A car has to move on a level turn of radius 45 m. If the coefficient of static friction between the tire and the road is `mu_s=2.0,` find the maximum speed the car can take without skidding.

Explanation

To find the maximum speed at which a car can take a turn without skidding, we can use the relationship between the forces acting on the car, the radius of the turn, and the coefficient of static friction. Here’s a step-by-step solution:

### Step 1: Understand the Forces Acting on the Car
When a car is moving in a circular path, the following forces are acting on it:
- The gravitational force (weight) acting downwards: \( F_g = mg \)
- The normal force (\( N \)) acting upwards
- The frictional force (\( F_f \)) acting towards the center of the circle, which provides the necessary centripetal force to keep the car moving in a circular path.

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