a table. The string passes over a string. The force of gravity and the force due to the table, such that it moves along the table mass M.

See figure. The tension in the D. The force of gravity, the tension of the string is the force that the string exerts where it is string, and the force due to M. It is generally true that the tension anywhere along 4. What are the forces on the mass M? The force of gravity and the upward force of the table.

The force of gravity, the upward force of the table, and the tension in the string. The force of gravity, the upward force of the table, and the force due to m. The force of gravity, the upward force of the table, the force due to m, and the tension in the string. What is the average velocity vavg for the In this experiment the mass m is initially at rest interval of time shown in the table? Its position x is measured downward from its initial position.

At various A. After the experiment has run a while, the 0. But mass M continues going forward 0. After the string goes slack but before M hits the pulley, what are 1. Which of the following is evidence that the the forces on mass M? There are no forces on M. The entries for x are nonnegative and B. The force of gravity, and the upward force B. The entries for v are nonnegative and of the table.

The force of gravity, the upward force of C. The entries for v are always greater than x. Passage 2 3. Referring to the chart, what evidence is there The space shuttle is a spaceship which was that the acceleration is increasing? When it stands A. The velocity v is linear with time. The velocity v increases with time. The orbiter is 7. The thrust at liftoff is 2. Which gives the best reason for the increase kg of fuel each second. The force provided by in acceleration?

The first law of motion states that an and the rate mass per time at which fuel is unbalanced force implies a change in burned. The second law of motion states that As the space shuttle ascends, the rate of fuel acceleration is proportional to force. The second law of motion states that mass of the shuttle decreases.

The following chart shows hypothetical data for D. The third law of motion states that there the liftoff of a shuttle. We are assuming the must be a second force, equal in magnitude shuttle moves in one dimension upward. The accelerating the shuttle. Consider a situation when the shuttle is in to gravity. The force of the shuttle on the air. The force of the exhaust gases on the shuttle.

What is the initial acceleration of the shuttle C. Biehle received his Ph. He has ten years experience at various levels in science education. The most comprehensive, rigorous analysis of MCAT physics available! Convert currency. Add to Basket. Compare all 4 new copies.

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