Question

this force must not be doing any work upon the object.

1. which of the following statements are true about power? include all that apply.

a. power is a time - based quantity.
b. power refers to how fast work is done upon an object.
c. powerful people or powerful machines are simply people or machines which always do a lot of work.
d. a force is exerted on an object to move it at a constant speed. the power delivered by this force is the magnitude of the force multiplied by the speed of the object.
e. the standard metric unit of power is the watt.
f. if person a and person b do the same job but person b does it faster, then person a does more work but person b has more power.
g. the newton·meter is a unit of power.
h. a 60 - kg boy runs up a 2.0 meter staircase in 1.5 seconds. his power is approximately 80 watt.
i. a 300 - newton force is applied to a skier to drag her up a ski hill at a constant speed of 1.5 m/s. the power delivered by the toe rope is 450 watts.

Explanation:

• A: Power is defined as work over time ($P=\frac{W}{t}$), so it depends on time.
• B: Power measures the rate of work done, i.e., how fast work is completed.
• C: Power depends on work and time; doing a lot of work slowly means low power.
• D: For constant speed, work $W=Fd$, so $P=\frac{Fd}{t}=Fv$ (since $v=\frac{d}{t}$).
• E: The standard metric unit of power is the Watt ($1\ Watt=1\ J/s$).
• F: Same job = same work; faster completion means higher power, so A does not do more work.
• G: Newton·meter is a Joule (unit of work/energy), not power.
• H: Work $W=mgh=60×10×2=1200\ J$; power $P=\frac{1200}{1.5}=800\ W$, not ~80 W.
• I: $P=Fv=300×1.5=450\ W$, which is correct.

Answer:

A. Power is a time-based quantity, B. Power refers to how fast work is done upon an object, D. A force is exerted on an object to move it at a constant speed. The power delivered by this force is the magnitude of the force multiplied by the speed of the object, E. The standard metric unit of power is the Watt, I. A 300-Newton force is applied to a skier to drag her up a ski hill at a constant speed of 1.5 m/s. The power delivered by the toe rope is 450 Watts.