Question

what is the formula for work done by a force $\boldsymbol{f}$ moving something a displacement $\boldsymbol{d}$, where the force is at an angle theta to the displacement

a. $w = \boldsymbol{f}cdot\boldsymbol{d}$
b. $w = |\boldsymbol{f}||\boldsymbol{d}|sin(\theta)$
c. $w = |\boldsymbol{f}||\boldsymbol{d}|cos(\theta)$
d. a and c
e. a and b

Explanation:

The work done by a force $\boldsymbol{F}$ moving an object through a displacement $\boldsymbol{d}$ when the force makes an angle $\theta$ with the displacement is given by the dot - product formula $W = \boldsymbol{F}\cdot\boldsymbol{d}=|\boldsymbol{F}||\boldsymbol{d}|\cos(\theta)$. The dot - product takes into account the component of the force in the direction of the displacement.

Answer:

C. $W =|\boldsymbol{F}||\boldsymbol{d}|\cos(\theta)$