Chapter 8: Q.19 (page 199)

The weight of passengers on a roller coaster increases by $50 %$ as the car goes through a dip with a $30 m$ radius of curvature. What is the car’s speed at the bottom of the dip?

Short Answer

Expert verified

The speed of the car at the bottom of the dip is $12.12 m / s$

Step by step solution

Given information

Given in the question that, The weight of passengers on a roller coaster increases by $50 %$ as the car goes through a dip with a $30 m$ radius of curvature.

Explanation

The force acting on the passenger is equal to:

$F = N - m g$

Where,

$N$ indicates the normal force

$m g$ shows the force of gravity

From the information we observed that, if a person feels like their weight is increased by $50 %$ at the bottom that means normal force is $50 %$ stronger that the Force of gravity.

Applying the equation of velocity

According to the information the value of $F = 0.5 m g$

The net force must be equal to the centripetal force.

Therefore,

$0.5 m g = \frac{m V^{2}}{R}$

Here,

$m$ is the mass, $V$ is the velocity and $R$ is the radius.

$V^{2} = 0.5 g R$

$V = \sqrt{0.5 g R}$

$R = 30 m$

$V = \sqrt{0.5 \times 9.8 \times 30}$

$V = 12.12435$

Final answer

The speed of the car at the bottom of the dip is $12.12 m / s$

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The weight of passengers on a roller coaster increases by $50 %$ as the car goes through a dip with a $30 m$ radius of curvature. What is the car’s speed at the bottom of the dip?

Short Answer

Step by step solution

Given information

Explanation

Applying the equation of velocity

Final answer

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The weight of passengers on a roller coaster increases by 50% as the car goes through a dip with a 30m radius of curvature. What is the car’s speed at the bottom of the dip?

Short Answer

Step by step solution

Given information

Explanation

Applying the equation of velocity

Final answer

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Nuclear Physics

Scientific Method Physics

Measurements

Atoms and Radioactivity

Astrophysics

Space Physics

Study anywhere. Anytime. Across all devices.

The weight of passengers on a roller coaster increases by $50 %$ as the car goes through a dip with a $30 m$ radius of curvature. What is the car’s speed at the bottom of the dip?