Kinetic Friction Problem (Truck Braking)

[Spartan Erik]

Homework Statement

"A bread truck is traveling at 18 m/s on a horizontal road. The brakes are applied and the truck skids to a stop in 3.6s. The coefficient of kinetic friction between the tires and the road is:"

Homework Equations

Kinetic Friction = coefficient of kinetic friction x normal force

The Attempt at a Solution

I'm not sure how you can manipulate velocity and time to get kinetic friction..

 

[Doc Al]

Hint: What's the truck's acceleration?

 

[Spartan Erik]

Well if brakes are being applied, the truck is decelerating until velocity is 0

 

[Doc Al]

Find the deceleration.

 

[Spartan Erik]

Well acceleration is in units of m/s^2, so 18 m/s / 3.6s = 5 m/s^2 if I'm not mistaken

 

[Doc Al]

Good! Now make use of it. Hint: What does Newton's 2nd law tell you?

 

[Spartan Erik]

Well F = MA, but I can't solve for force or mass.. unless of course there's something big that I'm missing..

 

[Doc Al]

Make use of what you had in your first post. The "F" is the kinetic friction force.

 

[Spartan Erik]

Alright so far I've established that the acceleration is 5 m/s^2, the velocity was 18 m/s, and that the time to stop was 3.6s.

Since Kinetic Friction Force = coefficient of kinetic friction x normal force

I can break the normal force into mass and acceleration, giving the equation
Kinetic Friction Force = coefficient of kinetic friction x mass x acceleration (5 m/s^2)

But I still don't see what unknowns I can solve for..

 

[Doc Al]

The normal force does not equal "mass X acceleration". To find the normal force add up the vertical components of all forces and set it equal to zero.

 

[Spartan Erik]

Oh man I feel like beating myself over the head with a stick right about now.. quite a eureka moment.

Alright so: kinetic frictional force = coefficient of k x normal force
coefficient of k = kinetic frictional force / normal force

Based off that, mass is irrelevant, so it is ultimately acceleration / gravity

So the coefficient is 0.51.. man.. thanks for spurring the ole noggin!

 

[Doc Al]

Sweet.