Question

A sled is initially at rest at the top of a hill at an elevation 55.0 m higher than the elevation at the bottom. Find the speed of the sled after it slides without friction down the slope to the bottom.

Answer 1

ANSWER

32.8 m/s

EXPLANATION

Given:

• The initial elevation of the sled, h = 55.0 m

,

• There is no friction

Find:

• The speed of the sled at the bottom of the hill, v

By the Law of Conservation of Energy, since there is no friction,

$PE-KE=0$

Therefore,

$PE=KE$

The expressions for the gravitational potential energy, PE, and the kinetic energy, KE, are,

$mgh=\frac{1}{2}mv^2$

We have to find v, so solving the equation above for v,

$v=\sqrt{\frac{2mgh}{m}}=\sqrt{2gh}$

As we can see, it does not depend on the mass of the sliding object. Replace the known values and solve,

$v=\sqrt{2\cdot9.8m/s^2\cdot55.0m}\approx32.8m/s$

Hence, the speed of the sled at the bottom of the hill is 32.8 m/s, rounded to the nearest tenth.