A system of two bodies and wall

In summary: I can’t give a definite answer as to whether or not equilibrium means that an object must be at rest.
  • #1
rudransh verma
Gold Member
1,067
95
Homework Statement
Consider the figure. The wall is smooth but the surfaces of A and B in contact are rough. Then-
1. System may remain in equilibrium
2. Both bodies must move together
3. System cannot remain in equilibrium
4. None
Relevant Equations
Newton second law.
I think there is normal force from wall and applied force will balance each other but there is no counter force against mg.Both bodies will slip and fall. I am not sure.
 

Attachments

  • image.jpg
    image.jpg
    28.1 KB · Views: 70
Physics news on Phys.org
  • #2
Did you manage to draw free body diagrams ?

[edit]
If you have to tick 1,2,3,4 (or more than one?), which is/are your best shot ?​
I have difficulties with this exercise: F is not mentioned in the text, but only appears in the picture ?​
The text uses 'remain' where you write 'be'. Also: 'must move together' and 'move together '​
Are there two versions ?​

##\ ##
 
  • #3
BvU said:
The text uses 'remain' where you write 'be'. Also: 'must move together' and 'move together 'Are there two versions ?
No I wrote it in my words and yes there is F.
 
  • #4
Then maybe it's only my personal interpretation problem: the wording 'remain in equilibrium' can (but apparently does not have to) mean that the picture is of an equilibrium (starting) situation. Never mind.

BvU said:
Did you manage to draw free body diagrams ?

##\ ##
 
  • #5
rudransh verma said:
No I wrote it in my words and yes there is F.
Would I be correct to assume that ##\vec{F}## is, as drawn, purely horizontal?
Would I be correct to assume that gravity is present and non-zero, even though it is not drawn?
Would I be correct to assume that "equilibrium" means that the system remains at rest if it began at rest?

If so, can you go through 1), 2) and 3) and explain why each holds or does not?
 
  • #6
jbriggs444 said:
If so, can you go through 1), 2) and 3) and explain why each holds or does not?
Force on B is balanced from all directions but not on A. There is no upward friction since the wall is smooth. So the system assuming is at rest in beginning cannot remain in rest and is not in equilibrium if that what we mean by equilibrium (rest).
 
  • #7
rudransh verma said:
Force on B is balanced from all directions
Q1. How do you know? What are the forces on B? What balances B's weight?
(Pity you haven't done free body diagrams as suggested by @BvU.)

rudransh verma said:
but not on A.
Q2. How do you know? What are the forces on A?

rudransh verma said:
There is no upward friction since the wall is smooth. So the system assuming is at rest in beginning cannot remain in rest and is not in equilibrium if that what we mean by equilibrium (rest).
Q3 If A and B start at rest, do you think B (which you think is in equilibrium) remain at rest?

Q4. Is there any friction between A and B? If not, why not?

Q5 (Bonus question.) If an object is in 'equilibrium' does that mean it must be at rest?

P.S. Dd you ever find the very easy way to solve your recent problem about the falling knife using potential energy and work (2 or 3 lines of simple working)? https://www.physicsforums.com/threads/knife-dropped-on-cardboard.1011687/
 
  • #8
Steve4Physics said:
Q1. How do you know? What are the forces on B? What balances B's weight?
Surface A and B are rough. Friction.
Steve4Physics said:
How do you know? What are the forces on A?
Wall is smooth.
Steve4Physics said:
Q3 If A and B start at rest, do you think B (which you think is in equilibrium) remain at rest?
After A slips B will too eventually.
Steve4Physics said:
If an object is in 'equilibrium' does that mean it must be at rest?
I think there is no acceleration.
Steve4Physics said:
P.S. Dd you ever find the very easy way to solve your recent problem about the falling knife using potential energy and work (2 or 3 lines of simple working)?
No!
 
  • #9
rudransh verma said:
After A slips B will too eventually.
Why not immediately? What is holding it in place?
 
  • #10
jbriggs444 said:
Why not immediately? What is holding it in place?
Body A
 
  • #11
rudransh verma said:
Body A
How is body A supposed to support body B if body A is, itself, falling down?

What forces do you imagine exist between the two of them. And why?
 
  • #12
jbriggs444 said:
How is body A supposed to support body B if body A is, itself, falling down?

What forces do you imagine exist between the two of them. And why?
I meant momentarily.
Friction. Given rough surface.
 
  • #13
See Post#7 for the original quetions.

rudransh verma said:
[Q1] Surface A and B are rough. Friction.
Q1. If A moves down and IF there is friction,between A and B there would be two downwards forces on B (weight and friction from A). So B would not be in equilibrium.

rudransh verma said:
[Q2] Wall is smooth.
Q2. But IF A exert a frictional force on B, then B exerts an equal magnitude and opposite direction frictional force on A (Newton’s 3rd law). So B would exert a frictional force on A (even though there is no frictional force on A due to the smooth wall).

rudransh verma said:
[Q3] After A slips B will too eventually.
Q3. Why ‘eventually’? What will make B start to move?

