car traveling in a flat(unbanked, 8m radius) circular track accelerates uniformly from rest with a tangential.

Question

...acceleration of 1.8m/s/^2.
The car makes it 0.6 of the way around the circle before skidding off the track.
acceleration of gravity=9.8m/s^2
What is the coeffcient of static friction between the car and track??

Answer 1

The centripetal force is
m*v^2/r

or in radians/sec
m*w^2

the acceleration in radians/s^2 is
1.8/r
the angular displacement is
.6*2*pi=.5*1.8*t^2/r
the speed at the point is
w=1.8*t/r
which is
g*u
u=1.8*t/(g*r)
t=sqrt(2*.6*2*pi*r/1.8)

solve for u
=0.133

I used pi=3.14

j