Force Dynamics and Static Friction

In summary: You have a horizontal force to the right in your diagram, but no vertical force to balance it.)In summary, a small box resting on a larger box on a table will accelerate together when a horizontal force is applied to the larger box. The small box does not slip due to the force of static friction. To determine the smallest coefficient of friction between the boxes that will prevent slippage, the equations F=ma and F=mg can be used to find the coefficient of static friction which is equal to the acceleration of the pair of boxes divided by the acceleration due to gravity. When drawing a free body diagram for the small box, only the forces directly acting on the box should be included, and the force causing the small box
  • #1
jwj11
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0

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

My friend and I got completely different final answers so I'm wondering if I'm wrong or right. Please help!
 
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  • #2
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?
 
  • #3
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.)
 
  • #4
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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  • #5
jwj11 said:
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]
[/URL]

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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1. What is force dynamics?

Force dynamics is the study of forces and their effects on objects, including how forces cause objects to move or accelerate.

2. What is static friction?

Static friction is the force that prevents two stationary surfaces from sliding past each other when a force is applied to one of them.

3. How is static friction different from kinetic friction?

Static friction occurs when two surfaces are not moving relative to each other, while kinetic friction occurs when the surfaces are in motion. Static friction is typically greater than kinetic friction.

4. How is static friction calculated?

The maximum static friction force can be calculated by multiplying the coefficient of static friction (a constant value determined by the materials in contact) by the normal force (the perpendicular force exerted by one surface on the other).

5. How does the angle of a surface affect static friction?

The angle of a surface does not affect static friction as long as the object is not moving. However, if the angle of the surface is increased beyond a certain point, the object may begin to slide due to a decrease in the normal force.

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