Question

A 8.2-kg box is being lifted by means of a light rope that is threaded through a single, light, frictionless pulley that is attached to the ceiling.

If the box is lifted, at constant acceleration, from rest on the floor to a height of 1.8 m above the floor in 0.42 s, what average power is delivered by the person pulling on the rope? Answer in kW

Answer 1

Given data, Mass of the box, m-8.2 kg Height to which box lifted, h-1.8 m Time taken to lift the box, t 0.42 s Write the expression for second equation of motion to calculate the acceleration of the box. Here, a is the acceleration of the box. Substitute the values in the above equation. 1.8 -хах (0.42)2 a 20.41 m/s Calculate the final speed of box at height h Here, v is the speed of box at height h Substitute the values in the above equation. 20.41x 0.42 8.57 m/s v

Write the expression to calculate the total work done. Here, W is the total work done on the box and g 9.8m/s is the acceleration due to gravity. Substitute the values in the above equation W 8.2x9.8x1.8+x8.2x(8.57) -(144.648+301.12) - 445.772J Calculate the average power delivered by the person Here, P is the average power delivered by person. Substitute the values in the above equation. 445.772 0.42 -1061.36 Ww -1.06kW Hence, the average power delivered by the person is 1.06kW