$22\mathrm{.}10$ A machine is used to raise a $100$ kg weight $1$ m vertically upwards over a period 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 themachine do while pushing the handle $($in J$)?($c$)$ How much electrical energy does the machine consume while raising the weight $($in J$)?($d$)$ What is the efficiency of the machine while it is raising the weight? $($e$)$ What is the apparent efficiency of the operator when raising the weight? $($f $)$ Explain why the efficiency found in part $($e$)$ does not violate any laws of energy conservation?