A loaded sled is pulled up a straight incline by a winch through a light
PHYSICS · Multi-part · CBSE · Physics · Work, Energy and Power · Work, Energy and Power
Problem
A loaded sled is pulled up a straight incline by a winch through a light, inextensible cable that stays parallel to the incline. The angle between the cable and the sled’s instantaneous velocity is a constant 15∘. Over the time interval 0≤t≤10s, the tension in the cable and the sled’s speed vary with time according to
F(t)=200+15t(F in N),v(t)=0.50t(v in m s−1).
Assume the tension is the only force doing work on the sled along the incline.
(a) Write an expression for the instantaneous rate at which the cable transfers energy to the sled as a function of time over the interval 0≤t≤10s.
(b) Calculate the instantaneous rate of energy transfer at t=6.0s.
(c) Determine the average rate at which energy is transferred to the sled during the entire 10s interval.
(d) Find the time within the interval 0≤t≤10s at which the instantaneous rate of energy transfer equals the average rate you determined in part (c). Justify your solution.