$22\mathrm{.}10$ A machine is used to raise a $100$ kg

weight $1$ m vertically upwards over a pe$-$

riod of $2$ s$.$

The machine is operated by pushing a

handle downwards with a constant force

of $15$ N over a distance of $0\mathrm{.}3$ m$,$ and the

machine uses $2$ kW of electrical power

while it$$s raising the weight.

$($a$)$ What is the increase in gravitational

potential energy of the weight $($in J$)?$

$($b$)$ How much work does the operator

of the machine do while pushing the

handle $($in J$)?$