Work and Potential Energy — Question 3

Question 3

Potential energy belongs to a specified interaction

A 2 kg load falls 4 m from rest in a uniform field with $g=10$ m/s$^2$. Ignore air drag and Earth recoil.

1. For the load alone, identify the external work and kinetic-energy gain.

2. For load plus Earth, identify the gravitational potential-energy change.

3. Explain why adding both external gravity work and an internal gravitational-energy decrease to one balance double-counts the transfer.

Question 3 - Solution

Potential energy belongs to a specified interaction

(a) Use the small system boundary.

For the load alone, gravity is external: $$\boxed{W_g=mg(4)=2(10)(4)=80\ \mathrm J},\qquad\boxed{\Delta K=W_g=80\ \mathrm J}.$$

(b) Include both interaction partners.

For load plus Earth, gravity is internal: $$\boxed{\Delta U_g=mg(-4)=-80\ \mathrm J},\qquad\Delta K+\Delta U_g=80-80=0.$$

(c) Choose one consistent description.

Choose one consistent system balance: $$\text{load: }\Delta K=W_g;\qquad\text{load + Earth: }\Delta K=-\Delta U_g.$$ Both describe the same 80 J transfer. Adding $W_g-\Delta U_g=160$ J counts that interaction twice.