Calculate Coefficient of Sliding Friction for Icy Road | 11m/s Car Braking

[halo9909]

Homework Statement

You are driving a 2410.0-kg car at a constant speed of 11.0 m/s along an icy, but straight and level road. While approaching a traffic light, it turns red. You slam on the brakes, Your wheels lock, the tires begin skidding, and the car slides to a halt in a distance of 29.0 m. What is the coefficient of sliding friction (µ) between your tires and the icy roadbed?

m=2410kg
vi=11m/s
vf=0m/s
d=29meter

Homework Equations

µ=F/N?

The Attempt at a Solution

i first did 2410kg * 9.8 =23618N so that would be the force normal, from there I dnt know how to get the force of friction

 

[alphysicist]

Hi halo9909,

Homework Statement

You are driving a 2410.0-kg car at a constant speed of 11.0 m/s along an icy, but straight and level road. While approaching a traffic light, it turns red. You slam on the brakes, Your wheels lock, the tires begin skidding, and the car slides to a halt in a distance of 29.0 m. What is the coefficient of sliding friction (µ) between your tires and the icy roadbed?

m=2410kg
vi=11m/s
vf=0m/s
d=29meter

Homework Equations

µ=F/N?

The Attempt at a Solution

i first did 2410kg * 9.8 =23618N so that would be the force normal, from there I dnt know how to get the force of friction

They give you the initial and final velocity, and the displacement. What kinematic quantity can you find using those values that would be helpful in finding a force?

 

[baba89]

.

To calculate the coefficient of sliding friction, we need to use the equation µ=F/N, where F is the force of friction and N is the normal force.

First, we need to calculate the force of friction. We can use the equation F=ma, where m is the mass of the car and a is the acceleration. Since the car is coming to a stop, the final velocity is 0 m/s, so the acceleration is vf^2=vi^2 + 2ad. Plugging in the values, we get a=-13.89 m/s^2.

Now, we can plug this value into the equation F=ma, along with the mass of the car, to get F=2410kg * (-13.89 m/s^2) = -33406.9 N. Note that the negative sign indicates that the force of friction is acting in the opposite direction of the car's motion.

Next, we can calculate the normal force, N, using the equation N=mg, where m is the mass of the car and g is the acceleration due to gravity (9.8 m/s^2). Plugging in the values, we get N=2410kg * 9.8 m/s^2 = 23618 N.

Finally, we can use the equation µ=F/N to calculate the coefficient of sliding friction. Plugging in the values, we get µ=(-33406.9 N)/(23618 N) = -1.41.

Since the coefficient of friction cannot be negative, we need to take the absolute value of this value, giving us a coefficient of sliding friction of 1.41. This means that the force of friction between the tires and the icy roadbed is 1.41 times the normal force.