Work Done on a System by an External Force — Question 8

Question 8

An energy audit can infer an average resistance

Assume no heat transfer across the stated system boundary during the process unless otherwise specified. An external agent does 70 J on a system consisting of a 2 kg slider, a rough guide and Earth. The slider speed changes from 2 to 6 m/s while gravitational potential rises 10 J. It travels 4 m; all unaccounted energy becomes thermal through sliding friction.

1. Find kinetic and thermal energy increases.

2. Find the average friction magnitude along the path.

3. If a calculation instead gives a negative thermal increase under these assumptions, what should be re-examined?

Question 8 - Solution

An energy audit can infer an average resistance

(a) Apply the full balance.

Compute the kinetic change before forming the residual: $$\boxed{\Delta K=\tfrac12(2)(6^2-2^2)=32\ \mathrm J},$$ $$\boxed{\Delta E_{\mathrm{th}}=70-32-10=28\ \mathrm J}.$$

(b) Use the complete rubbing distance.

The displacement-averaged friction magnitude satisfies $$\Delta E_{\mathrm{th}}=\int_0^s f_k\,ds=\overline f\,s\Rightarrow\boxed{\overline f=28/4=7\ \mathrm N}.$$ It need not equal the instantaneous friction everywhere.

(c) Check the data and boundary model.

The stated pure-dissipation model requires $$\Delta E_{\mathrm{th}}=\int f_k\,ds\geq0.$$ A negative residual would require re-examining measured input, endpoint data, system boundary, or an omitted transfer or storage change.