Q4. Unanswered.

rudransh verma said:
[Q5] I think there is no acceleration.
Q5 You haven’t answered the question asked.
“If an object is in 'equilibrium' does that mean it must be at rest?”.
The answer is ‘yes’ or ‘no’ plus a reason.

I'll tell you the answer since it isn't directly needed to answer your Post#1 question. The answer is:
No. It would also be in equlibrium if it were moving with a constant velocity.

rudransh verma said:
[P.S.] No!
P.S. How much gravitational potential energy did the knife lose in total? How much work did the resistive force do? If you can answer those two questions you can find the resistive force extremely easily.

I think you must take a step back. Drawing free body diagrams helps you to correctly think about what forces act. Until you can (correctly) draw the free body diagrams for A and B, I don't think you will be able to answer the question (IMHO).

Edited
 
Last edited:
  • #14
rudransh verma said:
I meant momentarily.
Friction. Given rough surface.
Static friction?
Kinetic friction?

Can you reason out why neither can produce any force? Not even momentarily.
 
  • Like
Likes Steve4Physics
  • #15
2

.
 
  • #16
rudransh verma said:
I meant momentarily.
Friction. Given rough surface.
Frictional forces act to oppose the relative motion that occurs, or would otherwise occur, between surfaces in contact.
For nonzero kinetic friction between two surfaces there must be some relative motion of the bodies.
For nonzero static friction between two surfaces there must be some tendency to relative motion of the bodies. I.e. in the absence of that friction there would be relative motion between them.
 
  • Like
Likes jbriggs444
  • #17
@rudransh verma:

If A and B were both perfectly smooth (zero friction between them) what would happen and why?

If A and B were both stuck together (effectively infinite friction) what would happen and why?
 
  • #18
Steve4Physics said:
If A and B were both perfectly smooth (zero friction between them) what would happen and why?
Both will fall down because of imbalance of forces.
I have made the diagram and I think all are balanced in the OP. So equilibrium!
 

Attachments

  • image.jpg
    image.jpg
    24.7 KB · Views: 61
  • #19
rudransh verma said:
Both will fall down because of imbalance of forces.
Yes, they both fall. Do they fall at the same rate?

rudransh verma said:
I have made the diagram and I think all are balanced in the OP. So equilibrium!
Your diagram is wrong. And the blocks are not in equilibrium.

Part of the problem is that the OP is badly worded.

Think of holding a stone stationary (in equilibrium) in your hand. You then release the stone. What force(s) act on the stone the moment after you release it? Is the stone now in equilibrium?

Think of the OP diagram as showing two blocks the moment after they were released.
 
  • #20
Steve4Physics said:
Think of holding a stone stationary (in equilibrium) in your hand. You then release the stone. What force(s) act on the stone the moment after you release it? Is the stone now in equilibrium?

Think of the OP diagram as showing two blocks the moment after they were released.
Gavity is acting on the stone.
If after they were released means removal of force F then both will fall.
 
  • #21
rudransh verma said:
Gavity is acting on the stone.
If after they were released means removal of force F then both will fall.
Will the (frictionless) blocks fall at the same rate? What is this rate?

Force F (in the OP diagram) acts horizontally and is always present. It does not get removed.

The force(s) initially suporting the blocks are not shown in the OP diagram. The OP diagram shows the blocks from the moment after the supporting force(s) have been removed.
 
  • #22
Steve4Physics said:
Will the (frictionless) blocks fall at the same rate? What is this rate?
No! Different rate since difference in mass. Acceleration due to gravity!
Steve4Physics said:
Force F (in the OP diagram) acts horizontally and is always present. It does not get removed.
yeah!
Steve4Physics said:
The force(s) initially suporting the blocks are not shown in the OP diagram. The OP diagram shows the blocks from the moment after the supporting force(s) have been removed.
What supporting forces? are you talking about normal forces and friction?
 
  • #23
rudransh verma said:
What supporting forces?
There are none. We expect that the blocks begin at rest relative to each other because we are not told otherwise. We might imagine that this was arranged by having the blocks held in place until just before we start looking at the system.
 
  • #24
rudransh verma said:
No! Different rate since difference in mass. Acceleration due to gravity!

yeah
No, not different rates! Identical rates!

A heavy mass accelerates the same as a light mass (ignoring air resistance). Both have acceleration = g (= 9.8 m/s² (approx.) downwards).

rudransh verma said:
What supporting forces? are you talking about normal forces and friction?
Suppose blocks A and B are initially stationary and each hang on a string.

The only supporting forces (the forces preventing the blocks falling vertically downwards) are the tensions in the strings.

Now cut both strings simultaneously!

You now have the setup described in the OP. There are now no supporting forces.
 
  • Like
Likes jbriggs444
  • #25
Steve4Physics said:
No, not different rates! Identical rates!

