You are driving a 2530.0-kg car at a constant speed of 14.0 m/s along a wet, but straight, level road. As you approach an intersection, the traffic light turns red. You slam on the brakes. The car's wheels lock, the tires begin skidding, and the car slides to a halt in a distance of 23.6 m. What is the coefficient of kinetic friction between your tires and the wet road?
KE=workbraking
1/2 m v^2=mu*mg*distance
solve for mu.
F = m a = rate of change of momentum
first work on a
average speed during braking = (14+0)/2
= 7 m/s
so
time to stop = 23.6 m / 7 m/s = 3.37 seconds
change of momentum = -2530*14 =-35420
so
F = -35420 / 3.37 = -10510 Newtons
mu m g = 10510
mu = 10510 / (2530*9.81)
= .423
good tires for wet road.
To find the coefficient of kinetic friction between the tires and the wet road, we can use the equations of motion and the concept of friction.
The first step is to calculate the deceleration (negative acceleration) of the car. We can use the equation:
v^2 = u^2 + 2as
where "v" is the final velocity (0 m/s in this case, as the car comes to a halt), "u" is the initial velocity (14.0 m/s), "a" is the acceleration, and "s" is the displacement (23.6 m).
Rearranging the equation to solve for "a," we have:
a = (v^2 - u^2) / (2s)
Plugging in the values, we get:
a = (0 - 14.0^2) / (2 * 23.6)
Calculating this, the acceleration a is approximately -4.69 m/s^2.
Now that we know the acceleration, we can use the following equation to calculate the force of friction:
F_friction = m * a
where "F_friction" is the force of friction, "m" is the mass of the car (2530.0 kg), and "a" is the acceleration (-4.69 m/s^2).
Plugging in the values, we have:
F_friction = 2530.0 kg * (-4.69 m/s^2)
Calculating this, the force of friction F_friction is approximately -11,853 N. Since friction always opposes motion, it has a negative sign.
Next, we need to calculate the normal force (N) exerted by the car on the wet road. The normal force is equal to the weight of the car. So, we can calculate the normal force using the equation:
N = m * g
where "m" is the mass of the car (2530.0 kg), and "g" is the acceleration due to gravity (approximately 9.8 m/s^2).
Plugging in the values, we have:
N = 2530.0 kg * 9.8 m/s^2
Calculating this, the normal force N is approximately 24,854 N.
Finally, we can calculate the coefficient of kinetic friction (μ_k) using the equation:
μ_k = |F_friction| / N
where |F_friction| is the magnitude of the force of friction, and N is the normal force.
Plugging in the values, we have:
μ_k = |-11,853| / 24,854
Calculating this, the coefficient of kinetic friction μ_k is approximately 0.477.
Therefore, the coefficient of kinetic friction between the tires and the wet road is approximately 0.477.