# Speed of a Roller Coaster, Conservation of Energy

• LiquidPi
In summary, the speed of the roller coaster at Point B is √(2*g*y), where g is the acceleration due to gravity and y is the height difference between Point A and Point B. The roller coaster will not reach Point C due to the conservation of energy principle, and the required speed at Point A for it to reach Point C is √(2*g*y) + 5.0 m/s.

## Homework Statement

A roller coaster travels on a frictionless track as shown in the figure.
(a) If the speed of the roller coaster at Point A is 5.0 m/s, what is its speed at Point B?
(b) Will it reach Point C?
(c) What speed at Point A is required for the roller coaster to reach Point C?

Please view the attached figure. In case the image is too blury, the height of Point A = 5.0 meters, and the height of Point C = 8.0 meters.

## Homework Equations

KE = 0.5*m*v^2
PE = m*g*y, where y = vertical position

## The Attempt at a Solution

KE = PE
0.5*m*v^2 = m*g*y
mass cancels
0.5*v^2 = g*y
v = √(2*g*y)

What confuses me is what to do with the starting speed at Point A, 5.0 m/s. If the velocity at the top was zero, then the problem would be relatively straightforward. Where do I go from here? Thanks in advance!

#### Attachments

• PhysicsProblem.jpg
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A) PE at point a and KE = KE at point b
So m*g*h + 0.5*m*u^2 = 0.5*m*v^2
I think you can do the rest
B) Nope
C) KE lost = PE gained
I can't see the numbers on the image attached!

alewisGB said:
A) PE at point a and KE = KE at point b
So m*g*h + 0.5*m*u^2 = 0.5*m*v^2
I think you can do the rest
B) Nope
C) KE lost = PE gained
I can't see the numbers on the image attached!

Excellent, thank you!

## What is the speed of a roller coaster?

The speed of a roller coaster can vary depending on its design and the forces acting on it. However, most roller coasters reach speeds between 50-100 miles per hour.

## How is the speed of a roller coaster determined?

The speed of a roller coaster is determined by several factors, including the height and steepness of the track, the weight and design of the train, and the forces of gravity and friction acting on the train.

## How does conservation of energy apply to roller coasters?

Conservation of energy is a fundamental principle of physics that states that energy cannot be created or destroyed, only transferred or transformed. This principle applies to roller coasters, as the potential energy gained from being pulled up a hill is converted into kinetic energy as the train speeds down the track.

## Why do roller coasters slow down at the end of the ride?

Roller coasters slow down at the end of the ride due to friction and air resistance. As the train travels through the air, it experiences resistance which slows it down. Additionally, the brakes on the track are used to control the speed and bring the train to a stop at the end of the ride.

## Can the speed of a roller coaster be accurately calculated?

Yes, the speed of a roller coaster can be accurately calculated using the principles of physics and mathematical equations. However, the actual speed may vary slightly due to external factors such as wind or temperature.

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