Loop the Loop, 1M40.20

Topic and Concept:

Work and Energy, 1M40.Conservation of Energy

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Location:

Cabinet: Mechanic (ME)
Bay: T7

Abstract:

A ball is placed at various initial heights and allowed to roll down an incline and around a loop, assuming the ball has enough energy.

Equipment	Location	ID Number

Loop the Loop	ME, Bay T6
Hard Nylon Ball	ME, Bay A2, Shelf #2

Important Setup Notes:

For fun, practice a few times before hand to gain a sense of the critical height for making a complete loop. (Then mark that spot.)
Note that the tack as a whole is not symmetrical. One ramp is longer then the other.
The ball will not compete the loop if started at the top of the shorter ramp.
Listen to the frictional sound of the ball on the track to see if ball makes or breaks contact with the top of the loop.

Setup and Procedure:

Orientate the loop the loop on the table so the audience can see the ball roll around the track.
A 1 1/2" hard nylon ball is placed on the track at it lowest point for the instructor to use.
Place the ball at varying heights on the longer ramp and then release.
A meter stick maybe useful.

Cautions, Warnings, or Safety Concerns:

If the ball is placed too low on the track, the ball will not make it around the loop.
If the ball is placed too high on the track, the ball will fly off the other end of the track after completing the loop.

Discussion:

When the ball is brought up to some point on the track, it is given gravitational potential energy m*g*h where m is the ball's mass, g is the acceleration due to gravity, and h is the height relative to the bottom of the loop. Throughout the demonstration, this quantity will be the total energy of the ball, it it will remain constant as per the conservation of energy, neglecting friction. The force that "compels" the ball to turn in a loop is the normal force of the track on the ball. That is to say the centripetal force is provided by the normal force. [ N = m * v²/ R ] Where N is the normal force, v the speed of the ball, and R the radius of the loop. Using this information, it is then possible to calculate a minimum speed for the ball to have at the top of the loop without falling or slipping off the track. Subsequently, a minimum initial height can be calculated, neglecting friction. As it turns out, this critical height is h_crit = (5/2) * R

See the references below for a detailed calculation of the minimum height necessary for which the ball can fall freely and make it around the loop.

This is also the basic building blocks for amusement rides and roller-coasters.

Videos:

Lecture Demonstration's Youtube Channel

References:

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