Question

A rollercoaster is designed to have a car full of riders (total mass = 610 kg) travel along a section of horizontal track at ground level with a speed of 25 m/s and then travel up a ramp, stopping at a height of 22 m.

Calculate the rollercoaster car’s:

(i) Input energy.

(ii) Useful output energy.

(iii) Percent efficiency.

If the rollercoaster was 100% efficient and all of the input energy was entirely transformed into useful output energy, what should have been the maximum height of the car?

Answer 1

i)

$$E_i=0.5(610)(25)^2=190625\ J$$

ii)

$$E_o=(610)(9.8)(22)=131516\ J$$

iii)

$$\eta=\frac{131516}{190625}=69\%$$

$$h=\frac{v^2 }{2g}=\frac{25^2 }{2(9.8)}=32\ m$$