# Force Dynamics and Static Friction

## Homework Statement

A small box is resting on a larger box, which in turn sits on a table. When a horizontal force is applied to the larger box, both boxes accelerate together. The small box does not slip on the larger box.

a)Draw a free body diagram of the small box as it accelerates.
b)What force causes the small box to accelerate horizontally?
c) If the acceleration of the pair of boxes has a magnitude of 2.5 m/s^2, determine the smallest coefficient of friction between the boxes that will prevent slippage.

## Homework Equations

F=ma
F=mg
F(normal)=-mg
F(staticfriction)=(coefficientofstatic)(Fnormal)
F(staticfriction)=(coefficientofstatic)(-mg)

## The Attempt at a Solution

a) http://img233.imageshack.us/img233/109/fstaticti4.jpg [Broken]

b) The force applied on the large box

c)

Find when Fs is equal to Fa
So let Fs=Fa

Fs=(coefficientofstatic)(-mg)
Fa=ma

ma=(coefficientofstatic)(-mg)
a=(coefficientofstatic)(-g)
2.5m/s^2=(coefficientofstatic)(9.8m/s^2)
(coefficientofstatic)=2.5/9.8
(coefficientofstatic)=0.26

Therefore the coefficient of static friction must be 0.26

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Edit: I know that my answer for c is right but I am not so sure about the FBD. Would Ffs be equal to Fa in terms of magnitude? Would it be greater? Would it be less?

I think Ffs is equal to Fa because the small box itself is not actually moving. This is because the Ffs equals the Fa so that the small box can remain on top of the large box. If Fa was greater than Ffs, then the small box would fall off the large box since the resulting net force would be less than the large box (not sure about this statement).

Another question. Can force of friction be greater than the applied force?

alphysicist
Homework Helper
HI jw11,

I don't believe your answer to a and b are correct. For the free body diagram, you only draw in the forces that are actually acting on that body. It looks to me like you have one too many forces.

For b, the issue is also related to why your force diagram is not quite right. The question asks for the force causing the small box to accelerate horizontally, so it has to be a force that is actually acting on the small box. Your answer of "the force applied on the large box" isn't true because that force is not directly acting on the small box at all.

(You can certainly argue that the force applied on the large box has an effect on the small box. But in a force diagram, and when deciding what's making an object accelerate, you want to find those forces that are directly acting on the object.)

First let's say that the whole system is accelerating to the right.

Wait!

So maybe the force of static friction for the small box is causing it to accelerate to the right? Since it is opposing the inertial effects of the acceleration?

So would this fbd be correct?

http://img401.imageshack.us/img401/61/fstaticgu2.jpg [Broken]

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alphysicist
Homework Helper
First let's say that the whole system is accelerating to the right.

Wait!

So maybe the force of static friction for the small box is causing it to accelerate to the right? Since it is opposing the inertial effects of the acceleration?
Yes, the force of static friction is causing the small box to accelerate. (I'm not sure what you are referring to by the inertial effects of the acceleration.)

So would this fbd be correct?

http://img401.imageshack.us/img401/61/fstaticgu2.jpg [Broken]
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Not if you know the acceleration is to the right. Since the static force is causing the acceleration, it has to point in the same direction.

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