## MCAT Physics and Math Review

## Chapter 2: Work and Energy

### Practice Questions

1. A man walks 30 m east and then 40 m north. What is the difference between his traveled distance and his displacement?

1. 0 m

2. 20 m

3. 50 m

4. 70 m

2. A 1000 kg rocket ship, travelling at is acted upon by an average force of 20 kN applied in the direction of its motion for 8 s. What is the change in velocity of the rocket?

1.

2.

3.

4.

3. A car is traveling at and the driver puts on the brakes, bringing the car to rest in a time of 6 s. What is the magnitude of the average acceleration of the car?

1.

2.

3.

4.

4. An elevator is designed to carry a maximum weight of 9800 N (including its own weight), and to move upward at a speed of after an initial period of acceleration. What is the relationship between the maximum tension in the elevator cable and the maximum weight of the elevator while the elevator is accelerating upward?

1. The tension is greater than 9800 N.

2. The tension is less than 9800 N.

3. The tension equals 9800 N.

4. It cannot be determined from the information given.

5. At a place where an object is thrown vertically downward with a speed of while a different object is thrown vertically upward with a speed of Which object undergoes a greater change in speed in a time of 2 s?

1. The first object has a greater change in speed.

2. The second object has a greater change in speed.

3. Both objects undergo the same change in speed.

4. It cannot be determined from the information given.

6. A firefighter jumps horizontally from a burning building with an initial speed of At what time is the angle between his velocity and acceleration vectors the greatest?

1. The instant he jumps

2. When he reaches terminal velocity

3. Halfway through his fall

4. Right before he lands on the ground

7. A 10 kg wagon rests on a frictionless inclined plane. The plane makes an angle of 30° with the horizontal. Approximately how large is the force required to keep the wagon from sliding down the plane?

1. 10 N

2. 49 N

3. 85 N

4. 98 N

8. Which of the following expressions correctly illustrates the SI base units for each of the variables in the formula below?

*m*Δ**v** = **F**Δ*t*

1. lb × mph = ft × lb × s

2.

3.

4.

9. A 20 kg wagon is released from rest from the top of a 15 m long lane, which is angled at 30° with the horizontal. Assuming that there is friction between the ramp and the wagon, how is this frictional force affected if the angle of the incline is increased?

1. The frictional force increases.

2. The frictional force decreases.

3. The frictional force remains the same.

4. It cannot be determined from the information given.

10.Which of the following quantities is NOT a vector?

1. Velocity

2. Force

3. Displacement

4. Distance

11.A 30 kg girl sits on a seesaw at a distance of 2 m from the fulcrum. Where must her father sit to balance the seesaw if he has a mass of 90 kg?

1. 67 cm from the girl

2. 67 cm from the fulcrum

3. 133 cm from the girl

4. 267 cm from the fulcrum

12.A BASE jumper runs off a cliff with a speed of Which of the following is closest to his speed after 0.5 seconds?

1.

2.

3.

4.

13.A rock (*m* = 2 kg) is shot up vertically at the same time that a ball (*m* = 0.5 kg) is projected horizontally. If both start from the same height:

1. the rock and ball will reach the ground at the same time.

2. the rock will reach the ground first.

3. the ball will reach the ground first.

4. the rock and ball will collide in the air before reaching the ground.

14.Centrifugal force is an apparent outward force during circular motion. It has been described as a reaction force according to Newton’s third law. Which of the following statements is most likely to be correct regarding centrifugal force?

1. Centrifugal force exists only for uniform circular motion, not nonuniform circular motion.

2. Centrifugal force exists only when tension or a normal force provides centripetal acceleration.

3. Centrifugal force always acts antiparallel to the centripetal force vector.

4. Centrifugal force is result of repulsive electrostatic interactions.

15.Which of the following statements is true of movement on a plane with friction?

1. Acceleration is a function of applied force only.

2. More force is needed to accelerate a stationary object than a moving object.

3. The force of friction is independent of the mass of objects.

1. I only

2. II only

3. I and II only

4. I and III only

PRACTICE QUESTIONS

### Answers and Explanations

1. **B**

Using the Pythagorean theorem, calculate the magnitude of the man’s displacement:

His total distance traveled is equal to 30 + 40 = 70 m. Therefore, the difference between these two is 20 m.

