An old car is traveling down a long, straight, dry road at 25.0 m/s when the driver slams on the brakes, locking the wheels. The car comes to a complete stop after sliding 305 m in a straight line. If the car has a mass of 755 kg, what is the coefficient of kinetic friction between the tires and the road?
vi= 25 m/s
vf=0
x=305
I used vf^2= vi^2+2ax
0=(25^2)+2a(305)
0=625+ 610 a
a=-625/610
a= -1.025 m/(s^2)
mu(k)= a/g
mu(k)= -1.025/9.8
mu(k)= -.1045
I put this in as an answer and it said I was wrong. Can anyone tell me what I'm doing wrong? Or possibly a different way to go about the problem? Help is much appreciated!
You did everything right. You just need to change the sign at the end. so your answer should be +0.1045
Hope this helps :)
Your approach is correct, but there seems to be a sign error in your final calculation. Let's go through the solution step-by-step correctly:
Given:
Initial velocity, vi = 25.0 m/s
Final velocity, vf = 0 m/s
Distance traveled, x = 305 m
Mass of the car, m = 755 kg
Acceleration, a = ?
First, calculate the acceleration using the kinematic equation:
vf^2 = vi^2 + 2ax
Rearrange the equation to solve for acceleration (a):
2ax = vf^2 - vi^2
Substitute the given values:
2a(305) = 0^2 - 25.0^2
610a = -625
a = -625/610 ≈ -1.0230 m/s^2
The negative sign indicates that the acceleration is in the opposite direction of the initial velocity.
Next, calculate the coefficient of kinetic friction (μk) using the equation:
μk = a/g
where g is the acceleration due to gravity (9.8 m/s^2):
μk = -1.0230/9.8
μk ≈ -0.1045
The negative sign indicates that the direction of the friction force is opposite to the motion of the car.
So, the coefficient of kinetic friction between the tires and the road is approximately -0.1045. The negative sign suggests that there might be an error in calculation or a discrepancy in the problem statement. The coefficient of friction is generally considered to be positive.
Your calculation of the acceleration seems correct, but there is a small error in your calculation of the coefficient of kinetic friction. The correct calculation should be:
μ(k) = a/g = -1.025 m/(s^2) / 9.8 m/(s^2) ≈ -0.1046
Notice that I used -1.025 as the numerator in the division, not the rounded value of -1.026. The more accurate value of μ(k) is approximately -0.1046, which is the correct answer.
Make sure to use the exact value for a/g when calculating the coefficient of kinetic friction to achieve the highest level of accuracy.