## MCAT Physics and Math Review

## Chapter 2: Work and Energy

### Practice Questions

1. A weight lifter lifts a 275 kg barbell from the ground to a height of 2.4 m. How much work has he done in lifting the barbell, and how much work is required to hold the weight at that height?

1. 3234 J and 0 J, respectively

2. 3234 J and 3234 J, respectively

3. 6468 J and 0 J, respectively

4. 6468 J and 6468 J, respectively

2. A tractor pulls a log with a mass of 500 kg along the ground for 100 m. The rope (between the tractor and the log) makes an angle of 30° with the ground and is acted on by a tensile force of 5000 N. How much work does the tractor perform in this scenario? (Note: sin 30° = 0.5, cos 30° = 0.866, tan 30° = 0.577)

1. 250 kJ

2. 289 kJ

3. 433 kJ

4. 500 kJ

3. A 2000 kg experimental car can accelerate from 0 to in 6 s. What is the average power of the engine needed to achieve this acceleration?

1. 150 W

2. 150 kW

3. 900 W

4. 900 kW

4. A 40 kg block is resting at a height of 5 m off the ground. If the block is released and falls to the ground, which of the following is closest to its total mechanical energy at a height of 2 m, assuming negligible air resistance?

1. 0 J

2. 400 J

3. 800 J

4. 2000 J

5. 5 m^{3} of a gas are brought from an initial pressure of 1 kPa to a pressure of 3 kPa through an isochoric process. During this process, the work performed by the gas is:

1. –10 kJ

2. –10 J

3. 0 J

4. +10 kJ

6. In the pulley system shown below, which of the following is closest to the tension force in each rope if the mass of the object is 10 kg and the object is accelerating upwards at

1. 50 N

2. 60 N

3. 100 N

4. 120 N

7. Which of the following is a conservative force?

1. Air resistance

2. Friction

3. Gravity

4. Convection

8. During uniform circular motion, which of the following relationships is necessarily true?

1. No work is done.

2. The centripetal force does work.

3. The velocity does work.

4. Potential energy depends on position of the object around the circle.

9. Which of the following best characterizes the work–energy theorem?

1. The work done by any force is proportional only to the magnitude of that force.

2. The total work done on any object is equal to the change in kinetic energy for that object.

3. The work done on an object by any force is proportional to the change in kinetic energy for that object.

4. The work done by an applied force on an object is equal to the change in kinetic energy of that object.

10.A massless spring initially compressed by a displacement of two centimeters is now compressed by four centimeters. How has the potential energy of this system changed?

1. The potential energy has not changed.

2. The potential energy has doubled.

3. The potential energy has increased by two joules.

4. The potential energy has quadrupled.

11.Josh, who has a mass of 80 kg, and Sarah, who has a mass of 50 kg, jump off a 20 m tall building and land on a fire net. The net compresses, and they bounce back up at the same time. Which of the following statements is NOT true?

1. Sarah will bounce higher than Josh.

2. For Josh, the change in speed from the start of the jump to contacting the net is

3. Josh will experience a greater force upon impact than Sarah.

4. The energy in this event is converted from potential to kinetic to elastic to kinetic.

12.A parachutist jumps from a plane. Beginning at the point when she reaches terminal velocity, which of the following is/are true?

1. The jumper is in translational equilibrium.

2. The jumper is not being acted upon by any forces.

3. There is an equal amount of work being done by gravity and air resistance.

1. I only

2. I and III only

3. II and III only

4. I, II, and III

13.Mechanical advantage and efficiency are both ratios. Which of the following is true regarding the quantities used in these ratios?

1. Mechanical advantage compares values of work; efficiency compares values of power.

2. Mechanical advantage compares values of forces; efficiency compares values of work.

3. Mechanical advantage compares values of power; efficiency compares values of energy.

4. Mechanical advantage compares values of work; efficiency compares values of forces.

14.If the gravitational potential energy of an object has doubled in the absence of nonconservative forces, which of the following must be true, assuming the total mechanical energy of the object is constant?

1. The object has been lifted to twice its initial height.

2. The kinetic energy of the object has been halved.

3. The kinetic energy has decreased by the same quantity as the potential energy has increased.

4. The mass of the object has doubled.

15.A consumer is comparing two new cars. Car A exerts 250 horsepower, while Car B exerts 300 horsepower. The consumer is most concerned about the peak velocity that the car can reach. Which of the following statements would best inform the consumer’s decision? (Note: 1 horsepower = 745.7 W)

1. Car A and Car B both have unlimited velocities, ignoring nonconservative forces.

2. Car A will reach its peak velocity more quickly than Car B.

3. Car A will dissipate less energy to the surroundings than Car B.

4. Car A will have a lower peak velocity than Car B.

PRACTICE QUESTIONS

### Answers and Explanations

1. **C**Because the weight of the barbell (force acting downward) is or about 2750 N, it follows that the weightlifter must exert an equal and opposite force of 2750 N on the barbell. The work done in lifting the barbell is therefore *W* = *Fd* cos *θ* = (2750 N)(2.4 m)(cos 0) ≈ 7000 J. Using the same equation, it follows that the work done to hold the barbell in place is *W* = *Fd* cos *θ* = (2750 N)(0 m)(cos *θ*) = 0 J. Because the barbell is held in place and there is no displacement, the work done is zero. This is closest to **choice (C)**.

