# Forces with friction problem, two block on each other

#### Asphyxiated

1. The problem statement, all variables and given/known data

The original problem with statement is http://images3a.snapfish.com/232323232fp733;9>nu=52::>379>256>WSNRCG=335:728:;4347nu0mrj".

2. Relevant equations

Newton's Laws 1-3

3. The attempt at a solution

Note that the table is frictionless, the only friction is between the two boxes

So first:

$$\mu = .45$$

and the T on M1 is

$$T_{m_{1}}=F_{a}$$

and T on M2 is

$$T_{m_{2}}=-F_{a}$$

and

$$F_{n_{1}}=m_{1}g$$

$$F_{n_{2}}=m_{1}g+m_{2}g$$

So the friction force on M1 from M2 should be:

$$F_{ \mu_{1}} = \mu F_{n_{1}}$$

and the friction on M2 from M1 should be:

$$F_{ \mu_{2}}=\mu F_{n_{1}}$$

So i am kind of confused as to how I should use the T forces... here is what I did:

$$F_{net_{x}} = F_{a}+F_{\mu_{1}-T-F_{\mu_{2}}=0$$

$$F_{net_{y}}=F_{n_{1}}+F_{n_{2}}-m_{1}g-m_{2}g=0$$

is that right? I am not sure how to set up T because for m1 t is opposite the friction force and for m2 T is opposite the Fa force... should I set up a relationship that way to do this correctly?

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#### cepheid

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Science Advisor
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It seems to me that Fa ≠ T. After all, the horizontal forces on block 1 must balance, and according to the FBD that YOU drew for it (which looks correct), there are three such forces. Fa is to the right and BOTH T and the frictional force from block 2 are pointing to the left.

#### ajith.mk91

Yes,horizontal forces on block 1 should balance.If T is the tension in the string acting to pull the body to left then the frictional force between the bodies will act to the right to counter the tension.So T=f.
Now coming to the second block it has got F acting to the right and tension acting to the left.Since the frictional force is acting to right on block 1,it acts to left on block 2.To sum up the whole thing,your F acts to counter both T(=f) and f.So F equals 2f.Any way i am not sure of this. #### cepheid

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Gold Member
Yes,horizontal forces on block 1 should balance.If T is the tension in the string acting to pull the body to left then the frictional force between the bodies will act to the right to counter the tension.So T=f.
Yeah, but you're forgetting the applied force (also points to the right). EDIT: and you also haven't specified which frictional force you're referring to. The one that acts on block 1 points to the left, in the SAME direction as the tension. I explicitly said that there were THREE horizontal forces acting on block 1 in my previous post. Let's let the OP take stock of things...

#### ajith.mk91

Block 1 is the top one and block 2 is bottom one right?Force acting on the bottom block cannot directly act on the top one.The only way for it is to use friction.Now if the friction tries to stop the relative motion it should act to right on the top block since it tends to move to left.

#### ashishsinghal

do not write vertical and horizontal equations for whole system that is unnecessary
just balance vertical and horizontal forces on each block.
Remember the tension in the string is uniform

#### cepheid

Staff Emeritus
Science Advisor
Gold Member
Block 1 is the top one and block 2 is bottom one right?Force acting on the bottom block cannot directly act on the top one.The only way for it is to use friction.Now if the friction tries to stop the relative motion it should act to right on the top block since it tends to move to left.
Hey -- I was referring to the bottom block as "block 1" without double-checking the labeling on the picture. Sorry.

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