High School

A 2,165 kg car moving at 14 m/s on dry pavement, skids to a stop

over 106 m. What is the force of friction between the car’s tires

and the pavement?

Answer :

The force of friction between the car's tires and the pavement can be calculated using the equation:

Force of friction = mass x acceleration

First, let's calculate the acceleration of the car. We can use the formula:

Final velocity^2 = Initial velocity^2 + 2 x acceleration x distance

Since the car comes to a stop, the final velocity is 0 m/s. The initial velocity is 14 m/s, and the distance is 106 m. Substituting these values into the equation, we get:

0^2 = 14^2 + 2 x acceleration x 106

Simplifying the equation, we have:

0 = 196 + 212 x acceleration

Rearranging the equation, we find:

Acceleration = -196 / (212)

Acceleration ≈ -0.925 m/s^2

Since the car is slowing down, the acceleration is negative.

Now, we can calculate the force of friction using the equation:

Force of friction = mass x acceleration

The mass of the car is given as 2,165 kg, and the acceleration is -0.925 m/s^2. Substituting these values into the equation, we get:

Force of friction = 2,165 kg x (-0.925 m/s^2)

Force of friction ≈ -2,000.125 N

Since force is a vector quantity, the negative sign indicates that the force of friction acts in the opposite direction to the car's motion. However, in this context, we can consider the magnitude of the force, which is approximately 2,000.125 N.

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