Question

Why is it important to know the direction of the force applied to a moving object and the direction in which the object is moving when determining the work done on the object?

Only the component of the force perpendicular to the motion is used to calculate the work.
If the force acts in the same direction as the motion, then no work is done.
When there is an angle between the two directions, the cosine of the angle must be considered.
A force at a right angle to the motion requires the use of the sine of the angle.

Answer 1

Answer: Only the third statement is correct.

Why: Work is the dot product of force and displacement: W = F · d = F d cosθ, where θ is the angle between the force and the displacement. That means only the component of the force parallel to the motion (F cosθ) contributes to work, so you must know both directions and the angle between them.

Consequences/clarifications:
- If the force is in the same direction as the motion (θ = 0), cos0 = 1 and W = Fd (maximum positive work). So statement 2 is false.
- If the force is opposite the motion (θ = 180°), cos180 = −1 and the work is negative (it removes energy).
- If the force is perpendicular to the motion (θ = 90°), cos90 = 0 and the work is zero. So you do not use the sine to compute work; statement 1 and statement 4 are false.