# Dynamics, Coefficient of Friction

1. Feb 20, 2010

### CursedAntagonis

1. The problem statement, all variables and given/known data
The coefficients of friction between the load and the flat-bed trailer shown are $$\mu$$s = 0.40 and $$\mu$$k = 0.30. Knowing that the speed of the rig is 45 mi/h, determine the shortest distance in which the rig can be brough to a stop if the load is not to shift.

The drawing shows a box sitting a top of a trailer bed with a distance of 10' between the box and the cabin.

2. Relevant equations

3. The attempt at a solution
I am not really sure how to begin this problem. I am thinking using the coefficient of friction I can find the acceleration of the box and use that to find the distance needed for the truck to stop, but I am not sure.

So far I have used the $$\mu$$k to find the acceleration of the box if it was to move, and was able to find the velocity of the box if it were to move.

2. Feb 20, 2010

### PhanthomJay

yes, but which coefficient would you use, and why?
But if the load is not to shift, it's not supposed to move relative to the flatbed.

3. Feb 20, 2010

### CursedAntagonis

I am guessing that would be static friction since the box is to stand still while the truck is to slow down and stop.

So if I to use the coefficient of static friction to find the acceleration, and use that acceleration to find the distance it takes for the truck to stop that would be the answer?

It is a bit frustrating that the book does not have the answer to this question, it has the answer for both odds and evens and yet somehow this number is omitted.

4. Feb 20, 2010

### PhanthomJay

yes...but watch your units
so watch your math...

5. Feb 20, 2010

### CursedAntagonis

Thanks. When I find the solution, would you mind double checking my work? I will post my work.

6. Feb 20, 2010

### PhanthomJay

Not at all. But it won't be 'til morning. maybe someone else will check it if it's urgent...but it's Sunday, and nothing is due on Sunday...

7. Feb 21, 2010

### CursedAntagonis

So here is what I have got so far:

F=($$\mu$$s)N
N=mg

F=($$\mu$$s)(m)(g)
ma=($$\mu$$s)(m)(g)

the mass cancels out and thus
a=($$\mu$$s)(g)
a=(0.40)(32.2ft/s^2)
a=12.88 ft/s^2

Converting the 45 mi/h gives us 66 ft/s, and using the acceleration found in the equation V^2=Vo^2+2a(X-Xo):

0=(66ft/s)^2+2(12.88 ft/s^2)(-X) gives us
X=169.1 feet.

This is the shortest distance for the truck to stop.

Does that sound about right? Thanks for going over my work.

Last edited: Feb 21, 2010
8. Feb 21, 2010

### PhanthomJay

Yes, good job; just round off your answer to 170 feet (2 significant figures).

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