# A 30 kg bear slides, from rest, 15 m down a lodgepole pine tree, moving with a speed of 3.7 m / s...

## Question:

A {eq}30\ kg {/eq} bear slides, from rest, {eq}15\ m {/eq} down a lodgepole pine tree, moving with a speed of {eq}3.7\ \rm m / s {/eq} just before hitting the ground.

(a) What change occurs in the gravitational potential energy of the bear-earth system during the side?

(b) What is the kinetic energy; of the bear just before hitting the ground?

(c) What is the average frictional force that acts on the sliding bear?

## Conservation of Energy:

Energy is a conserved quantity. The total energy of an isolated system remains constant. If an external force acts on the system, energy changes may result and the total energy of the system changes.

a: In our case, we have a bear that is initially 15m above the ground. The potential energy of an object on the ground is

{eq}U_f \ = \ 0 \ J {/eq}

and the potential energy of the bear when 15m up the tree is

{eq}U_i \ = \ m \ g \ h \ = \ 30 \ kg \ \times \ 9.81 \ m/s^2 \ \times \ 15 \ m \ = \ 4414.5 \ J {/eq}

The chnage in the gravitational potential energy of the bear-earth system during the slide is

{eq}\Delta U \ = \ U_f \ - \ U_i \ = \ 0 \ J \ - \ 4414.5 \ J \ = \ \mathbf{- \ 4.41 \ kJ} {/eq}

correct to three significant figures.

b: The speed of the bear just before hitting the ground is 3.7 m/s. Therefore, its kinetic energy is

{eq}K.E \ = \ 0.5 \ \times \ 30 \ kg \ \times \ (3.7 \ m/s)^2 \ = \ 205.35 \ J \ = \ \mathbf{205 \ J} {/eq}

correct to three significant figures.

c: The energy lost by the bear-earth system to friction during the slide is

{eq}|\Delta U| \ - \ K.E \ = \ 4209.15 \ J {/eq}

which is equal to the work done by the friction f during the slide. This is the product of the friction and the distance that the bear slid.

{eq}f \ \times \ 15 \ m \ = \ 4209.15 \ J {/eq}

Solving for f, we get that the average frictional force that acts on the sliding bear is

{eq}f \ = \ \dfrac{4209.15 \ J}{15 \ m} \ = \ \mathbf{281 \ N} {/eq}

correct to three significant figures.