# Radial acceleration, car sircular path

1. Sep 22, 2010

### eventob

1. The problem statement, all variables and given/known data
A car is travelling with constant speed over a hill and down a hill. The radius of the curve is the same. At the top of the hill, the driver experience no normal force from the ground. The mass of the driver is 70.0kg

a) calculate the value of the normalforce experienced by the driver at the bottom of the ground.

2. Relevant equations
A_c = (v^2/r)

3. The attempt at a solution
Drew a free-body-diagram of the forces acting on the car (modeled as a particle under uniform circular motion. Not sure how to approach this problem.

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2. Sep 22, 2010

### rock.freak667

Well at the bottom of the hill, what are the forces acting? What directions are they acting (towards or away from the center of the circle)?

3. Sep 22, 2010

### eventob

At the bottom there is the force of gravity (70kg*9.80*(m/s^2), the centripetal acceleration towards the center of the circle, and the normal force also towards the enter of the circle. I think.

At the top the normal force is going in the opposite direction, away from the center of the circle? I've tried to put the data into Newtons second law, but I get to many unknown variables I think.

Thanks. :)

4. Sep 22, 2010

### rock.freak667

The weight acts downwards and the normal reaction is opposite, so towards the center of the circle.

What is the resultant force then ? In terms of N and mg.

5. Sep 22, 2010

### eventob

sigma F_y= n-mg = m*(v^2/r)

Which means that the normal force acting on the driver at the bottom of the hill is:

n=m*(v^2/r)+mg
=m[(v^2/r)+g]

But, in order to calculate the speed, can I make a similar equation for the top of the hill and substitute for v?
:)

6. Sep 22, 2010

### rock.freak667

Yes but at the top remember, if the normal reaction is not present, then centripetal force mv2/r is?

7. Sep 23, 2010

### eventob

Sorry, but I still don't get it. At the top, the only force that acts on the object is the force of gravity? But if there is no normal force, what is preventing the car from falling through the ground?