Find the coefficient of friction between the car tires and the road.

[BlackCatXIII]

help needed! ><

Someone please help me with this question!
(at least show me how to do it~!)

A car slams on its brakes and skids to a halt from 65km/h in 2.67s. Find the coefficient of friction between the car tires and the road.

Thanks in advance~! ^^

 

[HallsofIvy]

You know the change in speed in a given time (65km/h in 2.67s) so you can find the acceleration. IF you knew the mass of the car, then you could calculate the friction force from F= ma.
Since you are asked for the "coefficient of friction" rather than the friction force itself, you don't need the mass: The friction force is F= k*weight= kmg.

That is, F= ma= kmg so k= a/g- the mass cancels out.

 

[M98Ranger]

To find the coefficient of friction between the car tires and the road, we can use the formula:
Coefficient of friction = (force of friction) / (normal force)

First, we need to calculate the force of friction. We can use Newton's second law, which states that force = mass x acceleration. In this case, the mass of the car is not given, but we can use the fact that the car is able to come to a stop from 65km/h in 2.67s to find its acceleration. We can use the formula:
Acceleration = (final velocity - initial velocity) / time
= (0 - 65km/h) / 2.67s
= -24.34 m/s^2 (note the negative sign indicates deceleration)

Next, we need to find the normal force, which is the force exerted by the road on the car. This is equal to the weight of the car, which can be calculated using the formula:
Weight = mass x gravity
= mass x 9.8 m/s^2

Now, we can plug in our values into the formula for coefficient of friction:
Coefficient of friction = (force of friction) / (normal force)
= (mass x acceleration) / (mass x 9.8 m/s^2)
= acceleration / 9.8 m/s^2
= -24.34 m/s^2 / 9.8 m/s^2
= -2.48

The negative sign indicates that the force of friction is in the opposite direction of motion (deceleration). The coefficient of friction between the car tires and the road is 2.48. This is a relatively high value, indicating that the road likely has a rough surface and/or the tires have good traction.