Centripetal Acceleration Question

[Alameen Damer]

Homework Statement

A skateboarder has to do a loop the vertical loop of a roller coaster track. The radius of the loop is 6.53 m, what is the minimum velocity the skateboarder must have to not fall off when he is at the top of the loop.

Homework Equations

Equation for centripetal acceleration.

Ac=v^2 / r

The Attempt at a Solution

I know how to get the answer, basically rearranging for v, and setting Ac to 9.8 to counteract the gravity pulling the rider down. However, I need help understanding the concept. Why does setting the centripetal acceleration as 9.8 give you the right answer? In this case that the skateboarder is at the top of the loop, the gravity is pulling down in the same direction as the centripetal force. I'm pretty sure I am misunderstanding the direction of the centripetal force. Basically my question is: Does the centripetal force act in the same direction as gravity in this case?

 

[Qwertywerty]

Basically my question is: Does the centripetal force act in the same direction as gravity in this case?

Yes , it does .

Why does setting the centripetal acceleration as 9.8 give you the right answer?

The normal force at the top must just tend to zero , for the boy to finish circular motion . Why ?
Hint : Because if the velocity would be zero , the force of gravity would do what ?

 

[Alameen Damer]

The gravity would simply pull down the boy, and he won't finish his loop

 

[Alameen Damer]

What I am confused on is if there is the force of gravity, in this case the centripetal force pulling down on the boy, what is the force that is counteracting it?

 

[Qwertywerty]

What I am confused on is if there is the force of gravity, in this case the centripetal force pulling down on the boy, what is the force that is counteracting it?

Gravity actually does pull the body during circular motion too , but only in the case of circular motion , it falls sideways .

I hope you can understand this .

 

[Alameen Damer]

What do you mean by it falls sideways? Do you mean that the net force cause the boy to continue on the loop rather than just fall off? If not, what is it that prevents the boy from just falling off at the top?

 

[Qwertywerty]

What do you mean by it falls sideways? Do you mean that the net force cause the boy to continue on the loop rather than just fall off?

Yes , this is it .

 

[Alameen Damer]

Ok thanks a lot!

 

[Chestermiller]

Ok thanks a lot!

Have you tried drawing a free body diagram? What are the forces acting on the boy? What is the force balance equation?

 

[Andrew Mason]

What do you mean by it falls sideways? Do you mean that the net force cause the boy to continue on the loop rather than just fall off? If not, what is it that prevents the boy from just falling off at the top?

Time. If the skateboarder's speed is just enough to do the loop, he is not at the top long enough for gravity to pull him down. Gravity has just enough time to deflect him from a straight line path so that he follows the curved rail at the top, but it does not have enough time to move him farther i.e to pull him away from the rail.

AM