2. **C**

The work done by the tractor can be calculated from the equation

*W* =* Fd *cos *θ* = (5000 N)(100 m)(cos 30°) = (5000)(100)(0.866) ≈ 5000 × 80 = 400,000 J = 400 kJ.

This is closest to **choice (C)**.

3. **B**

The work done by the engine is equal to the change in kinetic energy of the car:

The average power therefore is

4. **D**

Assuming negligible air resistance, conservation of energy states that the total mechanical energy of the block is constant as it falls. At the starting height of 5 m, the block only has potential energy equal to

Because the kinetic energy at this point is 0 J, the total mechanical energy is 2000 J at any point during the block’s descent.

5. **C**An isochoric process, by definition, is one in which the gas system undergoes no change in volume. If the gas neither expands nor is compressed, then no work is performed. Remember that work in a thermodynamic system is the area under a P–V curve; if the change in volume is 0, then the area under the curve is also 0.

6. **B**

To calculate the tension force in each rope, first draw a free body diagram:

From the force diagram, notice that there are two tension forces pulling the mass up. The net force for this system (**F**_{net}) is equal to 2**T** – *m***g**. Now we can use Newton’s second law:

7. **C**Gravity is a conservative force because it is pathway independent and it does not dissipate mechanical energy. Air resistance and friction—**choices (A)** and **(B)**—are nonconservative forces that dissipate energy thermally. Convection is not a force, but a method of heat transfer, eliminating **choice (D)**.

8. **A**In uniform circular motion, the displacement vector and force vector are always perpendicular; therefore, no work is done. Potential energy is constant for an object in uniform circular motion, whether it is the gravitational potential energy of a satellite orbiting the Earth or the electrical potential energy of an electron orbiting the nucleus of an atom. In both cases, potential energy does not change and does not depend on the position of the object around the circle, eliminating **choice (D)**.

9. **B**The work–energy theorem relates the total work done on an object by all forces to the change in kinetic energy experienced by the same object. While the work done by a force is indeed proportional to the magnitude of the force, it is also proportional to the displacement of the object, eliminating **choice (A)**. The change in kinetic energy is equal—not proportional—to the total work done on the object; further, it is the net force, not *any* force, that relates to the work done on an object, eliminating **choice (C)**. Finally, the change in kinetic energy of the object is equal to the work done by all of the forces acting on the object combined, not just the applied force, which eliminates **choice (D)**.

10.**D**Elastic potential energy, like kinetic energy, is related to the square of another variable, as shown by the equation Increasing the displacement by a factor of 2 increases the potential energy by a factor of 2^{2} = 4.

11.**A**

Sarah will not bounce higher than Josh. Assuming that mechanical energy is conserved, Sarah and Josh will start with a given amount of potential energy, which is converted into kinetic energy, then elastic potential energy, then kinetic energy again with no loss of energy from the system, eliminating **choice (D)**. By this logic, both individuals should return to the same starting height. Josh starts with

of potential energy. At the moment he hits the net, all of this potential energy has been converted into kinetic energy. Therefore,

eliminating **choice (B)**. Josh will experience a greater force upon impact because the net exerts a force proportional to weight; the higher the weight, the larger the force exerted by the net, eliminating **choice (C)**.

12.**B**At terminal velocity, the force of gravity and force of air resistance are equal in magnitude, leading to translational equilibrium. Thus, statement I is true. If these forces have the same magnitude and act over the same displacement, then the work performed is the same as well, making statement III true. Even though the net force is equal to zero, there are still forces acting on the parachutist, making statement II false.

13.**B**Mechanical advantage is a ratio of the output force generated given a particular input force. Efficiency is a ratio of the useful work performed by a system compared to the work performed on the system.

14.**C**In the absence of nonconservative forces, all changes potential energy must be met by an equal change in kinetic energy. Note that it is the difference in potential energy that is the same as the difference in kinetic energy, not the proportionality, eliminating **choice (B)**. Both **choices (A) **and **(D)** could be true statements but do not necessarily have to be—the object’s mass could have been quadrupled while its height was halved.

15.**A**Horsepower is a unit of power, as evidenced by the name and the conversion factor given in the question stem. Power is a rate of energy expenditure over time. Given unlimited time, both cars are capable of unlimited increases in (kinetic) energy, meaning that they have unlimited maximum velocities. The fact that Car B has a higher power rating means that it will reach any given velocity faster than Car A, eliminating **choice (B)**. There is not enough information to make any judgments on the efficiency of the cars, eliminating **choice (C)**. While it may take longer for Car A to reach a given velocity, both cars have unlimited maximum velocities according to the information given in the stem, eliminating **choice (D)**.