Discrete Practice Answers

  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 (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 × 90 = 450,000 J = 450 kJ.

    This is closest to (C). Since we estimated by rounding 0.866 up to 0.9, we can expect the actual answer to be less than the calculated answer.

  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:

    mass on two-pulley system; mg points down, 2T points up

    From the force diagram, notice that there are two tension forces pulling the mass up. The net force for this system (Fnet) is equal to 2T – mg. 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—(A) and (B)—are nonconservative forces that dissipate energy thermally. Convection is not a force, but a method of heat transfer, eliminating (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 idealized atom. In both cases, potential energy does not change and does not depend on the position of the object around the circle, eliminating (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 (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 (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 (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 22 = 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 (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 (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 (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 in 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 (B). Both (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 (B). There is not enough information to make any judgments on the efficiency of the cars, eliminating (C). While it may take longer for Car A to reach a given velocity, both cars have unlimited maximum velocities, eliminating (D).