[:PiraScheme#Mechanics: Table of Mechanics Demonstration] |
[:MEEquipmentList: List of Mechanics Equipment & Supplies] |
[:Demonstrations:Lecture Demonstrations] |
Loop the Loop, 1M40.20
Topic and Concept:
Work and Energy, [:WorkEnergy#ConservationOfEnergy: 1M40.Conservation of Energy]
Location:
Cabinet: [:MechanicsCabinet:Mechanic (ME)]
Bay: T7
attachment:LoopTheLoop01-400.jpg
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 |
ME, Bay T7 |
|
Ball |
ME, Bay , Shelf # |
|
Important Setup Notes:
- It is advisable to practice a few times before hand to gain a sense of the critical height for making a complete loop.
Setup and Procedure:
- Place loop on the table as shown.
- Place the ball at varying initial heights on the longer side of the two inclines and release.
Cautions, Warnings, or Safety Concerns:
- N/A
Discussion: See the link below for a detailed calculation of the minimum height necessary for which the ball can fall freely and make it around the loop.
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 mass, g the acceleration due to gravity, and h 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. 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 off. Subsequently, a minimum initial height can be calculated. As it turns out, this critical height is hcrit = (5/2) * R
attachment:LoopTheLoop03-250.jpg |
attachment:LoopTheLoop04-250.jpg |
attachment:LoopTheLoop05-250.jpg |
attachment:LoopTheLoop06-250.jpg |
Videos:
[https://www.youtube.com/user/LectureDemostrations/videos?view=1 Lecture Demonstration's Youtube Channel]
References:
[https://en.wikipedia.org/wiki/Conservation_of_energy Conservation of Energy - Wikipedia]
[http://physics.bu.edu/~redner/211-sp06/class-energy/looptheloop.html Calculating the Minimum Height from which the Ball Can Drop and Get Around the Loop]
[http://www.physicsclassroom.com/mmedia/circmot/rcd.cfm Forces on a Roller Coaster Loop-the-Loop]
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