A car is traveling at 20 meters per hour on the level road where the coefficient of kinetic friction between tires and road is 0.8.Find the minimum turning radius.

UM is a school subject I've never heard of. This looks more like physics, though.

To find the minimum turning radius of a car, we need to consider the maximum friction force that can be exerted by the tires on the road. In a turning scenario, the maximum friction force will act towards the center of the turn.

Step 1: Convert the speed of the car to meters per second.
Since the speed of the car is given in meters per hour, we need to convert it to meters per second by dividing by 3.6 (since there are 3.6 seconds in an hour):
20 meters per hour ÷ 3.6 = 5.56 meters per second (rounded to two decimal places).

Step 2: Calculate the maximum friction force.
The maximum friction force can be calculated using the equation:
maximum friction force = coefficient of kinetic friction × normal force.

In this scenario, we are assuming the car is on a level road, so the normal force is equal to the weight of the car, which can be calculated using the equation:
weight of the car = mass of the car × acceleration due to gravity.

Since the mass of the car is not given, we can assume a value for illustrative purposes. Let's assume the mass of the car is 1000 kg.

mass of the car = 1000 kg
acceleration due to gravity = 9.8 m/s²

weight of the car = 1000 kg × 9.8 m/s² = 9800 N

Now we can calculate the maximum friction force:
maximum friction force = 0.8 × 9800 N = 7840 N.

Step 3: Calculate the minimum turning radius.
The minimum turning radius can be determined using the equation:
minimum turning radius = speed of the car² / (maximum friction force × acceleration).

In this scenario, the acceleration of the car can be calculated using the equation:
acceleration = (speed of the car)² / (turning radius).

Let's assume the acceleration is equal to the gravitational acceleration for illustrative purposes:

acceleration = 9.8 m/s².

Now we can calculate the minimum turning radius:

minimum turning radius = (5.56 m/s)² / (7840 N × 9.8 m/s²)
≈ 0.037 meters or 37 millimeters (rounded to two decimal places).

Therefore, the minimum turning radius of the car is approximately 0.037 meters or 37 millimeters.

To find the minimum turning radius of the car, we need to consider the maximum friction force that can act on the car to keep it moving in a curved path. This maximum friction force occurs when the car is at the verge of sliding or just about to skid.

First, let's calculate the maximum friction force. This can be found using the formula:

F_max = coefficient of friction * normal force

The normal force is equal to the weight of the car, which can be determined using the formula:

Normal force = mass * gravity

Assuming the mass of the car is known, we can calculate the normal force. The value of gravity can be taken as 9.8 m/s².

Next, we need to determine the maximum centripetal force that can be provided by the friction force. This centripetal force is responsible for keeping the car moving in a curved path. It is given by the formula:

Centripetal force = mass * (v² / radius of curvature)

In this case, the velocity (v) of the car is given as 20 meters per hour. To convert this to meters per second, we divide it by 3.6.

Now, we can equate the maximum friction force to the maximum centripetal force:

F_max = mass * (v² / radius of curvature)

Solving this equation for the radius of curvature will give us the minimum turning radius of the car.

Let's plug in the given values and calculate the minimum turning radius step by step:

1. Find the weight of the car:
weight = mass * gravity

2. Calculate the maximum friction force:
F_max = coefficient of friction * normal force

3. Determine the maximum centripetal force using the formula:
Centripetal force = mass * (v² / radius of curvature)

4. Equate the maximum friction force to the maximum centripetal force and solve for the radius of curvature.

By following these steps and substituting the given values, we can find the minimum turning radius of the car.