To determine the force the mechanic must expend using the compound pulley with a mechanical advantage of 4, we can use the formula for mechanical advantage:
\[ \text{Mechanical Advantage (MA)} = \frac{\text{Load Force}}{\text{Effort Force}} \]
In this case, the load force (the weight of the go-kart) is 1,620 Newtons, and we need to find the effort force (the force the mechanic must exert).
Rearranging the formula to solve for the effort force gives:
\[ \text{Effort Force} = \frac{\text{Load Force}}{\text{Mechanical Advantage}} \]
Substituting the values we have:
\[ \text{Effort Force} = \frac{1,620 , \text{N}}{4} = 405 , \text{N} \]
Therefore, the force that the mechanic must expend is 405 N.
The correct response is:
405 N