Braking distance of a car(forces and friction)

[chaotiiic]

Homework Statement

the driver of a 1500 kg car traveling at 12.5 m/s slams on the brakes, locking the wheels, and bringing the car to a stop. If the coefficient of friction is .735, what is the braking distance of the car?

Homework Equations

W = K_f - K_i
friction force

The Attempt at a Solution

K_f = (1/2)(1500)(12.5)^2 = 117187.5
K_i = 0
W = 117187.5

F_n = 14700
friction force = 14700 * .735 = 10804.5

distance = 117187.5/10804.5 = 10.84m
correct?

 

[ehild]

Hi, chaotiiic,

The result is correct.

ehild

 

[chaotiiic]

Hi, chaotiiic,

The result is correct.

ehild

i can't find this in my book but why does normal force need to be multiplied with friction coefficient in order to get friction force? does friction force have a unit?

and why does Work need to be divided by friction force in order to get the distance? is there a name for this equation?

 

[ehild]

The force of friction is proportional with the force that presses two surfaces together. This force is normal to the surface of touch, parallel with it and opposes any relative motion of the objects. It is a force, so the unit is Newton (N) There is kinetic friction, when the surfaces slide on each other, and static friction which prevents any relative motion. The magnitude of kinetic friction is F_K=μ_KN, the static friction is the force needed to prevent relative motion, and F_S≤μ_SN.

Work is defined as the scalar product of the force vector F and displacement vector d. If the force and displacement are parallel, W=Fd. The work is positive when the force and displacement have the same direction, and negative when the force points in opposite direction as the motion.

You certainly find these in your textbook...


ehild

 

[asteriatic]

Your solution is correct. The braking distance of the car in this scenario would be 10.84 meters. This calculation takes into account the kinetic energy of the car and the friction force acting on it to bring it to a stop. It is important to consider these forces when driving and to maintain a safe distance from other vehicles to allow for proper braking distance. Additionally, this calculation can be used to compare different scenarios, such as changing the speed or weight of the car, to determine the impact on the braking distance.