# Homework Help: Friction & movement in a system with body above moving body

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1. Jul 22, 2016

### TheCapacitor

• Member advised to use the homework template for posts in the homework sections of PF.

I have a problem in analyzing movement with friction involved. I do not know how to correctly analyze systems as such and what is the correct view. I have tried to answer the several question below.

I have the following diagram. There is friction between all parts.

1) What force do we need to apply in order to give acceleration to the system when it is moving at constant velocity(so ∑F is not 0 on A)? I would say it must be greater the Fk, since Fk magnitude is a constant value.

Is it correct?

2)
Let's say the system is moving at constant velocity. What are the forces applied on B? Is there a static friction force? I find it hard to imagine what is happening to object B. ∑F is 0 on B too since it moves with constant velocity. The only one who can apply force on it is A.

if A was to apply force on B, then there would be also an opposite force applied by A (so ∑F is 0 on B) so it is a contradiction thus no force is applied on B.

However, lets look at the molecule level. B's molecules are moved by A molecules. So A must apply force on B! Like in this picture:

I'm really confused.

3) System is accelerating. B stays stationary above A. What are the forces applied to B and A?

According to Newton second law, now force is applied on B. The only one who can apply force on B is still A. I would guess that A is applying force in the direction of the acceleration and there is also static friction that is opposed to that force, also from A (since B does not move above A).

I find it really confusing that A is applying two different forces to B.

At the molecular level it seems easier to view it, it is very similiar to question 2.

The forces applied on A are Fk kinetic from both B and the ground and I just don't know which forces are applied to B.

Are my views wrong?

4) System is accelerating. B is moving backwards (opposite of acceleration direction) above A (A reference frame). What are the forces on A and B? What acceleration should be applied in order to make this situation?

I would say the forces on A are the forces from que 3. Now there must be kinetic friction on B. This force is opposite of acceleration.

However at the molecular level I would say A is trying to pull B with it, so it also must be a force in the direction of the acceleration.

I really can't get how to write the equations.

Any help will be much appreciated.

2. Jul 22, 2016

### Daymare

1)No,we will have to apply a force more than the kinetic friction between A and the ground.You need to consider the static friction between A and B too.

2)Now for this when both blocks are moving with constant velocity there is no force between them.You are imagining that if B has to move A needs to keep on pushing it.But thats not true.Initially for them to reach their current velocity A has to apply a force on B(say we are pushing A with a force F to accelerate it to reach a certain velocity).After both blocks attain the same velocity then there would be no force(hypothetically) between their molecules as with respect to each other they are stationary.

3)Forces applied on B would be the static friction between A and B(assuming B doesn't move when we accelerate A).That is the only force acting on B.While on A the forces are the one we apply,the frictional force from the ground and also the static friction between A and B.(One thing you should also note is that we can also move the system by pushing B not just A.)

4)When B is moving backwards it means that block A is acceleration is much higher than the static friction of block B.In truth B is not moving back,its still going forward but with respect to block A acceleration with which it goes forward is less.

3. Jul 22, 2016

### Daymare

1)No,we will have to apply a force more than the kinetic friction between A and the ground.You need to consider the static friction between A and B too.

2)Now for this when both blocks are moving with constant velocity there is no force between them.You are imagining that if B has to move A needs to keep on pushing it.But thats not true.Initially for them to reach their current velocity A has to apply a force on B(say we are pushing A with a force F to accelerate it to reach a certain velocity).After both blocks attain the same velocity then there would be no force(hypothetically) between their molecules as with respect to each other they are stationary.

3)Forces applied on B would be the static friction between A and B(assuming B doesn't move when we accelerate A).That is the only force acting on B.While on A the forces are the one we apply,the frictional force from the ground and also the static friction between A and B.(One thing you should also note is that we can also move the system by pushing B not just A.)

4)When B is moving backwards it means that block A is acceleration is much higher than the static friction of block B.In truth B is not moving back,its still going forward but with respect to block A acceleration with which it goes forward is less.

4. Jul 22, 2016

### TheCapacitor

Thank you very much for the answers, they made some things much clearer now.
I only would like to ask you about 4 - what forces will be applied to each body?
And also, saying "block A is acceleration is much higher than the static friction of block B" doesn't feel precise.

5. Jul 22, 2016

### Daymare

What I meant to say was that the acceleration of block A is more than the acceleration of block B.What force makes B accelerate?Its the kinetic friction.The forces acting on block A are the kinetic friction between block A and the ground,the kinetic friction between block A and B and also the force we are applying on A.(Note I haven't considered here the force due to gravity since they all just cancel themselves anyway)

6. Jul 22, 2016

### haruspex

No, they're the same force.
Frictional forces do not arise specifically to oppose other forces or accelerations. They arise to oppose relative motion (actual in the case of kinetic, potential in the case of static) of surfaces in contact. A's acceleration creates the potential for it to move relative to B, and friction arises to oppose that. From A's perspective, that force therefore acts against A's acceleration, whereas for B it acts with the A's acceleration. Thus, the force A applies to accelerate B is the static frictional force.
Don't confuse motion with acceleration. We are not told how B's molecules got moving initially, but at the time of interest they are moving at constant velocity, so there is no need for a horizontal force from A.
It is unclear which acceleration you are referring to. Is this B's absolute acceleration, B's acceleration relative to A, or maybe A's acceleration?

7. Jul 22, 2016

### TheCapacitor

I was refering to B's absolute acceleration,
However I would also like to know about the two other accelerations.

8. Jul 22, 2016

### haruspex

Which way is B's acceleration? What horizontal forces act on B? So which way is the frictional force on B?

9. Jul 22, 2016

### TheCapacitor

Let's assume force is acting on A and A is accelerating. B is accelerating too, but not in the same direction.
Forces on A are kinetic from the ground + B and the force applied, and forces on B is kinetic in the direction of the acceleration.
Why the kinetic force on B is in this direction?

10. Jul 22, 2016

### haruspex

if the external force is only on A, B's absolute acceleration will not be in the opposite direction. Assuming it is will not lead to any useful conclusions. Its absolute acceleration may be less than A's, so its relative acceleration may be in the opposite direction to A's absolute acceleration.

Last edited: Jul 22, 2016