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?

1 Answer
Matt
May 13, 2016

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

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