# How Do Rollercoasters Use Circular Motion and Acceleration?

• helpme101
In summary, the rollercoaster has an acceleration of -9.81ms^-2 when it starts down the initial slope and 0ms^-2 when it starts each loop.
helpme101

## Homework Statement

A rollercoaster consists of a 45 degree slope that is 100 m long followed by two loops which have radii of 40 m and 20 m respectively. If the rollercoaster accelerates down the initial slope due to gravity, determine:
a. The acceleration of the rollercoaster down the 45 degree slope.
b. The acceleration of the rollercoaster as it starts each loop. You can assume the speed of the roller coaster entering each loop is the same as the speed at the bottom of the initial slope.
c. The limit of the body's ability to withstand acceleration is approximately 5 g or 49.05ms^-2 is the roller coaster safe for the average person to ride?

F=ma

## The Attempt at a Solution

For part A: isn't the acceleration of the rollercoaster -9.81ms^-2? The start of the problem states that "if the rollercoaster accelerates down the initial slope due to gravity, determine..." If this isn't correct would I somehow use Newton's Second law, however I don't know the mass of the cart or the force.
For part B: I know that the two radii have a role on acceleration. Do I need to apply Newton's Second law?
For part C: would I be looking at the apparent weight? However, I'm not given the mass of the average person, so should I ask the professor for that??

This is a problem of strictly acceleration due to gravity relative to the slope of the ramp (think geometrically), the resulting velocity and centripetal acceleration in each loop.
F=ma is not relevant.. Your acceleration due to gravity is sqrt(9.81 * h) where h the the vertical distance of travel (again, think geometrically)

JBA said:
Your acceleration due to gravity is sqrt(9.81 * h) where h the the vertical distance of travel (again, think geometrically)
You statement is wrong. The expression in red is not acceleration.

helpme101 said:

## Homework Statement

A rollercoaster consists of a 45 degree slope that is 100 m long followed by two loops which have radii of 40 m and 20 m respectively. If the rollercoaster accelerates down the initial slope due to gravity, determine:
a. The acceleration of the rollercoaster down the 45 degree slope.
b. The acceleration of the rollercoaster as it starts each loop. You can assume the speed of the roller coaster entering each loop is the same as the speed at the bottom of the initial slope.
c. The limit of the body's ability to withstand acceleration is approximately 5 g or 49.05ms^-2 is the roller coaster safe for the average person to ride?

F=ma

## The Attempt at a Solution

For part A: isn't the acceleration of the rollercoaster -9.81ms^-2? The start of the problem states that "if the rollercoaster accelerates down the initial slope due to gravity, determine..." If this isn't correct would I somehow use Newton's Second law, however I don't know the mass of the cart or the force.
No, the acceleration along a slope is less than g. Look at your Lecture Notes or Book, or see: http://hyperphysics.phy-astr.gsu.edu/hbase/mincl.html
helpme101 said:
For part B: I know that the two radii have a role on acceleration. Do I need to apply Newton's Second law?
You always can apply Newton's Second Law. What force should act to make a circle of given radius? What is the corresponding acceleration?
helpme101 said:
For part C: would I be looking at the apparent weight? However, I'm not given the mass of the average person, so should I ask the professor for that??
The problem asks if the accelerations in the loops are less or greater than 5g. It is not the apparent weight.

ehild said:
You statement is wrong. The expression in red is not acceleration.

Supid mistake, I apologize to all.

## 1. How do rollercoasters maintain their circular motion?

Rollercoasters maintain their circular motion through the use of centripetal force. This force is directed towards the center of the circular path and keeps the rollercoaster moving in a circular motion.

## 2. What factors affect the speed of a rollercoaster?

The factors that affect the speed of a rollercoaster include the height of the rollercoaster, the angle of the track, and the amount of friction present. A steeper drop and less friction will result in a faster speed.

## 3. How does the shape of a rollercoaster track affect the ride experience?

The shape of the rollercoaster track can greatly affect the ride experience. A track with sharp turns and drops will create a more intense and thrilling ride, while a track with smoother curves will result in a more gentle and smooth ride.

## 4. What is the relationship between the radius of a rollercoaster loop and the forces experienced by riders?

The radius of a rollercoaster loop is directly related to the forces experienced by riders. A larger radius will result in lower forces, while a smaller radius will result in higher forces. This is because a larger radius allows for a smoother and less intense ride, while a smaller radius requires a greater centripetal force to maintain circular motion.

## 5. How does the design of a rollercoaster affect the feeling of weightlessness?

The design of a rollercoaster can greatly influence the feeling of weightlessness experienced by riders. A track with more drops and vertical loops will result in a greater feeling of weightlessness, while a track with fewer changes in elevation will result in a less intense feeling of weightlessness.

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