2. **A**

The average force on the rocket equals its mass times the average acceleration; the average acceleration equals the change in velocity divided by the time over which the change occurs. So, the change in velocity equals the average force times the time divided by the mass:

**Choice (B)** represents the new velocity of the rocket, not its change in velocity. **Choices (C)** and **(D) **neglect dividing by the mass of the rocket.

3. **C**

The magnitude of the average acceleration is the change in velocity divided by the time. The velocity changes by because the car comes to rest. The time, in hours, is The average acceleration is then

This question asked for the magnitude of this acceleration, which is

4. **A**The forces on the elevator are the tension upward and the weight downward, so the net force on the elevator is the difference between the two. For the elevator to accelerate upwards, the tension in the cable will have to be greater than the maximum weight so that there is a net force directed upwards.

5. **A**Each object experiences an acceleration of which means that each object’s velocity changes by each second. Therefore, both objects experience the same change in velocity over the 2-second period of However, this question asks for the change in speed. The first object starts with a velocity of and ends with a velocity of This represents a change in speed of The second object starts with a velocity of and ends with a velocity of This represents a change in speed of Therefore, the second object has a much smaller change in speed than the first. This is because the force acting on the object was the opposite direction from the object’s motion in the initial conditions.

6. **A**The firefighter’s acceleration is always directed downward, whereas his velocity starts out horizontal and gradually rotates downwards as his downward velocity increases. Therefore, as time progresses, the angle between his velocity and acceleration decreases, which means that the maximum angle occurs at the instant he jumps.

7. **B**The static force of friction acts parallel to the plane and is in the opposite direction from the parallel component of gravity in this setup. Because the wagon is in equilibrium, these two forces are equal in magnitude. Remember that gravity is often split into components in inclined plane problems. Rather than splitting into *x*- and *y*-components, however, it is more convenient to split the gravity vector into parallel and perpendicular components. The parallel component of gravity is given by the expression *m*g sin *θ*. Plugging in the values from the question, both the parallel component of gravity and static force of friction must be equal to (sin 30°) = 49 N.

8. **C**In SI units, mass is measured in kilograms (kg), velocity in meters per second and time in seconds (s). The newton is a derived unit, and is not considered to be a base unit of the SI system. A newton is equal to a

9. **B**The force of friction on an object sliding down an incline equals the coefficient of friction times the normal force. The normal force is equal in magnitude to the perpendicular component of gravity, which is given by *m*g cos *θ*. As *θ* increases, cos *θ* decreases. Therefore, the normal force and frictional force decrease as the angle of the incline increases.

10.**D**A vector is characterized by both magnitude and direction. From the given answer choices, all are vectors except for distance. Distance is a scalar because it has only a numerical value and lacks direction.

11.**B**

In order for the seesaw to be balanced, the torque due to the girl (*τ*_{g}) must be exactly counteracted by the torque due to her father (*τ*_{f}). In other words, the magnitudes of these torques must be equal (*τ*_{g} = *τ*_{f}):

Because *r* represents the distance of each person from the fulcrum, the father must sit 67 cm from the fulcrum.

12.**B**

This is a projectile motion question. The horizontal component of the jumper’s velocity will remain throughout the jump. The vertical component of his velocity starts at After 0.5 seconds, it will be:

To get the overall velocity, consider the horizontal and vertical velocities using vector analysis and find the resultant. Doing so gives This magnitude (speed) is just a bit under 6, which matches most closely to **choice (B)**.

13.**C**We only need to analyze the motion in the vertical dimension to answer this question. If both the rock and ball began with no vertical velocity, they would reach the ground at the same time. However, because the rock begins with an upward component of velocity, it will take time to reach a maximum height before falling back toward the ground. Functionally, the rock’s free fall thus starts higher and later than the ball’s. The rock will necessarily hit the ground after the ball.

14.**C**Because the question stem indicates that centrifugal force is reactionary and gives its direction, we can draw the conclusion that it is a reaction to the centripetal force. According to Newton’s third law, these forces must have equal magnitude and opposite directions (antiparallel).

15.**B**The presence of friction does not change the impact of Newton’s laws. A net force must still be applied to cause motion. This net force is not necessarily equal to an applied force, as friction and gravity also act on the object; thus, statement I is eliminated. Static friction opposes the movement of stationary objects, and is necessarily greater than the force of kinetic friction; thus, statement II is correct. Statement III is false because the normal force is related to mass, and friction is related to the normal force.