What Force Does the Top Link Exert on the Middle Link in a Suspended Chain?

[terryds]

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 light 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 15.0 N is applied to the chain by the string. Find the force exerted by the top link on the middle link.
A) 3.0 N
B) 6.0 N
C) 8.0 N
D) 10.0 N
E) None of the above

Homework Equations

ΣF = ma

The Attempt at a Solution

(The system)
ΣF = ma
15 - 3 mg = 3 ma
15 - 3 * 0.2 * 9.8 = 3 * 0.2 a
a = 15.2 m/s^2

(The top link)
ΣF = ma
15 - F = 0.2 * 15.2
F = 15 - 3.04 = 11.96 N

Is it right? I'm not sure about this

 

[Suraj M]

A small clarification in -
"
The top link)
ΣF = ma
15 - F = 0.2 * 15.2
F = 15 - 3.04 = 11.96 N"
What exactly is F?

 

[terryds]

A small clarification in -
"
The top link)
ΣF = ma
15 - F = 0.2 * 15.2
F = 15 - 3.04 = 11.96 N"
What exactly is F?

The force the top link exerts on the middle link

 

[TSny]

(The system)
ΣF = ma
15 - 3 mg = 3 ma
15 - 3 * 0.2 * 9.8 = 3 * 0.2 a
a = 15.2 m/s^2

(The top link)
ΣF = ma
15 - F = 0.2 * 15.2
F = 15 - 3.04 = 11.96 N

That looks good. Note that F in your calculation represents the force that the middle link exerts on the top link. The question asks for the force that the top link exerts on the middle link.

Are they the same? Why?

 

[HallsofIvy]

The force applied by one part of the chain on another, at any point, is the weight of the portion of the chain below that point.

 

[TSny]

The force applied by one part of the chain on another, at any point, is the weight of the portion of the chain below that point.

...only if the chain is not accelerating (assuming "weight" refers to the force of gravity).

 

[haruspex]

15 - 3 mg = 3 ma
15 - 3 * 0.2 * 9.8 = 3 * 0.2 a

I suspect that for the purposes of this question you need to use g=10m/s².
The quickest way to the answer involves a noninertial frame.

 

[terryds]

I suspect that for the purposes of this question you need to use g=10m/s².
The quickest way to the answer involves a noninertial frame.

15 - 3 mg = 3 ma
15 - 3 * 0.2 * 10 = 3 * 0.2 * a
9 = 0.6 a
a = 15 m/s^2

(the top link)
ΣF = ma
15 - F - mg = 0.2 * 15
15 - 0.2 * 10 - F = 3
F = 15 - 2 -3 = 10 N

That looks good. Note that F in your calculation represents the force that the middle link exerts on the top link. The question asks for the force that the top link exerts on the middle link.

Are they the same? Why?

It's the same because it is not slack.. In other words, the tension must be equal..

 

[TSny]

Note that F in your calculation represents the force that the middle link exerts on the top link. The question asks for the force that the top link exerts on the middle link.

Are they the same? Why?

It's the same because it is not slack.. In other words, the tension must be equal..

One of Newton's laws of motion is relevant here.

 

[haruspex]

15 - 3 mg = 3 ma
15 - 3 * 0.2 * 10 = 3 * 0.2 * a
9 = 0.6 a
a = 15 m/s^2

(the top link)
ΣF = ma
15 - F - mg = 0.2 * 15
15 - 0.2 * 10 - F = 3
F = 15 - 2 -3 = 10 N
.

Yes.
The noninertial frame method uses the chain as the reference frame. The acceleration then gives rise to an inertial force that looks like extra gravity. So we have a static chain under increased gravity weighing a total of 15N. Each link therefore weighs 5N.

 

[terryds]

One of Newton's laws of motion is relevant here.

Yup... The Newton 3 law (magnitude of action = reaction)

 

[mfb]

I suspect that for the purposes of this question you need to use g=10m/s².

The result is independent of g.
It is independent of the three masses as well, as long as all three pieces have the same mass.

Probably the shortest way:
No matter what the actual acceleration value is, accelerating three identical links needs 3/2 the force to accelerate two links. And 3/2 of the force the question asks for are 15 N...