Question

A roller coaster has a hill that is `20m` tall. If the roller coaster cart is moving at `20m/s` as it enters the bottom of the hill, how do you answer the following questions?

a) Will it make it all the way over the hill? (assume no friction)
b) If the roller coaster cart had a mass of `5000kg` and friction does `80kJ` of work on the cart, how high up the hill does the cart go?

Answer 1

the answer to (a) is yes and (b) is 18.76m (both assuming `g=9.81ms^-2` )

Explanation:

For part (a) we are to assume no friction. Hence all kinetic energy will be converted to potential energy.

Kinetic energy = KE=`1/2mv^2=1/2m20^2=m*200`
Potential energy is given by `PE=mgh` and we need to get to `h=20m` and since `g=9.81ms^-2`, then at the top of the hill we will have

`PE=m*9.81*20=m*196.2`

So we can see that there is sufficient KE to get tot the top of the hill. (if you take `g=10ms^-2` then it will only just get to the top and then stop since KE=PE)

For part (b), some of the energy is used in working against friction, so energy available for conversion into PE is given by:
`"KE-work done"=200*m-(80times10^3)=200*5000-80000=920000`

This will be converted to PE, so
`PE=5000*9.81*h=920000`
Solving gives `h=18.76m`