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.
1) (a) If the box is being lifted at a constant speed of 2.0 m/s, what is the power delivered by the person pulling on the rope?
power P = T*V = m*g*V = 8.2*9.806*2.0 = 160.8 watt
(b) If the box is lifted, at constant acceleration, from rest on the floor to a height of 1.6 m above the floor in 0.42 s, what average power is delivered by the person pulling on the rope?
2h = a*t^2
a = 2h/t^2 = 3.2/0.42^2 = 18,14 m/sec^2
Vf = a*t = 3.2/0.42^2*0.42 = 7.62 m/sec
tension T = m*(g+a) = 8.2*(9.806+18.14)
av. power P = T*Vf/2 = 8.2*(9.806+18.14)*7.62/2 = 873 watt (5.43 times the upper power)