Work Done on a System by an External Force — Question 2

Question 2

Pulling across a rough surface inside the system

Assume no heat transfer across the stated system boundary during the process unless otherwise specified. A 2 kg block starts from rest and is pulled horizontally 5 m by a constant 12 N force. Sliding friction is 4 N. Choose block plus floor as the system, and neglect floor recoil.

1. Find external pulling work and the increase in thermal energy.

2. Find final block speed.

3. Explain why subtracting friction work and also adding the same thermal rise on the energy-output side would double-count dissipation.

Question 2 - Solution

Pulling across a rough surface inside the system

(a) Separate input from internal conversion.

The pulling agent supplies energy while rubbing converts part into an internal thermal store: $$\boxed{W_{\mathrm{pull}}=12(5)=60\ \mathrm J},\qquad\boxed{\Delta E_{\mathrm{th}}=4(5)=20\ \mathrm J}.$$

(b) Use the full energy balance.

For block plus floor, $$60=K_f+20\Rightarrow K_f=40\ \mathrm J,$$ $$\boxed{v_f=\sqrt{2(40)/2}=\sqrt{40}=6.325\ \mathrm{m/s}}.$$

(c) Choose a consistent form.

The equivalent balances use different boundaries: $$\text{block motion: }W_{\mathrm{pull}}-f_kd=\Delta K,$$ $$\text{block + floor: }W_{\mathrm{pull}}=\Delta K+\Delta E_{\mathrm{th}}.$$ Using both $-f_kd$ and the same thermal term in the larger-system balance would count the 20 J conversion twice.