Question

You are on roller blades on top of a small hill. Your potential energy is equal to 1,000.0 joules. The last time

you checked your mass was 60.0 kilograms.
a. What is your weight in newtons?
b. What is the height of the hill?
c. If you start skating down this hill, your potential energy will be converted to kinetic energy. At the
bottom of the hill, your kinetic energy will be equal to your potential energy at the top. What will be
your speed at the bottom of the hill?

Answer 1

a) The weight of a person is given by:

`W=mg`
where m is the mass of the person and g is the gravitational acceleration. In this problem, the mass of the person is m=60.0 kg, while the value of g is
`g=9.81 m/s^2`, therefore the weight of the person is

`W=(60 kg)(9.81 m/s^2)=588.6 N`

b) The gravitational potential energy at the top of the hill is U=1000 J. The potential energy is also given by the product between the weight W and the height of the hill h:

`U=Wh`
If we rearrange the equation, we can calculate the height of the hill, h:

`h= (U)/(W) = (1000 J)/(588.6 N) =1.70 m`

c) At the bottom of the hill, all the potential energy at the top of the hill has converted into kinetic energy:

`U=K`

`U= (1)/(2) mv^2`
where m is the mass and v is the speed. If we rearrange the formula, we can calculate the speed at the bottom of the hill:

`v=\sqrt{(2U)/(m)}=\sqrt{(2\cdot 1000 J)/(60.0 kg)}=5.8 m/s`