Work, Energy and Power

Sample questions

Showing 20 of 70 questions from this chapter. The full bank is in the chapter test below.

1. 1

   The work done by a constant force on a body is zero when the angle between the force and the displacement of the body is

   • A.$0^\circ$
   • B.$45^\circ$
   • C.✓ $90^\circ$ (correct answer)
   • D.$180^\circ$

   Why: Since $W = Fd\cos\theta$, the work is zero only when $\cos\theta = 0$, that is when the force is perpendicular to the displacement. The work is maximum at $0^\circ$ and negative at $180^\circ$.
2. 2

   Which statement about work is correct?

   • A.✓ Work is a scalar quantity given by the dot product of force and displacement. (correct answer)
   • B.Work is a vector quantity directed along the applied force.
   • C.Work is a vector quantity given by the cross product of force and displacement.
   • D.Work is a scalar quantity whose SI unit is the newton per metre.

   Why: Work equals $\mathbf{F}\cdot\mathbf{d} = Fd\cos\theta$, which is a scalar, and its SI unit is the joule, $1\ \mathrm{J} = 1\ \mathrm{N\,m}$.
3. 3

   One joule of work is equivalent to

   • A.$1\ \mathrm{N\,m^{-1}}$
   • B.✓ $1\ \mathrm{N\,m}$ (correct answer)
   • C.$1\ \mathrm{N\,m^{2}}$
   • D.$1\ \mathrm{N\,s}$

   Why: Work is force multiplied by displacement, so $1\ \mathrm{J} = 1\ \mathrm{N} \times 1\ \mathrm{m} = 1\ \mathrm{N\,m}$.
4. 4

   A constant force acts on a body in a direction exactly opposite to the displacement of the body. The work done by the force is

   • A.zero
   • B.positive and equal to $Fd$
   • C.negative and equal to $-\frac{1}{2}Fd$
   • D.✓ negative and equal to $-Fd$ (correct answer)

   Why: With $\theta = 180^\circ$, $W = Fd\cos 180^\circ = -Fd$, so the force takes energy away from the body instead of giving it energy.
5. 5

   A constant force of 20 N moves a body through 3 m along the direction of the force. If instead the same force acts at $60^\circ$ to the displacement while moving the body through the same 3 m, the work done by the force is

   • A.60 J
   • B.52 J
   • C.✓ 30 J (correct answer)
   • D.15 J

   Why: $W = Fd\cos\theta = 20 \times 3 \times \cos 60^\circ = 30\ \mathrm{J}$. The value 60 J would be obtained only if the force acted along the displacement, and 52 J comes from using $\cos 30^\circ$ instead of $\cos 60^\circ$.
6. 6

   The work done by a variable force is obtained from a graph of $F\cos\theta$ against the displacement $d$ by finding

   • A.✓ the area between the curve and the displacement axis (correct answer)
   • B.the slope of the curve
   • C.the value of $d$ where the curve cuts the displacement axis
   • D.the reciprocal of the slope of the curve

   Why: The thin strip of width $\Delta d$ under the curve has area $F\cos\theta\,\Delta d$, which is the work done during that interval, so the total work is the whole area under the curve.
7. 7

   A force acts on an object along its displacement. The force is constant at 5 N from $d = 0$ to $d = 4\ \mathrm{m}$ and then falls uniformly to zero at $d = 6\ \mathrm{m}$. The work done by the force over the whole 6 m is

   • A.20 J
   • B.✓ 25 J (correct answer)
   • C.30 J
   • D.15 J

   Why: The rectangular part contributes $5 \times 4 = 20\ \mathrm{J}$ and the triangular part $\frac{1}{2} \times 2 \times 5 = 5\ \mathrm{J}$, so the total work is 25 J.
8. 8

   For a constant force acting along the direction of the displacement, the force-displacement graph is

   • A.a straight line passing through the origin
   • B.a parabola
   • C.a straight line with a negative slope
   • D.✓ a horizontal straight line (correct answer)

   Why: A constant force does not change as the body moves, so the graph is a horizontal line, and the area beneath it ($Fd$) is the work done.
9. 9

   Which of the following is a conservative force?

   • A.the kinetic frictional force
   • B.air resistance
   • C.✓ the gravitational force (correct answer)
   • D.the propulsion force of a rocket

   Why: The work done by gravity between two points is the same along every path and is zero around a closed path, which is the test of a conservative force. Friction, air resistance and rocket propulsion are all non-conservative.
10. 10

    Which of the following is NOT a conservative force?

