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## Physics Tutorials

### Centripetal Force and Boarders

Centripetal force: When an object is traveling in circular motion it experiences centripetal force (Fc), meaning a force "toward the center of the circle." This centripetal force can be a net force resulting from the simultaneous application of weight (Fg) and another force such as normal force.

Explanation: The normal force (Ft) is the force the inside of a loop exerts on an object. The net force (Fnet) for the circular loop is equal to the Fc. However, because of gravity, Fnet=Ft+Fg for the top and Fnet=Ft-Fg for the bottom. As long as Ft is greater than 0 the object will remain in the loop. Also, the Ft is smallest on the top and biggest on the bottom of the loop because on the bottom it must overcome gravity, while at the top it is assisted by gravity. The velocity of the object is always a tangent to the loop and should remain constant throughout the loop.

The centripetal force is found by the formula Fc=mv2/r and Fg=(9.8)m.

Centripetal force, normal force, and gravity can be used to determine whether an snow boarder is going to "stick" to the inside of a loop. The velocity that the boarder has going the loop will remain the same throughout. And as long as the normal force of the loop is greater than 0 the boarder should remain in contact with the surface of the loop. This can be used to calculate the minimum velocity to enter a loop of any size for a boarder of a given mass.

#### Question

A 90kg snow boarder approaches a loop. The loop has a radius of 5 m. His velocity directly at the bottom is 8 m/s. The loop can supply a normal force of no mare than 2500N. Assuming there is no friction will he make it all the way around?

SOLUTION: He makes it
Step1: Draw a Diagram

Step2: The top of the loop will have the smallest amount of tension on the loop it must be greater than 0 for the boarder to remain in the loop.
Fc=Fnet
Fc=Fg+FN
mv^2/r=9.8m+Ft
90*8^2/5=9.8*90+Ft
Ft=270N

Step3: The bottom of the loop will have the most normal force. This tension must be less than 2500N for the loop to stay together.
Fc=Fnet
Fc=Ft-Fg
mv2/r=Ft-9.8m
90*8^2/5=Ft-9.8*90
Ft=2034N

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