Question

A roller coaster car rolls down a frictionless track, reaching speed v at the bottom. a. If you want the car to go twice as fast at the bottom, by what factor must you increase the height of the track? b. Does your answer to part a depend on whether the track is straight or not? Explain.

Answer 1

Answer:

4

Explanation:

Given that

Track is friction less

As we know that ,the velocity of the particle only depends on the height difference and does not depends on the path is incline or curve .

The final speed(v) of the roller at the bottom given as

From energy conservation

$mgh=\dfrac{1}{2}mv^2$

$v=\sqrt{2gh}$

If we want to twice the speed ,it means that

v'= 2v

lets take height difference is h'

$v'=\sqrt{2gh'}$

$2v=\sqrt{2gh'}$

$2\sqrt{2gh}=\sqrt{2gh'}$

4 x 2 g h = 2 g h'

So

h'=4 h

The height have to increase by 4 factor.