Electric Potential Energy — Question 3

Question 3

External work includes both stored energy and a kinetic-energy change

A particle moves between two points with $U_B-U_A=12.0\,\mu$J. Its kinetic energy increases from $5.00$ to $9.00\,\mu$J. Electric force and one external actuator are the only agents doing work.

1. Find electric work and actuator work.

2. After a separate preparation step, the particle is returned from B to A quasistatically. Find actuator work on this return and on the two specified trips combined, excluding preparation.

Question 3 - Solution

External work includes both stored energy and a kinetic-energy change

(a) Method and calculation

$$W_e=-\Delta U=-12.0\,\mu\mathrm J,\quad\Delta K=9.00-5.00=4.00\,\mu\mathrm J.$$$$W_{\mathrm{ext}}=\Delta K+\Delta U=16.0\,\mu\mathrm J.$$

(b) Interpretation and further calculation

$$W_{\mathrm{ext,return}}=U_A-U_B=-12.0\,\mu\mathrm J\quad(\Delta K_{\mathrm{return}}=0).$$$$W_{\mathrm{ext,total}}=16.0-12.0=4.00\,\mu\mathrm J.$$The return is specified as a separate quasistatic process; preparation for it is not included in these two work values.

Physical check

The common equality $W_{\mathrm{ext}}=\Delta U$ requires zero kinetic-energy change and no other nonconservative work.