# Connected blocks on a surface with friction

1. Sep 22, 2011

### Swalker

This is not a homework problem rather it is a discussion that I have been having with friends. *Your thoughts and feedback would be appreciated.

1. The problem statement, all variables and given/known data
Blocks A and B are on a horizontal surface and connected to one another by a load cell.
Block A has mass m1 and Block B has mass m2.
Each block has difference coeff of static and dynamic friction.
Load cells are connected to the left and right of the blocks.
A right horizontal force F1 is applied to the*
All blocks accelerate at the same rate.
The applied force is much greater than the frictional force.

Diagram

-(1)-A-(2)-B-(3)-

Questions.

1) What are the forces at each load cell.
2) Assume that the system eventually hits a wall but F continues to be applied. *What are the forces a each load cell after impact.

-(1)-A-(2)-B-(3)-WALL

3. The attempt at a solution
1)*
The force at location (1) is:

u1*N1+u2*N2

Where u represents friction coeff and N is normal force.
The force at location (2) is:
u2*N2

The force at location (3) is simply zero.

In the case where*
The force at location (2) is*

2)*
Once we hit the wall we have a change in the reactionary forces.
The reactionary forces cancel out and the force throughout the entire chain is F.
Position 1 is F, position 2 is F, position 3 is F.

Last edited: Sep 22, 2011
2. Sep 22, 2011

### Swalker

Thoughts?.

3. Sep 23, 2011

### omoplata

Some things are not clear to me. Where exactly is the force acting on? Is it acting on load cell 1? Is it pushing load cell 1 (which is connected to the rest of the system of course) to the right?

4. Sep 23, 2011

### Swalker

Hello. Thank you for your response. The force is applied to load cell numb one and is pushing right.

5. Sep 23, 2011

### Swalker

I typed the question up in another application and just noticed that it did not properly paste all of the information. I can no longer edit the original post so I will provide the information below.

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

Blocks A and B are on a horizontal surface and connected to one another by a load cell.
Block A has mass m1 and Block B has mass m2.
Each block has difference coeff of static and dynamic friction.
Load cells are connected to the left and right of the blocks.
A constant right horizontal force F1 is applied to load cell (1)
All blocks accelerate at the same rate as the load cells are rigid connections.
The applied force is much greater than the frictional force.

Diagram

Force-->-(1)-A-(2)-B-(3)-

Questions.

1) What are the forces at each load cell?
2) Assume that the system eventually hits a wall but F continues to be applied. What are the forces a each load cell after impact?

Force-(1)-A-(2)-B-(3)-WALL

3. The attempt at a solution
1)
The force at location (1) is:

u1*N1+u2*N2 as this is the force require to move the blocks. Since there is a net force they will be accelerating to the right. Assume the static and dynamic friction coeff is the same to keep things simple.

Where u represents friction coeff and N is normal force.
The force at location (2) is:
u2*N2

The force at location (3) is simply zero.

In the case where the system is against a wall...
The force at location (2) is:

2)
Once we hit the wall we have a change in the reactionary forces.
The reactionary forces cancel out and the force throughout the entire chain is a constant F.
Position 1 is F, position 2 is F, position 3 is F.

Last edited: Sep 23, 2011
6. Sep 23, 2011

### omoplata

The way of solving this is to draw free body diagrams for all of the objects and apply Newton's laws.

If we take the load cells to be similar to rigid rods, then the compression forces on those rods would correspond to the readings on the load cells.

Your answer for question (1) is correct if the whole system is travelling at constant speed. But since you say the applied force F is much greater than the total frictional force, the system has to travel with acceleration. If you apply Newton's laws for each object, you'll see that the compression forces (readings) that can be calculated for the load cells are different when there is an acceleration.

For question (2), your readings for the load cells for the case when the system is stationary against a wall are correct.

7. Sep 24, 2011

### Swalker

Omoplata,

Thank you, this all makes perfect sense. If I may throw one more variable into the mix.

Assume I apply both a left horizontal force to load cell three and the fixed wall moves slowly moves back and forth with a sinusoidal x component. F1 is greater than F2 and both are much greater than the frictional forces.

The load cells and blocks start under compression. Are the forces at each load cell difference as the wall vibrates?

8. Sep 24, 2011

### omoplata

Is the force F2 the reaction force between the wall and load cell three, or is it another force that someone applies on load cell three?

Either way, all you have to do is draw free body diagrams for all the objects and apply Newton's laws. Try it, and post the results here.

9. Sep 24, 2011

### Swalker

It is the force between the wall and load cell three. I will try free body diagrams as suggested.