Work and Potential Energy — Question 2

Question 2

A supported ascent has two different work contributions

A 4 kg load rises 3 m at constant speed. Take $g=10$ m/s$^2$. A cable and gravity are its only forces; include Earth when assigning gravitational potential energy.

1. Find the gravitational potential-energy change and gravity work.

2. Find cable work and net work on the load.

3. Why is setting $\Delta U=-W_{\mathrm{net}}$ incorrect here?

Question 2 - Solution

A supported ascent has two different work contributions

(a) Associate U with the gravitational interaction.

With the load and Earth included in the potential-energy system, $$\boxed{\Delta U_g=mg\Delta y=4(10)(3)=120\ \mathrm J},\qquad\boxed{W_g=-120\ \mathrm J}.$$

(b) Use the unchanged kinetic energy.

Constant speed means unchanged kinetic energy: $$W_{\mathrm{net}}=\Delta K=0=W_T+W_g\Rightarrow\boxed{W_T=+120\ \mathrm J}.$$

(c) Identify the force in the definition.

The two distinct balances are $$\Delta U_g=-W_g,\qquad\Delta K=W_T+W_g.$$ Combining them gives $W_T=\Delta K+\Delta U_g=120$ J. Net work governs kinetic energy; gravitational work alone defines the gravitational potential change.