What was the car's acceleration while stopping?
How much work was done by friction to stop the car?
What is the coefficient of kinetic friction between tires and road?
bobpursley
answered
work=KE of car initially
or work=force*distance=ma*distance
force=mu(mg)=ma
mu=a/g
Explain Bot
answered
v^2 = u^2 + 2as
Where:
v = final velocity = 0 m/s (since the car comes to a halt)
u = initial velocity = 20 m/s (given)
a = acceleration (to be determined)
s = displacement = 64 m (given)
Rearranging the equation, we have:
a = (v^2 - u^2) / (2s)
Substituting the given values, we get:
a = (0^2 - 20^2) / (2 * 64)
a = (-400) / 128
a = -3.125 m/s^2
Therefore, the car's acceleration while stopping is -3.125 m/s^2 (negative sign indicates deceleration).
To calculate the work done by friction to stop the car, we can use the work-energy principle. The work done is equal to the change in kinetic energy of the car:
Work = ΔKE
Work = 1/2 * m * (v^2 - u^2)
Substituting the given values, we have:
Work = 1/2 * 1300 kg * (0^2 - 20^2)
Work = 1/2 * 1300 kg * (-400)
Work = -1/2 * 1300 kg * 400
Work = -260,000 joules
Therefore, the work done by friction to stop the car is -260,000 joules (negative sign indicates work against the direction of motion).
To find the coefficient of kinetic friction between the tires and the road, we can use the equation:
Force of friction = coefficient of friction * normal force
Since the car is skidding, the frictional force opposes the motion. It can be calculated using the equation:
Force of friction = mass * acceleration
Substituting the given values, we have:
mass * acceleration = coefficient of friction * normal force
Since the car is stopping, the acceleration is the deceleration we previously calculated: -3.125 m/s^2.
Therefore:
1300 kg * (-3.125 m/s^2) = coefficient of friction * normal force
Simplifying, we have:
coefficient of friction = (1300 kg * -3.125 m/s^2) / normal force
Unfortunately, we don't have the normal force information, so we cannot determine the coefficient of kinetic friction between the tires and the road without additional data.
