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Chapter 8: Q.20 (page 199)

A roller coaster car crosses the top of a circular loop-the-loop at twice the critical speed. What is the ratio of the normal force to the gravitational force?

Short Answer

Expert verified

The ratio of the normal force to the gravitational force is 3.

Step by step solution

01

Given information

Given in the question that, A roller coaster car crosses the top of a circular loop-the-loop at twice the critical speed.

02

Explanation

From the information we observed that mV2ris the result of Nand mg

Here,

m-The mass of the roller coaster

g-The acceleration due to gravity

r-The radius of the circular loop

V- The velocity

Therefore,

mV2r+N=mg

N=mg-mV2r

V2=4gr

Since roller coaster car crosses the top of a circular loop-the-loop at twice the critical speed.

Therefore,

N=mg-m(4gr)r

N=-3mg

Hence, the ratio of the normal force to the gravitational force is3

03

Final answer

The ratio of the normal force to the gravitational force is 3.

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