A driver of an 1800kg/hr including passengers travelling at 25m/s slams the brake locking the wheels on the dry pavement. The coefficient of kinetic friction between the rubber and the dry concrete is typically 0.7.calculate how far the car will travel before stopping.
answer is 38.6 but I can figure out how
how do I get frictional force and is the normal reaction mg or 0
1800 kg * 9.81 = 17,658 Newtons weight
friction force = .7 * 17,658 = 12,360 Newtons retarding force
acceleration = - force/mass = -12360/1800 = - 6.87 m/s^2
note - we could have said .7 g = 6.87
v = 25 - 6.87 t
v=0 when t = 3.64 seconds
x = Xi + Vi t - (6.87/2) t^2
= 0 + 25*3.64 - 3.44 *3.64^2
= 91 - 45.6 = 45.5 meters
BUT more easily the average speed during stop is 25/2 = 12.5 m/s
12.5 * 3.64 = 45.5 meters
By the way, no way 38.6 meters (on earth anyway).
M*g = 1800 * 9.8 = 17,640 N. = Wt. of vehicle = Normal force, Fn.
u*Fn = 0.7 * 17,640 = 12,348 N. = Force of kinetic friction.
-uFn = M * a.
-12,348 = 1800 * a.
a = -686 m/s^2.
V^2 = Vo^2 + 2a*d = 0.
25^2 + (-13.72)d = 0,
d = 45.6 m.
To calculate the distance the car will travel before stopping, we can use the principles of Newton's laws of motion and the equations of motion.
First, let's determine the deceleration (negative acceleration) of the car when the brakes are locked. The force of friction acting on the car can be calculated using the equation:
Friction force = coefficient of friction * normal force
The normal force acting on the car can be calculated as:
Normal force = mass * gravity
Since the car is on a horizontal surface, the normal force is equal to the weight of the car, which is:
Normal force = mass * gravity
Next, we need to calculate the friction force. The equation is:
Friction force = mass * acceleration
Since the car is decelerating (negative acceleration), the friction force will be in the opposite direction of motion.
Using the formula for friction force, we can set it equal to the mass times the acceleration (deceleration):
Coefficient of friction * Normal force = mass * acceleration
Rearranging the equation gives:
Acceleration = (Coefficient of friction * Normal force) / mass
Now let's substitute the values we know:
Mass of the car (including passengers) = 1800 kg
Coefficient of friction between rubber and dry concrete = 0.7
Acceleration = ?
Gravity = 9.8 m/s^2 (acceleration due to gravity)
Finding the normal force:
Normal force = mass * gravity
Normal force = 1800 kg * 9.8 m/s^2
Now we can substitute the normal force and mass into the equation for acceleration:
Acceleration = (0.7 * Normal force) / mass
Finally, we can use the equation of motion to find the distance travelled:
Distance = (Initial velocity^2) / (2 * acceleration)
Substituting the values:
Initial velocity = 25 m/s
Acceleration = calculated from the previous step
The calculated distance will give us the answer to how far the car will travel before stopping.