Answer to Question #142723 in Physics for kel

Question

A 1.25 kg squirrel runs east across the ground for 7.00 meters. She climbs, 0.50 meters before running west on a limb for 3.25 meters. She jumps up .85 meters onto another branch, travels west 3.75 meters. She stops and eats a nut. Calculate net work. What is the squirrel’s gravitational potential energy?

Answer 1

If we ignore friction that the squirrel experienced while traveled along the horizontal, the work is done only when it jumped up and climbed the tree. Indeed, the work is

$$W=Fd\text{ cos}\theta,$$

where $\theta$ is the angle between the force and displacement vectors. Thus, since the only force is the force of gravity (acting downward), the work is done only on vertical paths:

$$W_1=mgh_1=1.25\cdot9.8\cdot0.5=6.13\text{ J}.\\ W_2=mgh_2=1.25\cdot9.8\cdot0.85=10.4\text{ J}.\\ W_{\text{net}}=W_1+W_2=6.13+10.4=16.5\text{ J}.$$

The gravitational potential energy above the ground is

$$GPE=mgh=mg(h_1+h_2)=16.5\text{ J}.$$