What Is the Force Exerted by the Top Link on the Middle Link?

[Prof. 27]

Homework Statement

A student tries to raise a chain consisting of three identical links. Each link has a mass of 200 g . The three-piece chain is connected to a string and then suspended vertically, with the student holding the upper end of the string and pulling upward. Because of the student's pull, an upward force of12 N is applied to the chain by the string. Use Newton's laws to answer the following questions.

a) Find the acceleration of the chain.
b) Find the force exerted by the top link on the middle link.

Homework Equations

F = ma

The Attempt at a Solution

MIT Opencourseware
Physics Clasroom
Hyperphysics
Lots of scratch paper and failed attempts

 

[Chestermiller]

Let's see some of your failed attempts. We can't help you if we can't see what your hangup is.

Chet

 

[Prof. 27]

Okay:

So we know each link is 200g. So the total mass of the three chains is 600 g, which we convert to 0.6 kg.
We know the chain is initially suspended (at rest, i.e. there is no vertical acceleration); therefore the vertical force upward equals the vertical force downward (gravity) - 12 N. Since the string is massless, frictionless, etc. We can plug it into Newton's second law.

12 N = 0.6 kg*a
So 12 N/0.6 kg = a
So: a = 20 m/s^2

This is wrong according to the Mastering Physics.

 

[Chestermiller]

This force balance omits an important force. Have you drawn a free body diagram? What are the forces acting on the chain?

 

[haruspex]

the vertical force upward equals the vertical force downward (gravity) - 12 N.

Do you mean the net force will be a vertically upward force equal to that? If so, doesn't something there seem backwards?

12 N = 0.6 kg*a

You mentioned gravity before, but I don't see that in this equation.

 

[Prof. 27]

Thanks so much. Got it.

 

[Prof. 27]

So now having trouble with part two. Wouldn't the only force the top link exerts on the middle one be the force of gravity on the top link since the person pulling the string upward is applying the other force (and it is upward, so the force of the middle would be applied to the force on the top, vice versa) and so its not part of the force of the top chain on the middle?

 

[Chestermiller]

So now having trouble with part two. Wouldn't the only force the top link exerts on the middle one be the force of gravity on the top link since the person pulling the string upward is applying the other force (and it is upward, so the force of the middle would be applied to the force on the top, vice versa) and so its not part of the force of the top chain on the middle?

I can't follow what you are saying here. Please draw a free body diagram of the top link showing all the forces acting on it. Please say in your own words what these forces are (there are three of them). (You really need to get used to always drawing free body diagrams).