How Much Force Must Each Person Exert to Carry the Couch Levelly?

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Homework Help Overview

The problem involves two individuals carrying a 2 m long couch with a mass of 20 kg while a third person weighing 60 kg sits on it. The goal is to determine the upward force each person must exert to keep the couch level while accounting for the center of mass and the additional weight of the person sitting on the couch.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the concept of center of mass and its relevance to the problem. Some suggest using moments about a specific point to analyze the forces involved. Others explore the implications of the external weight on the center of mass and question how to set up the equations for equilibrium.

Discussion Status

Participants are actively engaging with the problem, sharing diagrams and reasoning through the physics concepts involved. There is a recognition that the forces exerted by the two individuals are not equal and that moments must be considered to solve for the unknown forces. Some participants express confusion about the application of moments and the concept of rotational equilibrium, while others provide clarifications and hints.

Contextual Notes

There is an emphasis on understanding the relationship between forces and moments in the context of equilibrium. Participants note that the center of mass of the couch itself does not change, but the overall system's center of mass is affected by the additional weight. The discussion reflects the constraints of a homework setting, where complete solutions are not provided, and understanding is prioritized.

mxh91
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Homework Statement


Two people are carrying a 2 m long couch with a mass of M=20kg level with the horizontal by lifting it from it ends. The center of mass of the couch is 1 m from each end. While it is being carried, another person with a mass m of 60 kg sits on the couch 0.5 m from one end. How much force will each person carrying the couch have to exert upwards in order to continue carrying the couch levelly?


Homework Equations


I don't have a clue on how to start this problem. Does anyone know?


The Attempt at a Solution


Well I know that this is a center of mass problem. I know that Center of mass is equal to sum of each mass times its position all over the total mass of particles.
 
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I've drawn a free body diagram here: http://4.bp.blogspot.com/_-h5patrZ790/TP5DhJfAiNI/AAAAAAAAAV4/xFnT20VqzrI/s1600/Couch+question.PNG

Couch+question.PNG


See if it helps u.
 
Last edited:
Kikora said:
I've drawn a free body diagram here: http://4.bp.blogspot.com/_-h5patrZ790/TP5DhJfAiNI/AAAAAAAAAV4/xFnT20VqzrI/s1600/Couch+question.PNG

See if it helps u.

Thanks for the picture! The way I would think about solving this problem is that since no one is sitting on the right side of the couch, the person on the right is lifting the right half of the couch's weight. So that would be 20 kg / 2 = 10 kg. Then you multiply this weight with gravity's acceleration and I got 98 N. So the person on the right would have to put 98 N into lifting that side of the couch up. After that, we can do the similar steps for the left side. Is this logic correct?
 
Eh. No. Use moments about a point.

Clue: Take moments about the left person.

Note: By the way, In your 3rd sentence, its "multiply this mass with gravity's acceleration" and not "multiply this weight with gravity's acceleration".
 
So I have to take moments about the left person because the 60 kg person is siting closer to him right? So would it be (60 kg)(0.5 m)/(60 kg + 20 kg) ?
 
Erm. Actually, after solving for the force exerted by the right person, you'll need to find the force exerted by the left person later as well. The forces exerted by the right and left person are not equal.

No. Use

Taking moments about left person,

Clockwise moments = anti-clockwise moments
 
Kikora said:
Erm. Actually, after solving for the force exerted by the right person, you'll need to find the force exerted by the left person later as well. The forces exerted by the right and left person are not equal.

No. Use

Taking moments about left person,

Clockwise moments = anti-clockwise moments

Hmm, I'm confused about the moments of left person. Would the total force exerted by both right and left person be 784N since the total mass is 80 kg and I multiplied it by 9.8 m/s^2?
 
You are right. The total force exerted by both right and left person is 784N.

What i meant was force exerted by left person is not equal to force exerted by right person. You will need to take moments about left person to find the force exerted by right person. And hence, find out the force exerted by left person.
 
Kikora said:
You are right. The total force exerted by both right and left person is 784N.

What i meant was force exerted by left person is not equal to force exerted by right person. You will need to take moments about left person to find the force exerted by right person. And hence, find out the force exerted by left person.

Hmmm, the Center of Mass of the couch is at located in the middle of the couch. But since we have external forces acting on the couch, would this center of mass point move? If so, I have to find this new point?
 
  • #10
The centre of mass of the couch will not move.(It is still in the middle) However, the centre of mass of the couch and the person sitting on the couch will be between the arrow(weight of the person sitting on couch) and the arrow (weight of couch). You do not have to find the new point.

More clues to help you:

Taking moments about left person,

Clockwise moments = anti-clockwise moments
(weight of person sitting on couch)(0.5) + (weight of couch)(1.0) = (force exerted by right person)(2.0)
 
  • #11
Kikora said:
The centre of mass of the couch will not move.(It is still in the middle) However, the centre of mass of the couch and the person sitting on the couch will be between the arrow(weight of the person sitting on couch) and the arrow (weight of couch). You do not have to find the new point.

More clues to help you:

Taking moments about left person,

Clockwise moments = anti-clockwise moments
(weight of person sitting on couch)(0.5) + (weight of couch)(1.0) = (force exerted by right person)(2.0)

Ohh! Let me see if I get this right. The reason why we take moments about the left person is because there is an external force (weight of 60 kg person) acting on the left side of couch right? So we set the moments about the left equal the moments about the right (not sure why).

So (60 kg x 0.5 m) + (20 kg x 1.0 m) = (20 kg x 2.0 m) right? But since they are asking for force, we have to multiply both sides by 9.8 m/s^2.

294N m + 196 N m = F (2 m)

F (right person) = 245 N

F (left person) = 784 N - 245 N = 539 N

Right?
 
  • #12
Actually, the reason why we take moments about the left person is so that we do not need to take into account of the unknown force exerted by the left person. Hence, we can solve the equation with 1 unknown(force exerted by right person) instead of having two unknowns(if you take moments about the centre of the couch). You can take moments about the right person instead if you wish(hence solving for the force exerted by the left person).

mxh91 said:
So we set the moments about the left equal the moments about the right (not sure why).
No. We set the clockwise moments about a point = anti-clockwise moments about that same point. This is rotational equilibrium.

Since the couch is in equilibrium, it must have rotational equilibrium and translational equilibrium. Translational equilibrium is all the upwards forces = all the downwards forces. Hmm, maybe i should have told you this earlier.Your numerical answers are correct. But i think you have a poor understanding of the topic.(or maybe i never explain well.)
 
  • #13
Kikora said:
Actually, the reason why we take moments about the left person is so that we do not need to take into account of the unknown force exerted by the left person. Hence, we can solve the equation with 1 unknown(force exerted by right person) instead of having two unknowns(if you take moments about the centre of the couch). You can take moments about the right person instead if you wish(hence solving for the force exerted by the left person).


No. We set the clockwise moments about a point = anti-clockwise moments about that same point. This is rotational equilibrium.

Since the couch is in equilibrium, it must have rotational equilibrium and translational equilibrium. Translational equilibrium is all the upwards forces = all the downwards forces. Hmm, maybe i should have told you this earlier.


Your numerical answers are correct. But i think you have a poor understanding of the topic.(or maybe i never explain well.)



Thank you! =] I understand it now. You explained it well, it was just my understanding. Initially, I didn't realize that this was a torque problem, lol.
 

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