A person carries a heavy box horizontally across a room at constant velocity. What is the net work done on the box?
APositive, equal to the carrying force times the distance
BEqual to the weight of the box times the distance
CZero, because the kinetic energy does not change
DNegative, because friction opposes the motion
Net work equals the change in kinetic energy (work-energy theorem). Since velocity is constant, ΔKE = 0, so net work = 0. The person's horizontal force does positive work, but friction does equal negative work, summing to zero. Note also that the person's upward supporting force and gravity act perpendicular to the horizontal displacement, contributing no work.
Question 2 True / False
A force that is typically perpendicular to an object's velocity can do positive work on that object.
TTrue
FFalse
Answer: False
Work is W = F·d·cosθ where θ is the angle between the force and displacement. When force is perpendicular to motion, θ = 90° and cos90° = 0, so W = 0 regardless of the force's magnitude. This is why gravity does no work on a horizontally moving object, and why the centripetal force in circular motion never changes the object's speed — it can change direction but cannot transfer energy.
Question 3 Short Answer
A spring compressed by distance x is released and pushes a block until the block leaves the spring. How is the work done by the spring force calculated, and why can't you simply use W = Fd?
Think about your answer, then reveal below.
Model answer: Work must be computed as the integral W = ∫F dx (the area under the force-displacement graph). For a spring, F = kx varies with position, so the simple product Fd applies only to constant forces. For a spring obeying Hooke's law, this integral gives W = ½kx².
The formula W = Fd assumes a constant force in the direction of motion. Because the spring force changes continuously as it extends (F = kx decreasing from kx to 0), you must sum infinitesimal contributions — which is the definite integral. This connects directly to why calculus enters mechanics: real forces are rarely constant.