Tell Me More
about:
|
Conservation of Energy
|
To prevent the car from rolling backwards before it reaches the top of the loop, we need to reduce the loop's height.
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 the car rolling down the hill and then up the loop.
|
|
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 car rolls down the hill, some of its potential energy is changed into kinetic energy. At the bottom (assuming h = 0 there), the kinetic energy is equal to the potential energy it had at the top. Then, as the car rolls up the loop, the kinetic energy changes back into potential energy.
If there were no other forces acting on the roller coaster car, the potential energy would be the same as before, and the car would return to exactly the same height where it began. However, in a real roller coaster, some energy is converted into heat due to friction. So here, the loop must be lower than the first hill.
The potential and kinetic energy depend only on the height and velocity, respectively. It doesn't matter what path the car takes. Thus, the same analysis above applies to a roller coaster car moving up a hill or a loop.
|
Apply Your Knowledge
|
Your Task:
|
Knowing the initial velocity of the roller coaster car, how high it will go before it stops?
|
What We Know:
|
For our simplified analysis, we will ignore the affect of friction.
The known parameters are:
|
mass of the car = 453.59 kg
g = 9.82 m/s².
|
For the loop where the car fell backwards, use the "Coaster Lab" Option in
Coaster Dynamics,
to determine the initial velocity of the car as it entered the loop.
|
What To Do:
|
Using the equations for the kinetic and potential energy below, solve for the height, h, at which the velocity will be zero:
|
1) PE = mgh (at top, v=0 )
2) KE = (1/2)(mv²) (at bottom, h=0 ).
|
Calculate the value of h using the known values from above.
To test your work, change the height of the loop to your calculated value, and then re-run the roller coaster ride.
Remember that you did not include the affect of friction, so what do the expect the car to do?
Finally, reset the height of the loop to fix the problem of the car rolling backwards.
|