A 31 kN roller coaster starts from rest and is launched along a horizontal secti

Question

A 31 kN roller coaster starts from rest and is launched along a horizontal section of track. It takes 23 m to reach a speed of 29 m/s. (I already know that the the first three I got right)

1) What force is applied to the roller coaster during the launch?

= 57770N

2) A meter measures the energy input into the motors during the launch as 0.696 kW-hour. What is the efficiency of the motors?

=53.03%

3) After the launch, the roller coaster goes straight up, shooting out of the mountain. A minimum speed of 6.1 m/s is required at the top. Assuming no losses, how high above the initial elevation can the coaster go?

=40.97m

I was good up until this point, but I'm stuck on 4. I would really appreciate a good explanation.

4) As the coaster comes down the hill to the same elevation at which it started, it loses 20000 J of energy. What is the speed at the bottom of the hill?

5) After the run, the roller coaster comes into the station with a speed of 0.45 times the speed at the end of the launch. What percent of energy was lost during the run?

THANKS. :)

Explanation / Answer

4)

using work energy principle,

0.5*(31000/9.8)*29^2 - 20000 = 0.5*(31000/9.8)*v^2

So, v = 28.8 m/s <------------answer

5)

per of energy lost = 0.45^2*100 = 20.25 percent

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