Tell Me More about: Conservation of Energy



Coaster Dynamics

Tell Me More   about:

Conservation of Energy

One way to prevent the car from stopping before it reaches the top of the hill is to move the entire hill downward. That helps because we increase the kinetic energy of the car by reducing the potential energy when it is moved downward.

One of the fundamental concepts in physics is the Conservation of Energy. That's just a fancy way of saying that the total amount of energy for the roller coaster car remains constant -- but the energy can change from one form to another.

For a roller coaster, the two most important types of energy are Potential Energy and Kinetic Energy.

Potential energy is the energy resulting from gravity. The higher up the car goes, the more potential energy it has.

Kinetic energy is the energy of motion. The faster it goes, the more kinetic energy it has.

Consider the case of lowering the position of the hill, by the amount H1, as shown below.


The potential energy is equal to:

PE = mgh

m = mass (Kg)
g = gravity constant (9.82 m/s²)
h = height (m).
The kinetic energy is equal to:

KE = (1/2)(mv²)

m = mass (Kg)
v = velocity (m/s).
When the hill is lowered by the amount, H1, some of the potential energy is converted into kinetic energy. The change in potential and kinetic energies are equal, so in this case, the velocity at the top of the hill, v2, increases from what it was before.

Apply Your Knowledge

    Your Task:

If you lower the position of the hill by 30 m, what will the car's velocity be at the top of the hill?
    What We Know:

For our simplified analysis, we will ignore the affect of friction.

The known parameters are:
H1 = 30 m
mass of the car = 453.59 kg
g = 9.82 m/s².
Using the "Coaster Lab" Option in Coaster Dynamics, determine the values of the following parameters:
v1 = initial velocity (m/s)
H2 = height of the hill (m).
    What To Do:

Using the equations below for the change in potential and kinetic energies, solve for the v2, the velocity at the top of the hill:
1)   Net change in PE = (mg)(H1 - H2)

2)   Net change in KE = (1/2)(m)(v1² - v2²).
To test your work, change the height of the hill of track element #4 to 30 m (the amount you assumed for your calculations), and then re-run the roller coaster ride.

Pause the ride after the car passes the top of the hill, and use the "Coaster Lab" option in
Coaster Dynamics to determine the velocity at the top of the hill.

Remember that you did not include the affect of friction, so what do the expect the velocity to be?