# Friction On 2 Blocks + Angled Pull

1. Aug 16, 2013

### sandman203

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

Hi all, greetings from aus! having mad trouble with this question:

so i've figured out that the friction limit for block B is 11.35N when it is stationary. Putting my co-ords parrallel to the 15 degree incline means the force due to gravity in the x direction is 5.0728N.. so effectively ill need to make up the 6.2772N so the block B will slide down block A.

Now i've toyed with the idea of makign F Large enough to lift the whole body to an angle where the force due to gravity will overcome friction. However there are no dimensions on the block so i can't make an equation for work needed. SO block A will remain horizontal and slide across. I just don't understand how force F will be able to make block B fall down if it doesn't angle up? It;s probably got something to do with Fy but i just can't see it. Any help would be greatly appreciated. Have been racking my brain for like 5 hrs obver this.

2. Aug 16, 2013

### TSny

Hello, sandman203. Welcome to PF!

If F causes the system to accelerate, then the normal force between A and B will be reduced and so the friction force between A and B will be reduced. If the acceleration is enough, B will begin to slip.

The best approach to these types of problems is the standard recipe of drawing free-body diagrams and applying Newton's laws.

See what you can deduce from Newton's 2nd law applied to a free-body diagram of block B when block B is just on the verge of slipping.

3. Aug 16, 2013

### verty

Hint: what is happening at the interface between B and A? What is making B accelerate?

4. Aug 16, 2013

### haruspex

More Fx than Fy. Imagine pulling the wedge left with a sharp yank. What do you think would happen to the block?

5. Aug 16, 2013

### sandman203

i imagine the block would slide right off if the acceleration is high enough.. I just don;t know how to set that up mathematically. Do i want to break down F in terms of the co-ord system i used on block B, so fx is parrallel to the 15 degree incline? then i will will a force going up towards block B (reducing the normal force?). I dont see how fx acts on block B, does it do anything at all? obviously up until it surpasses the friction limit. am i on the right track here?

6. Aug 16, 2013

### TSny

How many forces act on block B? Can you describe them?

7. Aug 16, 2013

### sandman203

We have gravity going straight down. This is broken into 2 forces Fxb (Parrallel to the incline) and Fxy (perpandicular) to the incline + the normal force Nab which is equal to Fxy. We also have a force of friction opposite to Fxb which is helping the block stay stationary atm. When F is applied then i get confused. Does all components of F get applied to block B? Im thinking maybe only an amount until it reaches the friction limit. If block A is pulled to the left will there be an opposite reaction from block B? causing acceleration in the opposite direction??

8. Aug 16, 2013

### TSny

The force F is applied to block A. It does not act on block B. So, you have 3 forces acting on B:

(1) Force of gravity
(2) Normal force (from the surface of A and perpendicular to the surface)
(3) Friction force (from the surface of A and parallel to the surface)

Draw a diagram showing just block B and these 3 forces acting on B.

Next, you want to introduce a coordinate system for block B. It is generally a good idea to choose one of your axes of your coordinate system to be in the direction of the acceleration of the block. As long as B is not yet slipping on A, think about the direction of the acceleration of B. Choose your x-axis in that direction and then the y-axis will be perpendicular to that.

Finally, set up Newton's 2nd law for block B for the x and y components of motion:

$\sum$Fx = mBax
$\sum$Fy = mBay

Then see what you can deduce from these equations.

9. Aug 16, 2013

### sandman203

yeah i have drawn the free body diagram many times.. i dont know what the hell im missing here dude. I not seeing how force F reduces the normal force and hence friction ?

10. Aug 16, 2013

### haruspex

While everything is stationary, the block experiences a normal force, a frictional force acting up the plane, and gravity. These balance both horizontally and vertically. If the wedge now accelerates to the left and the block stays with it, there must be a net horizontal force on the block to provide that acceleration. This changes the equations. Pls post those equations.

11. Aug 16, 2013

### sandman203

This is where im at:
Block B

X dimension is parrallel to incline, y dimension is perpandicular

When stationary

ƩFy = mbay = 2 × - 9.8 + Nab = 0

ƩFx = mbax = 19.6 sin 15 - Ff = 0

Nab = 2 × 9.8

Limiting friction force for this surface = 0.6 × Nab = 11.76N

Block A When stationary

* Do i put co-ords parrallel to the ground here? so the 2 blocks have different co - ords? or stick with the same co - ords i used for block B?

ƩFy = mab × ay = 7 × - 9.8 + Na = 0 so Na = 68.6

Limiting friction for for this surface = 0.6 × Na = 41.16N

ƩFx = mab × ax = 0

When F is applied

ƩFy = mab × ax = - F cos30 + Ff

So we can see that in order to make AB move we need ax = (41.16 - F cos30)/7

I dont know where to go from here.

