Loop-the-loop Conservation of energy

[erice]

Homework Statement

A small car is given an initial velocity of 4 m/s (prior to reaching the loop), what is the largest value that the radius of a loop the loop can have so that the car remains in contact with the track at all times?

This one really has me stumped... please help

 

[putongren]

OK ... not sure if this is right... When the car is at the top of the loop the loop, the force of gravity has to equal the centrifugal force. If you draw a free body diagram at the moment it reaches the top of loop the loop, the car will have an arrow pointing downwards representing gravity and an arrow pointing upwards representing centrifugal force. Now, what is the equation for the centrifugal force? If you know that, equate the equation of gravity and the centrifugal force and solve for r.

 

[putongren]

Actually I think I'm wrong... Let me think about it a little more until I get the right answer and get back to you.

 

[AEM]

OK ... not sure if this is right... When the car is at the top of the loop the loop, the force of gravity has to equal the centrifugal force. If you draw a free body diagram at the moment it reaches the top of loop the loop, the car will have an arrow pointing downwards representing gravity and an arrow pointing upwards representing centrifugal force. Now, what is the equation for the centrifugal force? If you know that, equate the equation of gravity and the centrifugal force and solve for r.

Don't you have to take into account the loss of velocity as the car goes up the loop?

 

[AEM]

Homework Statement

A small car is given an initial velocity of 4 m/s (prior to reaching the loop), what is the largest value that the radius of a loop the loop can have so that the car remains in contact with the track at all times?

This one really has me stumped... please help

I'll give you a couple more hints. You need to use the fact that the centrifugal force and force of gravity must be equal and opposite and you need to note that the kinetic energy at the start goes into gravitational potential energy plus kinetic energy as the car goes up the loop. Thus you will have two equations for two unkonwns: the velocity at the top of the loop and the radius of the track.