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) $E_i=\frac{mv^2}{2}=\frac{610\cdot25^2}{2}=160625(J)$

(ii) $E_{out}=mgh=610\cdot9.8\cdot22=131516(J)$

(iii) $\eta=\frac{E_{out}}{E_i}\cdot100 \ \%=\frac{131516}{160625}\cdot100\ \%=82\ \%$

$h=\frac{E_i}{mg}=\frac{160625}{610\cdot9.8}=26.87(m)$