Question

A cable hauls a car with a mass of 1000kg straight up to an initial height to start the ride. The motor hauling the cable is capable of developing no more than 40 kW of power. If the motor takes 30 s to haul the car up at its maximum power output, and the motor lifts the car at a constant speed, find the height to which the car is raised.

Answer 1

Since, Power(P) = E/t

here , E = change in potential energy of car

E = m*g*h - 0 (Since initial height is zero.)

So,

P = m*g*h/t,

given,

P = 40 kW

m = mass of car = 1000 kg

g = 9.81 m/sec^2

power applies for 30 sec.

So, distance travel in 30 sec,(h) = P*t/(m*g)

h = 40000*30/(1000*9.81)

h = 122.3 m

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