Work Done on a System by an External Force — Question 5

Question 5

Two boundaries for one sliding-and-stopping event

Assume no heat transfer across the stated system boundary during the process unless otherwise specified. A 1 kg puck slides at 4 m/s across a fixed rough horizontal plate and stops after 2 m. No other horizontal force acts. Neglect plate recoil.

1. Find friction work on the puck and its average magnitude.

2. For puck plus plate, find external horizontal work and thermal-energy increase.

3. Can the data determine how much of the thermal increase belongs to the puck alone?

Question 5 - Solution

Two boundaries for one sliding-and-stopping event

(a) Use the puck kinetic-energy loss.

For the puck alone, $$\boxed{W_f=K_f-K_i=0-\tfrac12(1)(4)^2=-8\ \mathrm J},$$ $$\boxed{\overline f=|W_f|/s=8/2=4\ \mathrm N}.$$

(b) Move the rubbing interaction inside the boundary.

For puck plus plate, rubbing lies inside the boundary: $$\boxed{W_{\mathrm{ext,h}}=0},\qquad0=\Delta K+\Delta E_{\mathrm{th}}=-8+\Delta E_{\mathrm{th}}.$$ Thus $\boxed{\Delta E_{\mathrm{th}}=8\ \mathrm J}$.

(c) Do not infer an unmeasured partition.

The measurements fix only the sum: $$\Delta E_{{\mathrm{th}},puck}+\Delta E_{{\mathrm{th}},plate}=8\ \mathrm J.$$ Material properties and contact behavior determine the partition. The puck’s 8 J kinetic loss is not necessarily its own thermal gain.