Work and Energy
Beginner
work-energy
Source: High school physics (Chinese)
Problem
A person uses a fixed pulley to lift a 60 kg cargo from the ground.
- If the cargo is lifted 2.0 m at a constant velocity, how much work did the person do?
- If the cargo is lifted 2.0 m from rest with constant acceleration, reaching a velocity of 20 m/s at that height, how much work did the person do?
[Q1] $W_p = 1176$ J [Q2] $W_p = 13176$ J
The work done by the person, $W_p$, equals the work done by the tension force, which changes the mechanical energy of the cargo. Let $h = 2.0$ m.
[Q1] For constant velocity, the pulling force $F$ equals the gravitational force $mg$. The work done is:
$$W_p = Fh = mgh$$ $$W_p = (60 \text{ kg})(9.8 \text{ m/s}^2)(2.0 \text{ m})$$[Q2] By the work-energy theorem, the net work done by all forces equals the change in kinetic energy: $W_{net} = \Delta K$. The net work is the sum of work done by the person ($W_p$) and work by gravity ($W_g = -mgh$).
$$W_p + W_g = K_f - K_i$$ $$W_p - mgh = \frac{1}{2}mv_f^2 - 0$$Solving for the work done by the person:
$$W_p = mgh + \frac{1}{2}mv_f^2$$ $$W_p = (60 \text{ kg})(9.8 \text{ m/s}^2)(2.0 \text{ m}) + \frac{1}{2}(60 \text{ kg})(20 \text{ m/s})^2$$