A car has a mass of 1200 kg and is traveling perfectly horizontally on a road at 20 m/s. The car then applies the brakes and skids to a stop. If the coefficient of friction between the tires and road is .70, how much distance was required to get the car to stop?
F = m a = -mu m g (neg because braking)
so
a = - mu g = 0.70 * 9.81 m/s^2 = -6.87m/s^2
now the kinematics
v = Vi - 6.87 t = 20 - 6.87 t = 0 at stop
so t = 20/6.87 = 2.91 seconds to stop
distance = average speed * time
= 10 m/s * 2.91 s = 29.1 meters
notice, mass does not matter, on both sides of equation
in my world g = 9.81 m/s^2
Yours may be different.
thanks Damon
To find out the distance required to stop the car, we need to calculate the deceleration first.
The formula for deceleration is:
deceleration = acceleration = frictional force / mass
The frictional force can be calculated using the formula:
frictional force = coefficient of friction * normal force
The normal force can be calculated using the formula:
normal force = mass * gravitational acceleration
Since the car is moving horizontally on a road, the normal force is equal to the weight of the car, which can be calculated as:
weight = mass * gravitational acceleration
Given:
mass = 1200 kg
gravitational acceleration = 9.8 m/s^2
coefficient of friction = 0.70
Step 1: Calculate the weight
weight = mass * gravitational acceleration
weight = 1200 kg * 9.8 m/s^2
Step 2: Calculate the normal force
normal force = weight
normal force = 1200 kg * 9.8 m/s^2
Step 3: Calculate the frictional force
frictional force = coefficient of friction * normal force
frictional force = 0.70 * (1200 kg * 9.8 m/s^2)
Step 4: Calculate the deceleration
deceleration = frictional force / mass
deceleration = (0.70 * (1200 kg * 9.8 m/s^2)) / 1200 kg
Now we can calculate the distance required to stop the car using the formula:
distance = (initial velocity^2) / (2 * deceleration)
Given:
initial velocity = 20 m/s
Step 5: Calculate the distance
distance = (20 m/s)^2 / (2 * deceleration)
To find the distance, let's substitute the value of deceleration from step 4 into the equation and solve it.
To find the distance required for the car to stop, we need to calculate the deceleration of the car using the given information and then use the kinematic equation relating distance, initial velocity, final velocity, and acceleration.
1. Calculate the deceleration:
The deceleration of the car can be determined using the coefficient of friction between the tires and the road. The formula for deceleration is:
deceleration = coefficient of friction * acceleration due to gravity (g)
The acceleration due to gravity is approximately 9.8 m/s^2.
So, deceleration = 0.70 * 9.8 m/s^2 = 6.86 m/s^2
2. Use the kinematic equation:
The kinematic equation relating distance (d), initial velocity (u), final velocity (v), and acceleration (a) is:
v^2 = u^2 + 2ad
In this case, the initial velocity (u) is 20 m/s, the final velocity (v) is 0 m/s (as the car stops), and the acceleration (a) is -6.86 m/s^2 (negative because it's decelerating).
Plugging in the values, the equation becomes:
0^2 = 20^2 + 2 * (-6.86) * d
3. Solve for distance (d):
0 = 400 - 13.72d
Move -400 to the other side:
13.72d = 400
Divide both sides by 13.72:
d = 400 / 13.72 ≈ 29.16 meters
Therefore, the car required approximately 29.16 meters to come to a stop.