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?
a) Will it make it all the way over the hill? (assume no friction)
b) If the roller coaster cart had a mass of
1 Answer
the answer to (a) is yes and (b) is 18.76m (both assuming
Explanation:
For part (a) we are to assume no friction. Hence all kinetic energy will be converted to potential energy.
Kinetic energy = KE=
Potential energy is given by
So we can see that there is sufficient KE to get tot the top of the hill. (if you take
For part (b), some of the energy is used in working against friction, so energy available for conversion into PE is given by:
This will be converted to PE, so
Solving gives