How do the forces on block B affect its motion?

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The discussion focuses on determining the horizontal force required to drag block B at constant speed while block A remains at rest. Participants analyze the forces acting on both blocks, including gravitational forces, normal forces, and frictional forces. Key points include the identification of two frictional forces acting on block B—from block A and the ground—and the distinction between the normal forces for each block. The correct relationship between the normal forces and frictional forces is emphasized, leading to a clearer understanding of the dynamics involved. Ultimately, the participant successfully arrives at the solution with the help of the community's guidance.
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Homework Statement


Block A in the figure View Figure weighs w_1 and block B weighs w_2. The coefficient of kinetic friction between all surfaces is u_k.

Find the magnitude of the horizontal force \vec{F} necessary to drag block B to the left at constant speed if A is held at rest (figure (b)).

Homework Equations


F = ma
a = 0

The Attempt at a Solution


I attempted by drawing two FBDs for A and B. I have for

B: w_2 downward, F_aonb downward, normal force upward, F to the left dragging, and fk_ground
A: w_1 downward, normal force upward, F_bona, and fk_ab

Then I solved for the normal force and I got n = (w_1+w_2)/2 and then I plugged it into the fk = ukn, but well wrong answer.

I have a few questions because I don't really understand the whole picture. There's two frictional forces acting on B right? From A and from the ground? Is this correct? Also, the normal force for both B and A...are they the same or are they different? They're different right?
 

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Peach said:

Homework Statement


Block A in the figure View Figure weighs w_1 and block B weighs w_2. The coefficient of kinetic friction between all surfaces is u_k.

Find the magnitude of the horizontal force \vec{F} necessary to drag block B to the left at constant speed if A is held at rest (figure (b)).


Homework Equations


F = ma
a = 0

The Attempt at a Solution


I attempted by drawing two FBDs for A and B. I have for

B: w_2 downward, F_aonb downward, normal force upward, F to the left dragging, and fk_ground what about the magnitude and direction of the friction force from A on B ? [/color]
A: w_1 downward, normal force upward, F_bona, and fk_ab Specify the directions of the ones you have identified.[/color]

Then I solved for the normal force and I got n = (w_1+w_2)/2 and then I plugged it into the fk = ukn, but well wrong answer.how did you get this?[/color]

I have a few questions because I don't really understand the whole picture. There's two frictional forces acting on B right? From A and from the ground? Is this correct? correct[/color] Also, the normal force for both B and A...are they the same or are they different? They're different right?correct[color]
Draw the FBD's again and identify the forces on each block. The normal force on block A is the force upwards of B on A.
 
Peach said:
B: w_2 downward, F_aonb downward, normal force upward, F to the left dragging, and fk_ground
You left out the friction force of A on B. Note also: the force you call F_aonb downward is the normal force between A and B. A and B exert two forces on each other: a normal force and a friction force.
A: w_1 downward, normal force upward, F_bona, and fk_ab
Seems like you are counting the normal force twice: F_bona is the normal force. And you left out the tension in the rope pulling on A. (You don't need to analyze the forces on A to solve this problem, but it's good exercise.)

Then I solved for the normal force and I got n = (w_1+w_2)/2 and then I plugged it into the fk = ukn, but well wrong answer.
I assume you mean the normal force between the ground and B. How did you solve for it? (Consider vertical forces only.)

I have a few questions because I don't really understand the whole picture. There's two frictional forces acting on B right? From A and from the ground? Is this correct?
Absolutely correct.
Also, the normal force for both B and A...are they the same or are they different? They're different right?
Yes. The normal force between A & B is different from the normal force between B & ground.
 
Okay, the friction force from A to B is going in the same direction as the friction force from the ground to B right? Because friction forces are always in the opposite direction from the acceleration and perpendicular to normal forces..? If that's not wrong, then this is what I'm getting:

n_gb: n_ab + w_2

F: fk_ab + fk_gb

Is this correct? Am I going in the right direction, no pun intended?

Edit: Oh! And n_ab is w_1 right? Because the normal force on A = n_bona = w_1? That's what I'm getting from my FBD of A...
 
Last edited:
Peach said:
Okay, the friction force from A to B is going in the same direction as the friction force from the ground to B right? Because friction forces are always in the opposite direction from the acceleration and perpendicular to normal forces..? If that's not wrong, then this is what I'm getting:

n_gb: n_ab + w_2

F: fk_ab + fk_gb

Is this correct? Am I going in the right direction, no pun intended?

Edit: Oh! And n_ab is w_1 right? Because the normal force on A = n_bona = w_1? That's what I'm getting from my FBD of A...
Yes, this seems correct...
 
I got the answer. Many thanks for both the help. ^^
 
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