How Do Roller-Coasters Work?

For roller coasters to work they need the correct balance between Potential Energy and Kinetic Energy.  Also the physicists who construct them need to find out the maximum speed the roller coaster can handle.  If the roller coaster exceeds the limit of that velocity then that puts the riders' lives aboard in jeopardy.  The amount of potential and kinetic energy fluctuates during the ride.  There is more potential energy the higher you are and the lower you are there is greater kinetic energy.  When there is greater kinetic energy then that means there is a greater velocity there as well.  The total amount of kinetic energy and potential energy remains the same during the ride although the amount of each may change.

 As you can see above, the scale on the right shows the amount of KE and PE there is.  It also shows how the amount of each changes throughout the ride.  To find the amount of speed necessary or the amount of kinetic energy used, physicians would use the equation KE=mv^2 or to find the amount of PE in they would use: PE=1/2mgh