Circular Motion Practice

Question

A 1,100kg car is turning on a flat roadway, moving in a circle with a radius of 12m. The car is going maximum speed through the turn without skidding. If the coefficient of friction between the car and the road is 0.57, find the speed of the car.

Answer 1

Hi Lilyana R.!

Step 1: Free Body Diagram

With nearly all physics problems relating to dynamics, we want to start with a free body diagram.

In our example, the car is turning on a flat roadway. This tell us we need not consider angles in our calculation here.

The drawing of a free body diagram here is a bit tricky, as we do not have access to any drawing tools. So, if we consider our car as point, we can construct the following diagram:

^ n

|

fs <________|

|

|

\/ Fg

Admittedly, this is not much of a diagram. Let's see if the next step helps us with it.

*Please note, the formatting might come out a bit wonky in the diagram above.

Step 2: Newton's 2nd Law

Now, we want to consider the forces involved. First, we will take those in the vertical orientation:

∑F_y = n - F_g = ma = 0

That these forces sum to zero tells us the forces in the vertical orientation are in equilibrium. We can then leverage this information to our advantage:

n - F_g = 0 => n = F_g = mg

Let us now consider the horizontal orientation:

∑F_y = fs = ma

There is only one force acting in the horizontal orientation, and that force is the force due to static friction. This force is responsible for the circular motion, and therefore the centripetal acceleration.

Step 3: Solve

fs = ma

=> fs = μ_sn

=> a = v²/r

μ_sn = m(v²/r) ---> μ_s(mg) = m(v²/r)

μ_sg = v²/r => v = (μ_sgr)^1/2

1. NOTE: I am making use of the exponent in place of a square root symbol

<=> [(0.57)(9.8 m*s^-2)(12m)]^1/2

v = 8.2 m*s^-1

Hope this helps!

Cheers