How Do You Calculate Forces in a Multi-Block System with Friction?

[MP2491]

Three identical blocks are pushed across a table at constant speed. The hand pushes horizontally. Let the stack of two blocks be system A and the single block be system B. Now suppose the mass of each block is 2.5kg, the coefficient of kinetic friction between the bottom surfaces of the blocks and the table is 0.20, and the blocks are moving at 0.50 m/s. Determine the magnitude of each force.

So for the first step I drew a FBD for both systems. For system A there is a Normal force pointing to the right, and Normal force and Kinetic Friction force to the left. There is also a Normal force pointing up and a weight force pointing down. For system B there is a Normal force pointing to the right and a Friction force to the left. There is also a Normal force pointing up and a Weight force pointing down.

I was able to find that the weight for system A is 50N and the weight for system B is 25N. Normal force pointing up for system A is also 50N and for system B is 25N.

I know the total force is zero because there is no acceleration but I am having trouble figuring out how to find the Normal force. I know I need to use F=ma and Fk=coefficient of friction x Normal force.

 

[mfb]

I guess you called the force from the hand "normal force". That is confusing. There is nothing horizontal that would be called "normal force" here.

Did you calculate Fk? How does the horizontal force balance look like?Edit@SammyS: The bold part looks like the full problem statement, probably minus a sketch showing two blocks being pushed and one block being pushed.

 

[SammyS]

Three identical blocks are pushed across a table at constant speed. The hand pushes horizontally. Let the stack of two blocks be system A and the single block be system B. Now suppose the mass of each block is 2.5kg, the coefficient of kinetic friction between the bottom surfaces of the blocks and the table is 0.20, and the blocks are moving at 0.50 m/s. Determine the magnitude of each force.

So for the first step I drew a FBD for both systems. For system A there is a Normal force pointing to the right, and Normal force and Kinetic Friction force to the left. There is also a Normal force pointing up and a weight force pointing down. For system B there is a Normal force pointing to the right and a Friction force to the left. There is also a Normal force pointing up and a Weight force pointing down.

I was able to find that the weight for system A is 50N and the weight for system B is 25N. Normal force pointing up for system A is also 50N and for system B is 25N.

I know the total force is zero because there is no acceleration but I am having trouble figuring out how to find the Normal force. I know I need to use F=ma and Fk=coefficient of friction x Normal force.

Hello MP2491. Welcome to PH !

Is this a problem that you have been given to solve? If so, please state the complete problem as it was given to you. That will help us in guiding you to discover the solution.

 

[MP2491]

I guess you called the force from the hand "normal force". That is confusing. There is nothing horizontal that would be called "normal force" here.

Did you calculate Fk? How does the horizontal force balance look like?Edit@SammyS: The bold part looks like the full problem statement, probably minus a sketch showing two blocks being pushed and one block being pushed.

No I have not calculated Fk because I figured i need the Normal force in order to do that.

 

[MP2491]

Hello MP2491. Welcome to PH !

Is this a problem that you have been given to solve? If so, please state the complete problem as it was given to you. That will help us in guiding you to discover the solution.

I have stated the complete problem as it was given to me.

 

[mfb]

No I have not calculated Fk because I figured i need the Normal force in order to do that.

You do have the normal force:

Normal force pointing up for system A is also 50N and for system B is 25N.

 

[MP2491]

You do have the normal force:

I have the normal force in the y direction. I have the normal force of the table on the system but I am looking for the normal force in the x direction. The normal force of the hand on system A, normal force of system B on A, and the normal force of system A on B. These three are the ones that I am looking for.

 

[SammyS]

I have the normal force in the y direction. I have the normal force of the table on the system but I am looking for the normal force in the x direction. The normal force of the hand on system A, normal force of system B on A, and the normal force of system A on B. These three are the ones that I am looking for.

So, now we find that system A and system B are in contact and apparently the hand pushes directly on system A.

None of this was mentioned before. Do you have a figure to accompany this problem?

How is the upper block connected to the lower block in system A?