# Force equations

1. Nov 19, 2012

### Kartik.

How do we say(or prove) that when two bodies are moving together , they can be considered as one system?

Suppose we have two blocks of wood kept on a friction less surface side by side and you apply a force on any one of them. I suppose from left to right, then the force equations for each block would be

F - FBA -F1= MAAA
FAB= MBAB

And we say that both blocks will move with same accelerations.(Is this right?)

F1 is the force or say resistance which block B gives to A when a Force F is applied(does this force exist?)

Can we prove the accelerations equal? Or its something else?

2. Nov 19, 2012

### Staff: Mentor

If the applied force F is small, the blocks stick together (static friction), and their accelerations are equal. If you know the coefficient of static friction μs, you can calculate the maximum force for which this is true.

If the applied force is larger than this, the blocks start to slide against each other (kinetic friction), and their accelerations are not equal.

3. Nov 19, 2012

### Kartik.

How do you relate friction with the movement of the blocks?
The case i took is on a friction less plane and assuming no friction between the blocks
And i would really like you to answer the few questions i wrote in those brackets

4. Nov 19, 2012

### HallsofIvy

You seem too be assuming that one of the blocks is on top of the other. If two blocks are side by side (as said in the initial post), and you push on one, so that it pushes on the other (not said in the initial post but if not, one block would have moved independently of the other) then, yes, the two blocks move together, at the same acceleration. If one block has mass m and the other mass M, then together they will move with acceleration a= F/(m+ M).

5. Nov 21, 2012

### Kartik.

Like for the two blocks if you write the force equations the equations would be

For both the blocks considered as a single system -
F = (M+m)a

And for just the block on which the force is applied
F-N = ma1

and we say that a = a1; my questions is why?

6. Nov 21, 2012

### nasu

It is actually an approximation good for rigid bodies.
If the accelerations were different, on of two things will happen:
If the pushed body has lower acceleration, the first one will travel a larger distance than the first one. The pushed body being in the way, it (or both) will have to stretch to make room
If the pushed body has higher acceleration, it will loose contact with the pushing body.

Same idea applies to a rope. We assume the rope is inextensible so the bodies connected with a rope under tension have same acceleration (otherwise the rope will have to change its length).
If you allow for elasticity of rope or bodies, then the accelerations are not necessarily equal.

7. Nov 21, 2012

### Staff: Mentor

Sorry, I missed that.

Carry on...

8. Nov 21, 2012

### HallsofIvy

Because they both represent the same thing- the acceration of that block!