# Center of Mass Problem

## 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.

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.

Last edited:

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

Clockwise moments = anti-clockwise moments

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

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.

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?

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.

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)

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.

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?

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).

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.)

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.