A driver in a 1000kg car traveling at 2.0m.s slams on the brakes and skids to a stop. If the coefficient of friction between the tires and the horizontal road is 0.8 how long will the skid marks be.
First, we need to find the stopping distance, which is the distance the car travels before coming to a complete stop. We can use the equation:
stopping distance = (initial velocity)^2 / (2 * acceleration)
where the acceleration is the frictional force acting on the car, which is equal to the coefficient of friction multiplied by the gravitational acceleration (9.81 m/s^2).
Initial velocity = 2.0 m/s
Acceleration = 0.8 * 9.81 m/s^2 = 7.848 m/s^2
Stopping distance = (2.0 m/s)^2 / (2 * 7.848 m/s^2) = 0.255 m
Therefore, the length of the skid marks will be 0.255 meters.
To find the length of the skid marks, we can use the equations of motion. The key equation we need to use is:
v^2 = u^2 + 2as
where:
v = final velocity (in this case, it is 0 m/s as the car comes to a stop)
u = initial velocity (in this case, 2.0 m/s)
a = acceleration
s = distance (skid marks)
Rearranging the equation, we have:
s = (v^2 - u^2) / (2a)
First, let's calculate the acceleration (a) using the coefficient of friction (μ):
a = μ * g
where g is the acceleration due to gravity and is approximately 9.8 m/s^2.
a = 0.8 * 9.8 m/s^2
a = 7.84 m/s^2
Now, we can substitute the values into the equation to find the skid marks:
s = (0 - (2.0)^2) / (2 * 7.84)
s = -4.0 / 15.68
s = -0.2551 m
Since distance cannot be negative, we take the magnitude of the distance:
s = 0.2551 m
Therefore, the length of the skid marks is approximately 0.2551 meters.