A car skids to a stop at a traffic light, leaving behind a 8.25m skid mark as it comes to a rest. Assuming that the car is travelling at 14.5m/s and only the friction from the tires on the roadway stop the vehicle. Find the coefficient of friction
vf^2=vi^2+2ad=vi^2-2 (mu*mg)/m * ad
mu* g=vi^2/2d
solve for mu
To find the coefficient of friction, we can use the equation:
μ = a / g
where:
μ is the coefficient of friction,
a is the acceleration of the car, and
g is the acceleration due to gravity (approximately 9.8 m/s^2).
First, let's find the acceleration of the car by using the equation of motion:
v^2 = u^2 + 2as
where:
v is the final velocity (which is 0, as the car comes to a stop),
u is the initial velocity (14.5 m/s), and
s is the distance (8.25 m).
Rearranging the equation, we have:
0 = (14.5 m/s)^2 + 2a(8.25 m)
Simplifying:
210.25 m^2/s^2 = 16.5a
Dividing both sides of the equation by 16.5 m, we get:
a = 210.25 m^2/s^2 / 16.5 m
a = 12.74 m/s^2
Now we can substitute the value of 'a' in the equation for the coefficient of friction:
μ = a / g
μ = 12.74 m/s^2 / 9.8 m/s^2
μ ≈ 1.30
Therefore, the coefficient of friction between the tires and the roadway is approximately 1.30.