To find the amount of force the mechanic must exert using the compound pulley, we can use the concept of mechanical advantage. The mechanical advantage (MA) of the pulley system tells us how much it reduces the input force needed to lift a load.
The formula is:
\[ \text{Input Force} = \frac{\text{Output Force}}{\text{Mechanical Advantage}} \]
The output force in this case is the weight of the go-kart, which is 1,620 N. The mechanical advantage is given as 4.
Now we can plug in the values:
\[ \text{Input Force} = \frac{1,620 , \text{N}}{4} = 405 , \text{N} \]
Thus, the mechanic must expend 405 N of force.
The correct response is: 405 N.