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Chapter 10: Q.3 (page 255)

A roller-coaster car rolls down a frictionless track, reaching speed v0 at the bottom. If you want the car to go twice as fast at the bottom, by what factor must you increase the height of the track? Explain.

Short Answer

Expert verified

As the speed depends only on the vertical height and not the shape of the track, the height of the track is increased by two times.

Step by step solution

01

Content Introduction

As we know the track is frictionless, let us consider the car and Earth as an isolated system. So, firstly find the equation of the final velocity at the bottom, when the car starts from the rest at height h.

∆E=0Ef=EiKf+Ug,f=Ki+Ug,i12mv2fmgyf=12mvi2+mgyi

Note that car starts from rest, vi=0, yf=0because it is at ground andyi=h1

hi=v2fg

02

Content Explanation

To make car go twice as fast at the bottom, we will use above equation.

h2=v2f2gNote:vf2=2vfh2=(2vf)2gh2=4v2fgh2=4h1

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