Finding friction from tangential acceleration

[pcandrepair]

[SOLVED] Finding friction from tangential acceleration

Homework Statement

A car traveling on a flat (unbanked) circular track accelerates uniformly from rest with a tangential acceleration of 2.25 m/s^2. The car makes it one quarter of the way around the circle before it skids off the track. Determine the coefficient of static friction between the car and track from these data.

Homework Equations

$$\theta$$final = 90
$$\theta$$initial = 0

friction = mass(net acceleration)

$$\mu$$ = (sqrt((tan accel.)^2) + ((radial accel.)^2))) / g

The Attempt at a Solution

I know the above equation is used to find the coefficient of friction but I do know how to find the radial acceleration from what is given. Any help would be greatly appreciated. Thanks.

 

[pcandrepair]

Nevermind...I figured it out.

 

[ogb p]

To find the radial acceleration in this problem, we can use the equation a = v^2/r, where v is the tangential velocity and r is the radius of the circular track. Since the car is starting from rest, we can also use the equation v = at, where t is the time it takes for the car to reach its final velocity. We can find t by using the equation x = 1/2at^2, where x is the distance traveled (in this case, one quarter of the way around the circle). Once we have the value for t, we can plug it into the equation v = at to find the tangential velocity. Then, we can plug both values (tangential velocity and radius) into the equation a = v^2/r to find the radial acceleration. Once we have the radial acceleration, we can use the equation \mu = (sqrt((tan accel.)^2) + ((radial accel.)^2))) / g to find the coefficient of static friction. I hope this helps!