Work Done on a System by an External Force — Question 4

Question 4

Controlled descent with energy extracted by an agent

Assume no heat transfer across the stated system boundary during the process unless otherwise specified. A 2 kg load descends 3 m at constant speed against a 4 N drag force. Choose load, Earth and the drag medium as the system. A separate controlling cable is external. Use g=10 m/s$^2$.

1. Find gravitational and thermal energy changes.

2. Find cable work on the system.

3. Find cable tension and explain the direction of energy transfer.

Question 4 - Solution

Controlled descent with energy extracted by an agent

(a) Record storage changes with signs.

Record the signed changes for the descending load: $$\boxed{\Delta U_g=mg\Delta y=2(10)(-3)=-60\ \mathrm J},\qquad\boxed{\Delta E_{\mathrm{th}}=4(3)=12\ \mathrm J}.$$

(b) Use work equal to net system-energy change.

Kinetic energy remains unchanged: $$\boxed{W_T=\Delta K+\Delta U_g+\Delta E_{\mathrm{th}}=0-60+12=-48\ \mathrm J}.$$

(c) Cross-check forces and work.

Upward force balance gives $$T+4-mg=0\Rightarrow\boxed{T=16\ \mathrm N},\qquad W_T=T(-3)=-48\ \mathrm J.$$ The controller receives 48 J and the medium retains 12 J thermally, accounting for the full 60 J potential decrease.