Question

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 crnae? Do the caranes consume the same or different amount of fule? Neglect power dissipation against friction.

Answer 1

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)`.