A heavy mass accelerates the same as a light mass (ignoring air resistance). Both have acceleration = g (= 9.8 m/s² (approx.) downwards).
O right!
Steve4Physics said:
If A moves down and IF there is friction,between A and B there would be two downwards forces on B (weight and friction from A). So B would not be in equilibrium.
Due to weight of B there is upward friction on A but due to weight of A there is downward friction on B. So both will come down the moment they are released at same rate g.
I have two possibilities. Which one? 1 or 2 ?
What if we treat it as a system? I think both will come down because there is no upward forces on either of them.
 

Attachments

  • image.jpg
    image.jpg
    37.7 KB · Views: 78
Last edited:
  • #26
Well, well. After 24 posts we now have free body diagrams. The reason I asked for them is that I would like you to discover that there are no vertical forces except the two from gravity. And they cause the two blocks to fall with exactly the same acceleration. That means there is no tendency for the blocks to move wrt each other in any direction.

You have drawn friction forces, but exactly because there are no other vertical forces, the actual friction forces are zero, which makes your 1) and 2) diagrams identical. At best you have drawn the maximum friction forces, something like ##\mu F_N##.
 
  • #27
BvU said:
Well, well. After 24 posts we now have free body diagrams. The reason I asked for them is that I would like you to discover that there are no vertical forces except the two from gravity. And they cause the two blocks to fall with exactly the same acceleration. That means there is no tendency for the blocks to move wrt each other in any direction.
I think there should be no friction too because there is no upward force on any of the bodies.
 
  • #28
rudransh verma said:
I think there should be no friction too because there is no upward force on any of the bodies.
But there is a downward force on both bodies. What makes upward forces special in your mind?
 
  • #29
jbriggs444 said:
But there is a downward force on both bodies. What makes upward forces special in your mind?
There have to be relative motion between A and B for the friction to occur here. Wall is smooth and no upward force on B. So both will fall at same rate due to gravity after we remove supporting forces.
 
  • #30
rudransh verma said:
There have to be relative motion between A and B for the friction to occur here.
As I wrote, that is for kinetuc friction. For static friction there does not need to be any actual relative motion, only that there would be relative motion if the friction were not there.
 
  • #31
rudransh verma said:
There have to be relative motion between A and B for the friction to occur here.
No. That's only true for kinetic friction. I will add to @haruspex's comment...

Suppose a small parachute is attached to block B. Since A and B are pressed together, there could be enough static friction to prevent them sliding relative to each other. A and B would then fall together (in the same way as if they were stuck together).

Of course If you use a sufficiently big parachute and A is very heavy, then A will fall faster than B. Sliding occurs between A and B and the friction is kinetic.
 
  • #32
Steve4Physics said:
No. That's only true for kinetic friction. I will add to @haruspex's comment...
O yeah! But there is also no static friction here because of the absence of any upward force. Both will fall as one system.
 
  • Like
Likes BvU and Steve4Physics
  • #33
rudransh verma said:
O yeah! But there is also no static friction here because of the absence of any upward force. Both will fall as one system.
Yes indeed! If you read through the previous posts, you will see that this is the message we have been trying to convey!
 
  • Like
Likes BvU

1. What is a system of two bodies and wall?

A system of two bodies and wall refers to a physical system consisting of two objects or bodies interacting with each other and a third object, typically a wall, that serves as a boundary or constraint for the system.

2. What are some examples of a system of two bodies and wall?

Some examples of a system of two bodies and wall include a pendulum swinging back and forth between two walls, a ball bouncing between two walls, or two objects colliding with each other against a wall.

3. How is the motion of a system of two bodies and wall determined?

The motion of a system of two bodies and wall is determined by the initial conditions of the system, such as the mass, velocity, and position of the two bodies, as well as the properties of the wall, such as its elasticity and surface friction.

4. What is the significance of studying a system of two bodies and wall?

Studying a system of two bodies and wall allows scientists to better understand the principles of mechanics and the behavior of objects in motion. It also has practical applications in fields such as engineering and physics.

5. How does the presence of a wall affect the motion of a system of two bodies?

The presence of a wall can affect the motion of a system of two bodies in various ways, such as limiting the range of motion, causing changes in velocity or direction, or transferring energy between the bodies. The properties of the wall, such as its rigidity and surface characteristics, can also impact the behavior of the system.

Similar threads

  • Introductory Physics Homework Help
Replies
19
Views
1K
  • Classical Physics
Replies
24
Views
723
  • Introductory Physics Homework Help
Replies
8
Views
165
  • Introductory Physics Homework Help
Replies
7
Views
2K
  • Introductory Physics Homework Help
Replies
4
Views
1K
Replies
1
Views
328
Replies
1
Views
805
  • Introductory Physics Homework Help
Replies
17
Views
611
Replies
18
Views
1K
  • Introductory Physics Homework Help
Replies
5
Views
2K
Back
Top