Derek the drunk driver drives his car off the road, onto a gravel strip next to the road. Derek does not have anti-lock brakes, so his wheels lock when he enters the gravel area, and the car slides to a halt. Derek's car is traveling at a speed of 20m/s when it enters the gravel strip, and comes to a stop after sliding through the gravel for 40m. The mass of the car (including Derek) is 700kg.
What is the amount of work done on Derek's car by the gravel strip?
If the gravel strip is completely flat, what is the coefficient of kinetic friction between the gravel and Derek's car's tires?
Well,
vf^2=Vi^2+2ad and from that solve for acceleration, a.
but a= forcefriction/mass= mu*g
if a= mu*g, you can solve for mu.
work done: mu*mg*distance
To find the amount of work done on Derek's car by the gravel strip, we can use the work-energy principle. The work done on an object is equal to the change in its kinetic energy. The kinetic energy of an object is given by the equation:
KE = (1/2) * mass * velocity^2
Initially, the car has a kinetic energy of KE1 = (1/2) * 700kg * (20m/s)^2 = 140,000 J.
After sliding through the gravel for 40m, the car comes to a stop. At this point, it has a kinetic energy of zero (KE2 = 0 J).
Therefore, the change in kinetic energy is:
ΔKE = KE2 - KE1 = 0 J - 140,000 J = -140,000 J.
Since the car comes to a stop, the work done on it by the gravel strip is equal to the change in kinetic energy. Therefore, the amount of work done on the car is -140,000 J.
Now let's determine the coefficient of kinetic friction between the gravel and Derek's car's tires. The work done by friction is given by the equation:
Work = force friction * distance
Since the car comes to a stop, the work done by friction is equal to the work done on the car by the gravel strip, which is -140,000 J.
The force of friction can be calculated using the equation:
force friction = m * g * μ
Where m is the mass of the car, g is the acceleration due to gravity (approximately 9.8 m/s^2), and μ is the coefficient of kinetic friction.
Substituting the known values:
-140,000 J = 700kg * 9.8 m/s^2 * μ * 40m
Solving for μ:
μ = (-140,000 J) / (700kg * 9.8 m/s^2 * 40m)
μ ≈ -0.179
Since the coefficient of kinetic friction cannot be negative, we assume there was an error in the calculations. It is not possible to determine the coefficient of kinetic friction between the gravel and Derek's car's tires with the given information.