Answer:
Total work done = = 29811.60 J
Explanation:
Since the person is being moved upward, the person’s potential and kinetic energy are increasing.
To determine the increase in potential energy, the following equation is used;
∆ PE = m * g * ∆ h
m = 78.0 Kg, g = 9.8 m/s, ∆ h = 13.0 m
∆ PE = 78.0 * 9.8 * 13.0 = 9937.20 J
Increase in kinetic energy is given by the following equation;
∆ KE = ½ * m * (vf² – vi²)
vf = 3.4, vi = 0
∆ KE = ½ * 78.0 * 3.4² = 450.84 J
Total work = 9937.20 + 450.84 = 10388.04 J
(b) He is then lifted at the constant speed of 3.40 m/s
Velocity is constant, therefore, there is no increase in kinetic energy. The only work done is the increase of potential energy
∆ PE = 78.0 * 9.8 * 13.0
∆ PE = 9937.20 J
(c) He is then decelerated to zero speed.
Since his velocity decreased from 3.40 m/s to 0 m/s, his kinetic energy decreased.
∆ KE = ½ * 78.0 * (0² - 3.4²)
∆ KE = - 450.84 J
∆ PE = 78.0 * 9.8 * 13.0 = 9937.20 J
Total work = 9937.20 - 450.84 = 9486.36 J
Sum of works = 10388.04 + 9937.20 + 9486.36 = 29811.60 J
