Work Done by the Gravitational Force — Question 3

Question 3

Controlled lowering transfers energy out through the supporting force

Take a uniform gravitational field with $g=10$ m/s$^2$, upward y positive, and neglect air resistance. A 3 kg load is lowered 2.5 m at constant nonzero speed by an ideal vertical cable. Ignore start and stop intervals.

1. Find gravity work and the kinetic-energy change.

2. Find cable tension and its work.

3. If the cable is instead removed at the initial instant, how much would kinetic energy increase after the same descent?

Question 3 - Solution

Controlled lowering transfers energy out through the supporting force

(a) Compare the unchanged speed.

The governing relation is $$\boxed{\Delta K=0\Longrightarrow W_T=-W_g}$$

$$\Delta K=0,$$ while $$W_g=-3(10)(-2.5)=+75\ \mathrm J.$$

(b) Balance forces and then use displacement.

Constant speed gives $$T=mg=30\ \mathrm N$$ upward. Its work is $$W_T=30(-2.5)=-75\ \mathrm J,$$ cancelling gravity work. The supporting agent receives mechanical energy from the load.

(c) Change the force inventory.

With only gravity, $$\Delta K=+75\ \mathrm J$$ over the same descent. Gravity work is unchanged; the absence of negative cable work changes the result.