# Accelerating Wedge and block on top of it -- Dynamics

1. Jun 10, 2013

### andyrk

1. The problem statement, all variables and given/known data
In the figure a block of mass 'm' is placed on a wedge of mass M. The wedge is subject to a horizontal force 'F' and slides on a friction less surface. The coefficient of static friction between the block and wedge is μs. Find the range of values of 'F' for which the block does not slide on the incline.

2. Relevant equations
If the bodies (block+wedge) move together then:
F=(M+m)a

3. The attempt at a solution
If 'F' is too less, then the block of mass 'm' will have a tendency to come down the incline.
If 'F' is too much, the block will have a tendency to move up the incline.
So 'F' need to be in between these minimum and maximum values and that's how we get the range. But my doubt is that why do the above 2 conditions i.e when F is too less and when F is too much happen?

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2. Jun 11, 2013

### haruspex

Why or when? Are you able to write out and solve the equations?
Note that in the case of sliding down, it may be that F needs to go negative if the angle is low or the friction is high.

3. Jun 11, 2013

### andyrk

"When" is the statement itself..That is , the 2 respective cases happen when their respective conditions are met. Namely, F being very less or very large. My question is for the "why" part. As to does the block specifically move upwards when F is too large? If it moves up there has to be some force acting up the incline..how does that force arise, i.e the force that makes the block move up the incline when F is too large? Is it because of a pseudo force that we have included, opposite to the acceleration of the (wedge+block) since this system is an accelerating one with respect to an inertial frame namely us or the ground? If that happens then we can resolve this pseudo acceleration into two components, and one those components acts up the incline so the block moves up the incline. But then, are we considering ourselves or the ground as the frame of reference or the system itself as the frame of reference?
The thing is I maybe having the answers to my queries but I am just too doubtful to accept my answer..

4. Jun 11, 2013

### Tanya Sharma

Hi andyrk

The component of pseudo force acts up the incline,whereas the component of weight acts down the incline.In case the component of pseudo force is greater than the component of weight then the block has the tendency to move up.Hence friction acts downwards.In case the former is less than the latter ,the block has the tendency to slide down.So,friction acts upwards.

Since we are applying pseudo force ,we are surely working from the accelerated frame of reference,i.e the wedge .The observations are made from the wedge ,not the ground.

5. Jun 11, 2013

### andyrk

What are the observations that we are making from the frame of reference of the (block+wedge) system?

6. Jun 11, 2013

### Tanya Sharma

The frame of reference is wedge ,not wedge+block.The block is seen sliding up,stationary,sliding down the wedge depending on the force applied to the wedge.

Last edited: Jun 11, 2013
7. Jun 11, 2013

### andyrk

8. Mar 14, 2015

### andyrk

Can the reason for why the block moves up the incline and down the incline be explained without using pseudo force method and just normal application of Newton's Second Law?

9. Mar 15, 2015

### haruspex

Of course. Applied corectly, inertial frames and non-inertial frames should lead to the same answer. It's only a question of which is more convenient.

10. Mar 15, 2015

### andyrk

So how would one do that? I am not able to think of an explanation without using Pseudo Force which explains why the block moves up or down the incline depending on the magnitude of the force.

11. Mar 15, 2015

### haruspex

Down the incline is ok, yes? If little force is applied and the friction is weak it will slide down.
For the block to slide up the incline, it is only required that the horizontal acceleration of the wedge exceeds that of the block. We can make the wedge accelerate as fast as we like by applying a large enough force. The acceleration of the block in that direction depends on the normal force from the wedge (limited by g) and the frictional force (limited by g and mu).

12. Mar 15, 2015

### andyrk

So even if the wedge accelerates faster than the block, why would the block move upwards?

13. Mar 15, 2015

### haruspex

Because the only other option is for it to penetrate the block.

14. Mar 15, 2015

### andyrk

Yep. That makes some sense intuitively. But can we explain it a bit more quantitatively rather than qualitatively?

15. Mar 15, 2015

### andyrk

Anybody there?

16. Mar 15, 2015

### haruspex

I had the impression you were after a qualitative explanation.
To go quantitative, write some equations.

17. Mar 15, 2015

### andyrk

I did. But I was unable to find a reasonable explanation for this without including pseudo forces in. How do you do that?

18. Mar 15, 2015

### haruspex

You have the acceleration. Suppose it is on the point of slipping up the plane. Put in an unknown for the normal force. What equations do you get?

19. Mar 15, 2015

### andyrk

The equations for the block are: Rcosθ = mg and Rsinθ = mA, where A is the acceleration of the block+wedge system.
This is for the case when the block is at rest (assuming that it is).
When it is not, what proof do we have that it moves upwards when the force is a lot and it moves downwards when the force is low? How can we be sure this is going to happen? I know it seems right intuitively and by using pseudo forces we can even prove it. But can we prove it without intuition and pseudo forces?

20. Mar 15, 2015

### haruspex

Where R is the normal force? You've left out friction.