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?
A. Only the component of the force perpendicular to the motion is used to calculate the work.

B. If the force acts in the same direction as the motion, then no work is done.

C. When there is an angle between the two directions, the cosine of the angle must be considered.

D. A force at a right angle to the motion requires the use of the sine of the angle.

Answer 1

C is correct.  The work-force relation is given by W=F·d, where F is force vector, and d is the displacement vector.  The dot is the dot product, which is a measure of how parallel the two vectors are.  It can be restated as the product of two vector magnitudes times the cosine of the angle between them.  Therefore work is a scalar, not a vector, since the dot product returns a scalar.  
$W=Fdcos(\theta)$