    • A.the electrostatic force
    • B.the elastic spring force
    • C.the gravitational force
    • D.✓ the tension in a string (correct answer)

    Why: Tension, like friction, air resistance and the normal force, is non-conservative, whereas electrostatic, spring and gravitational forces are conservative.
11. 11

    The work done by a conservative force in moving a body once around a closed path is

    • A.always positive
    • B.✓ zero (correct answer)
    • C.always negative
    • D.equal to the kinetic energy gained by the body

    Why: For a conservative force the work depends only on the end points, and in a closed path the end points coincide, so the total work is zero.
12. 12

    The work done by the gravitational force in moving a body from one point to another in the Earth's field does not depend on

    • A.✓ the path followed between the two points (correct answer)
    • B.the mass of the body
    • C.the height through which the body is displaced
    • D.the value of $g$

    Why: For this conservative force the work is $-mg\Delta h$ along any path, so it depends only on the vertical displacement and not on the route taken.
13. 13

    A body of mass $m$ is raised through a height $H$ above the ground. The work done by the gravitational force of the Earth on the body is

    • A.zero
    • B.$+mgH$
    • C.✓ $-mgH$ (correct answer)
    • D.different for different paths

    Why: The displacement is opposite to the weight $mg$, so $\theta = 180^\circ$ and $W = mgH\cos 180^\circ = -mgH$.
14. 14

    A box is carried horizontally through a distance $d$ while its weight $mg$ acts vertically downward. The work done by the weight is

    • A.$mgd$
    • B.$-mgd$
    • C.✓ zero (correct answer)
    • D.$mgd\cos 0^\circ$

    Why: The weight is perpendicular to the horizontal displacement, so $\theta = 90^\circ$ and $W = mgd\cos 90^\circ = 0$, however large the force may be.
15. 15

    The work done by the kinetic frictional force on a sliding object depends on

    • A.only the initial and final positions of the object
    • B.✓ the length of the path followed (correct answer)
    • C.the height through which the object moves
    • D.the time taken by the object

    Why: Friction always opposes the motion, so it does work $-fd$ that grows with the distance travelled; a longer path between the same two points therefore means more work, which is why friction is non-conservative.
16. 16

    Why is the work done against friction a non-conservative process?

    • A.✓ Because the work depends on the length of the path and the mechanical energy is dissipated as heat. (correct answer)
    • B.Because friction is a contact force.
    • C.Because friction acts along the direction of motion.
    • D.Because friction never does any work.

    Why: The work against friction depends on the path length and cannot be recovered as mechanical energy, so a force of this kind is non-conservative; being a contact force does not matter, since the elastic spring force is also a contact force yet conservative.
17. 17

    Power is defined as

    • A.the total work done by a force
    • B.✓ the rate of doing work (correct answer)
    • C.the product of force and displacement
    • D.the energy stored in a body

    Why: Power tells how quickly work is done, $P = \frac{\Delta W}{\Delta t}$; the same work done in a shorter time means a greater power.
18. 18

    One watt is equal to

    • A.$1\ \mathrm{J\,s}$
    • B.$1\ \mathrm{N\,m}$
    • C.$1\ \mathrm{J\,s^{-2}}$
    • D.✓ $1\ \mathrm{J\,s^{-1}}$ (correct answer)

    Why: One watt is one joule of work done in one second, so $1\ \mathrm{W} = 1\ \mathrm{J\,s^{-1}}$. Note that $1\ \mathrm{N\,m}$ is the joule, which is a unit of energy and not of power.
19. 19

    One kilowatt-hour is equal to

    • A.$3.6 \times 10^{3}\ \mathrm{J}$
    • B.$1.0 \times 10^{3}\ \mathrm{J}$
    • C.✓ $3.6 \times 10^{6}\ \mathrm{J}$ (correct answer)
    • D.$6.0 \times 10^{4}\ \mathrm{J}$

    Why: $1\ \mathrm{kWh} = 1000\ \mathrm{W} \times 3600\ \mathrm{s} = 3.6 \times 10^{6}\ \mathrm{J} = 3.6\ \mathrm{MJ}$.
20. 20

    The absolute unit of work in the C.G.S. system is the erg. One erg is equal to

    • A.✓ $10^{-7}\ \mathrm{J}$ (correct answer)
    • B.$10^{7}\ \mathrm{J}$
    • C.$10^{-5}\ \mathrm{J}$
    • D.$9.8\ \mathrm{J}$

    Why: One erg is one dyne centimetre, and $10^{-5}\ \mathrm{N} \times 10^{-2}\ \mathrm{m} = 10^{-7}\ \mathrm{J}$.