# 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