the driver of a 1200kg car travelling 45km/h west on a slippery road applies the brakes, skidding to a stop in 35m. Determine the coefficient of friction between the road and the car tires
0.25
To determine the coefficient of friction between the road and the car tires, we can use the equation of motion for uniform deceleration:
v^2 = u^2 + 2as
where
v = final velocity (0 m/s, since the car comes to a stop)
u = initial velocity (45 km/h converted to m/s)
a = acceleration (unknown, but related to the coefficient of friction)
s = displacement (35 m)
First, let's convert the initial velocity from km/h to m/s:
u = 45 km/h × (1000 m/1 km) × (1 h/3600 s) = 12.5 m/s
Next, we can rearrange the equation of motion to solve for the acceleration:
a = (v^2 - u^2) / (2s)
a = (0 m/s)^2 - (12.5 m/s)^2 / (2 × 35 m)
Simplifying the equation, we have:
a = - (156.25 m^2/s^2 / 70 m)
a ≈ -2.232 m/s^2
The negative sign indicates that the acceleration is in the opposite direction to the car's initial motion.
The acceleration of the car is related to the coefficient of friction (μ) by the equation:
a = -μg
where
g = acceleration due to gravity (9.8 m/s^2)
So, we can solve for the coefficient of friction (μ):
μ = a / g
μ = -2.232 m/s^2 / 9.8 m/s^2
Simplifying the equation, we have:
μ ≈ -0.227
The negative sign indicates that the coefficient of friction is acting in the opposite direction to the car's initial motion, which means it opposes the car's motion. Since friction is always positive, we can take the absolute value:
μ ≈ 0.227
Therefore, the coefficient of friction between the road and the car tires is approximately 0.227.