A 850 kg car skidding on an icy highway at
32.5 km/h slides onto some bare pavement. If the
coefficient of friction between the tires and the bare
pavement is 0.200, what time(s) does it take for the
car to stop? HOW do i get the answer!!!!
Initial momentum = (Friction force) x Time
Solve for the time
The friction force is
m * g * Uk = 850*9.8*0.2 = 1666 N
Be sure to convert 32.5 km/hr to m/s when computing the momentum.
thats wtong tho, the answer is 4.60s i just don't know how to get that
My answer was NOT wrong. You just did not follow my directions in finishing it.
The speed is 9.03 m/s.
The momentum is m*v = 7674 kg m/s
The time is 7674/1666 = 4.60 s
It would be the same for any mass; m cancels out in the end.
To find the time it takes for the car to stop, you can use the concept of kinetic friction and the equation of motion.
First, let's convert the initial speed of the car from km/h to m/s since it is the SI unit. We know that 1 km/h is equal to 0.2778 m/s. So, converting 32.5 km/h to m/s:
Speed = 32.5 km/h * (0.2778 m/s)/(1 km/h) ≈ 9.0278 m/s
Next, we need to calculate the frictional force acting on the car. The frictional force can be determined using the equation:
Frictional force = Coefficient of friction * Normal force
The normal force is the force exerted by the ground on the car and is equal to the car's weight. The weight is the mass of the car multiplied by the acceleration due to gravity (9.8 m/s^2). Therefore:
Weight = mass * acceleration due to gravity
Weight = 850 kg * 9.8 m/s^2 ≈ 8330 N
Now, we can calculate the frictional force:
Frictional force = 0.200 * 8330 N ≈ 1666 N
The frictional force acts in the opposite direction of the car's motion, so it will decelerate the car until it comes to a stop. The equation of motion that relates the acceleration, initial velocity, final velocity, and time is:
Final velocity = Initial velocity + acceleration * time
Since the car comes to a stop, the final velocity is 0. The initial velocity is 9.0278 m/s, and the acceleration is determined by dividing the frictional force by the car's mass:
Acceleration = Frictional force / mass
Acceleration = 1666 N / 850 kg ≈ 1.957 m/s^2
Now, let's substitute these values into the equation of motion:
0 = 9.0278 m/s + (1.957 m/s^2) * time
Solving for the time:
9.0278 m/s = (1.957 m/s^2) * time
time = 9.0278 m/s / 1.957 m/s^2 ≈ 4.61 seconds
Therefore, it takes approximately 4.61 seconds for the car to stop sliding on the icy highway and come to a rest on the bare pavement.