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If the speed decreases, the required centripetal force would be less and less. There comes a point where the gravitational force (weight) would be all that is required to keep the car moving in a circle. In that case, the normal force is zero. In this special situation where no normal force is required, you could actually have a small gap in the top of the track and the car would continue to move in a circle.
At the bottom of the roller coaster, the car would need a normal force of the track on the car that would be greater than the weight since the weight is not providing any help for the required centripetal force.
This is summarized in the following tables.
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The force of gravity pulling you down is used to move you in a circle. You are moving down but you are also moving across. If the speed of the roller coaster were not sufficient, you would require a centripetal force less than the gravitational force to move you in a vertical circle. The gravitational force would cause you to fall. It's your large speed that keeps you from falling when you are upside down.
Apparent Weight and the
Roller Coaster Ride
You discovered earlier that an elevator ride could give you a sense of weight changes during accelerations. |
| Fast-moving roller coaster |
| |
Required
centripetal force |
Force of gravity (weight) |
Normal force
(the force of the track on the car) |
At the top
of the loop |
5000 N |
1000 N |
4000N |
At the bottom
of the loop |
9000 N |
1000 N |
10,000 N |
| Slow-moving roller coaster |
| |
Required
centripetal force |
Force of gravity (weight) |
Normal force
(the force of the track on the car) |
At the top
of the loop |
2100 N |
1000 N |
1100 N |
At the bottom
of the loop |
6100 N |
1000 N |
7100 N |
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