# Kinetic and Potential Energy on a roller coaster

• NathanLeduc1
In summary, to barely make it to the top of a second hill that is 20 m high, the initial speed of the roller coaster must be at least 14 m/s, assuming a frictionless roller coaster. This can be calculated using the equation v = sqrt(2*g*(h2-h1)).
NathanLeduc1

## Homework Statement

A roller coaster starts at the top of hill that is 10 m high. If it is to barely make it to the top of a second hill that is 20 m high, how fast must the initial speed of the roller coaster be? Assume that the roller coaster is frictionless.

KE = 0.5mv^2
PE = mgh

## The Attempt at a Solution

mgh=0.5mv^2
gh = 0.5v^2
v = sqrt(2gh)
v = sqrt(2*9.81*20)
v = 20 m/s needed at bottom of second hill.

mgh=0.5mv^2
gh = 0.5v^2
v = sqrt(2gh)
v = sqrt(2*9.81*10)
v = 14 m/s at bottom of hill if initial velocity at top of first hill is 0m/s.

20 m/s - 14 m/s = 6 m/s

6 m/s is the velocity of the roller coaster at the top of the first hill.

Does that look right?

No, this is not right. Check it this way: compute KE with v = 6 m/s and PE with h = 10 m; the sum is the total energy initially. It must be equal to the total energy finally, which is KE with v = 0 m/s and PE with h = 20 m.

Hm, okay. I tried setting the total energy at the top of hill one equal to the total energy at the top of hill two.
0.5m(v1)^2+mg(h1) = 0.5m(v1)^2+mg(h2)
0.5(v1)^2 + g(h1) = 0.5(v1)^2 + g(h2)
v = sqrt(2*g*(h2-h1))
v = sqrt (2*9.81*(20-10))
v = 14 m/s

Would that work?

The result is correct, but the first two equations are not correct, having the same v1 symbol on both sides.

Oh, yeah... I meant (v2) on the right side of the equations. That was simply a typo.

Very well then.

## What is kinetic and potential energy on a roller coaster?

Kinetic energy is the energy an object possesses due to its motion, while potential energy is the energy an object has due to its position or height. On a roller coaster, kinetic energy is at its peak when the coaster is moving at its fastest speed, while potential energy is at its peak when the coaster is at its highest point.

## How does kinetic and potential energy affect a roller coaster ride?

Kinetic energy helps the roller coaster overcome friction and other forces, allowing it to move along the track. Potential energy is converted into kinetic energy as the coaster travels down the track, providing the thrill and excitement of the ride.

## Why does a roller coaster slow down at the top of a hill?

At the top of a hill, the roller coaster has reached its maximum potential energy and begins to lose speed as it travels down the hill. This is due to the conversion of potential energy into kinetic energy, as the coaster accelerates downward.

## How is energy conserved on a roller coaster?

The total amount of energy on a roller coaster remains constant throughout the ride, as energy cannot be created or destroyed. However, the energy is constantly changing form between kinetic and potential energy as the coaster moves along the track, following the law of conservation of energy.

## What factors affect the amount of kinetic and potential energy on a roller coaster?

The height and speed of the roller coaster, as well as its mass, all play a role in determining the amount of kinetic and potential energy at any given point. The design of the track and the forces of gravity and friction also impact the energy of the ride.

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