Two people push a box equal distances along an effectively frictionless surface. One pushes the box at an angle of 30° to horizontal with force F while the other pushes the box horizontally with force Fcos30°. Which person does the most work?
a) Person A
b) Person B
c) Person A and B do equal amounts of work
d) cannot be determined
Explanation
Work is only done by force parallel to the direction of motion per the relationship W=Fdcosθ, and proportional to the distance over which the force is applied. For person A, the vertical component of force F, Fsin30°, does no work since the box moves neither up nor down. Only the horizontal component of the force, Fcos30°, does any work. For both person A and B, only the force parallel to the motion of the box over the surface does any work. Therefore, the work done by person A and B is equal.
a) Person A, incorrect.
b) Person B, incorrect.
c) Person A and B do equal amounts of work, correct.
d) cannot be determined, incorrect.
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