Work and Kinetic Energy — Question 8

Question 8

Do not subtract a friction loss twice

Use the work–kinetic-energy theorem $W_{\mathrm{net}}=\Delta K$ for the specified particle in an inertial frame. A 1 kg block slides at 6 m/s on a fixed floor and stops under a constant 6 N kinetic friction force. No other force does work.

1. Find the stopping distance.

2. Assess the proposed equation $K_f=K_i+W_f-18\ \mathrm J$, where the last term is labeled heat produced.

3. Can these data alone determine how much thermal energy enters the block rather than the floor?

Question 8 - Solution

Do not subtract a friction loss twice

(a) Use the one mechanical energy change.

The governing relation is $$\boxed{0-K_i=W_f=-fd_{\mathrm{stop}}}$$

$$K_i=18\ \mathrm J$$ and $0-18=-6d$, giving $$d=3\ \mathrm m.$$

(b) Identify the repeated contribution.

Friction work is already $$W_f=-18\ \mathrm J.$$ Subtracting a further 18 J from the particle kinetic-energy equation counts the same loss again and predicts an impossible negative K. The correct relation is $0=18-18$.

(c) State what the model does not specify.

No. In an idealized block-plus-floor accounting, the lost mechanical energy can appear in internal stores, but its distribution between block and floor needs additional thermal information. The particle theorem does not assign that partition.