# Homework Help: Acceleration and friction problem

1. Nov 1, 2009

### PhilCam

1. The problem statement, all variables and given/known data

A car is on a circular track of radius r=120 m. It accelerates from rest to a speed of 20 m/s in 8 seconds with constant acceleration. At the end of the 8 second the car is next to a marker on the track.

A) Find the ratio of the tangential acceleration to the centripetal acceleration as the car reaches the marker.

B) Find the minimum coefficient of friction between the tires and track's pavement so that the car does not go out of the track at the marker.

C) At the marker the tires are rolling without slipping. The radius of the tires is .25m. Find the angular velocity of the tire at the marker.

3. The attempt at a solution

A) Tangential acceleration = radius x angular acceleration
=120 x 2.5 = 300

Centripetal = radius x angular velocity squared
=120x 20^2=48,00

I am very unfamiliar with these concepts and I know that this answer is not right; however I have read the chapter in the book but I am still unsure on how to solve this portion of the problem using the formulas given.

B) F=(N) (Coeff of friction)
I do not know how to use this formula because a mass was not given to me to solve for force.

C) Well if the radius of the tire is .25 m and the car is going 20 m/s, then I would assume the wheel has an angular velocity of 80 rad/s.

I am really having trouble with this chapter and any help would be appreciated.

2. Nov 1, 2009

### Delphi51

Part (a) does not seem to have anything to do with angular velocity or acceleration. The tangential acceleration can be found using a = Δv/Δt.
The centripetal acceleration may be found using a = v²/R.

For (b), you are looking for the "grip" the car needs on the road so that it will not slip. That is, the friction needed to provide the centripetal force. Begin with Ff = Fc.

Part (c) looks correct!

3. Nov 1, 2009

### PhilCam

Okay I found the correct answer for A. Thank you so much for simplifying, those equations were much less confusing than the ones listed in my text book.

And then for part B:

Ff = V^2/(g)(r)
Ff = .34

Is this correct?

4. Nov 1, 2009

Correct!