A car of mass 2000 kg is lifted up a distance of 30m by a crane in 1 min. A second crane does the same job is 2 min. What is the power applied by each crane? Do the crane? Do the cranes consume the same or different amount of fuel? Neglect power dissipation against friction.

Explanation

Here, mass of the car to be lifted, `m = 2000kg`
height through which the car is to be lifted, `h = 30m`
time taken by second crane, `t_1 = 1 min =60s`
time taken by second crane, `t_2 =2min =120s`
Amount of work done by each crane, i.e.,` W = mgh = (2000kg)(10m//s^2)(30m) = 6xx10^5J`
Power of the first crane, `P_1 = ("work done"(W))/("time taken"(t_1)) = (6xx10^5J)/(60S) = 10000 W =10kW`
Power of the second crane, `P_2 = ("work done("W)/("time taken"(t_2)) = (6xx10^5J)/(120s) = 5000 W =5kW`
The two cranes would consume the same amount of fuel as these have to perform the same amount of
work `(i.e., 6xx10^5J)`.