# How Is the Force on a Child in a Roller Coaster Calculated?

• Austin Gibson
In summary, the question asks for the force of the car seat on the child at point B, given the child's mass, the car's speed at points A and B, and the radius of the loop. The student attempted to solve it by using the equation Fc = [(mv^2)/r * cos30] - mg, but incorrectly applied cos30 to the gravitational force instead of the centripetal force. The correct equation is Fc = [(mv^2)/r] * cos30 - mg.
Austin Gibson

## Homework Statement

:[/B]
A child of mass 40.0 kg is in a roller coaster car that travels in a loop of radius 7.30 m. At point A the speed of the car is 15.0 m/s, and at point B, the speed is 15.6 m/s. Assume the child is not holding on and does not wear a seat belt.

What is the force (in N) of the car seat on the child at point B? (Enter the magnitude.)

Fc = [(mv^2)/r]
Fc = ma

## The Attempt at a Solution

:

I solved (a) and (c).
I solved (a) by inserting the mass, speed, and radius into the equation [(mv^2)/r] and subtracting by (mass*gravity).
My equation for (b) was [(mv^2)/r * cos30] - mg = [(40*(15.6^2)/7.3*cos30) - (40*9.8) = 762.8 N. That was incorrect. What's improper about my equation? [/B]

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Austin Gibson said:

## Homework Statement

:[/B]
A child of mass 40.0 kg is in a roller coaster car that travels in a loop of radius 7.30 m. At point A the speed of the car is 15.0 m/s, and at point B, the speed is 15.6 m/s. Assume the child is not holding on and does not wear a seat belt.

What is the force (in N) of the car seat on the child at point B? (Enter the magnitude.)

View attachment 232155

Fc = [(mv^2)/r]
Fc = ma

## The Attempt at a Solution

:[/B]

I solved (a) and (c).
I solved (a) by inserting the mass, speed, and radius into the equation [(mv^2)/r] and subtracting by (mass*gravity).
My equation for (b) was [(mv^2)/r * cos30] - mg = [(40*(15.6^2)/7.3*cos30) - (40*9.8) = 762.8 N. That was incorrect. What's improper about my equation? [/B]
In what direction is the centripetal force at point B ?

Also, is there any net force on the child at point B ?

Austin Gibson
SammyS said:
In what direction is the centripetal force at point B ?
120 degrees(90+30)?

I solved it by applying (cos 30) to mg instead of the centripetal force.

## What is the force experienced on a roller coaster?

The force experienced on a roller coaster is a combination of gravitational force, normal force, and centripetal force. These forces are responsible for the thrilling and sometimes intense sensations felt while riding a roller coaster.

## What is the difference between positive and negative G-forces on a roller coaster?

Positive G-forces, also known as "Gs", are forces that push riders down onto their seats. Negative G-forces, on the other hand, lift riders out of their seats. These forces are created by the acceleration and deceleration of the roller coaster.

## How do roller coasters maintain safety while experiencing high forces?

Roller coasters are designed with safety in mind. The tracks are carefully engineered to ensure the forces experienced by riders are within safe limits. In addition, riders are secured with restraints and the trains are equipped with various safety features.

## Can the force on a roller coaster be calculated?

Yes, the force on a roller coaster can be calculated using Newton's laws of motion. The mass of the train, the acceleration and deceleration, and the angle and radius of the track can all be used to calculate the forces experienced by riders.

## Are there any health risks associated with riding roller coasters?

While roller coasters are generally safe, there are some potential health risks associated with riding them, such as whiplash, dizziness, and motion sickness. It is important for individuals with pre-existing health conditions to consult with a doctor before riding a roller coaster.

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