Last edited: Aug 16, 2013
12. Aug 16, 2013

### haruspex

You want to know the max F such that B moves with A. So suppose B does move with A, but the friction between them is at maximum. If the acceleration is a, what are the force equations for B (I suggest using horizontal and vertical resolution)? What are the equations for the combined system? You should have four equations and four unknowns: normal force between A and B, acceleration, frictional force from the ground, and F.

13. Aug 17, 2013

### sandman203

Cool dude, what about friction force between AB isnt that another unknown?? as block B accelerates with block A it will have x/y components, this will adjust the normal and hence friction force right?

14. Aug 17, 2013

### sandman203

Also, when F is applied does it only take into account block B or do the equations just need mass of A... i guess if we apply enough to override friction then B's mass wont matter, is this correct?

15. Aug 17, 2013

### sandman203

Hey guys, thanks for the help i have managed to come up with an answer! so here we go.

First of all here are my fbd's of block A and block B

Now for the math:
When stationary - Block A

ƩFx = mAaA = mA × 0 = 0

ƩFy = mAaA = 0 = -49N + NA

∴ NA = 49N

When Stationary - Block B

ƩFx = mB × g × sin15 - Ffab = 0

ƩFy = - mB × g × cos15 + NAB = 0

∴ NAB = mB × g × cos15

When F is applied - Block A

ƩFx = mA × -ax = F cos30 + Ffa

ƩFy = mA × ay = 0 = Na - 49 + F sin30

∴ Na = 49 - F sin 30

∴ Static Friction Limit → FfA = 0.6 × (49 - F sin30)
When F is applied - Block B

ƩFx = -2ax cos15 + (mB × g × sin15) ± FfAB

ƩFy = 0 = NAB - (mb × g × cos15) - 2ax sin15

∴ NAB = (mb × g × cos15) - 2ax sin15

∴ Static friction limit → FfAB = 0.6 × 2×g×cos15 + 2axsin15

SO we want to find the acceleration in which B needs to go in order to make equilibrium (anymore N and block B will slide down)

∴ Fx = 0 = -2axcos15 + (2×g×sin15) - 0.6 × 2×g×cos15 + 2axsin15

Solving for ax = - 4.445m/s2

So Now we find out how this acceleration works on Block A.

We will need ƩFx = -4.445 x 5 = -22.225N in the x direction from force F to act on Block A and put block B in equilibrium.

Fx = -22.225N - FfA

Fx = -22.225N - (0.6×49 - Fsin30)

Now Fx = Fcos30 = -22.225 - 0.6(×49 - Fsin30)

Solving for F we get 44.5N!!!!!

So this will keep block B on block A so i guess the answer is F > 44.5N ?

16. Aug 17, 2013

### verty

You have some mistakes and I think you are still not quite knowing what to do.

Start again but from this point of view: A and B are stuck together but B is about to slip. F is pulling the mass of both. So the result of whatever forces are acting on B is a horizontal force giving to B exactly the acceleration that F gives to A+B. With this in mind, draw your diagram being very careful with sin and cos and where to put right angles, these were some of the mistakes made before.

If you do all that, you should be in a good position to solve it.

17. Aug 17, 2013

### haruspex

Are you treating Ffa as negative? (You drew the arrow oppositely to F's)
Again, what about NAB and FfAB? As I suggested, it's simpler to treat A and B combined instead of A in isolation.
In your diagram you have x perpendicular to the slope and y parallel to it.
Is g acting in the direction of a or against it? Shouldn't you write
ƩFx = 2ax cos15 = -(mB × g × sin15) + (friction term)
(Which way is friction acting here? )
I get a little over 60N.

18. Aug 17, 2013

### TSny

If you consider the forces on B alone, you will be able to determine the numerical value of the acceleration of the system that will put B on the verge of slipping.

See if you can complete the free body diagram of block B that I have attached here. I leave it to you to identify the forces (blue vectors) and the appropriate angles.

As pointed out before, it will be best to choose the x-axis horizontally and the y-axis vertically.

Since we are assuming that B is on the verge of slipping there is a relationship between the friction force acting on B and the normal force acting on B.

What can you deduce from $\sum$Fy = may ?

Then, what can you get from $\sum$Fx = max ?

#### Attached Files:

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19. Aug 18, 2013

### sandman203

ok one question.. when calculating force of friction for block A do i need to take into account the friction created from accelerating block B to the left?

20. Aug 18, 2013

### TSny

You can find the friction force that the floor exerts on A by considering A and B together as one object, drawing a free body diagram for that object, and applying the 2nd law.

[EDIT: If you are referring to the normal force that A exerts on B, then you will be able to get that from applying $\sum$Fy = may to the diagram for B alone( if you choose the y-axis vertical).]

Last edited: Aug 18, 2013