Tricking Theoretical Thinking Question

[I Like Pi]

Tricky Theoretical Thinking Question

Homework Statement

Two equal-weight kids each hang from the ends of a rope passing over a weightless, frictionless pulley. If one child accelerates up the rope, what happens to the other?

Homework Equations

The Attempt at a Solution

At first, I believed that if one goes up, then the other will also go up, creating an equilibrium.

Then I thought about the tension of the rope and the classical: two-horses-pulling-on-a-rope problem. If the tension is the same, and one climbs up, shouldn't the other just stay where he/she is? Though this doesn't seem right, its the only one i can explain using physics. It would be the same if one side of the rope was tied to an object, right? Then the tension would also be the same, supporting my second belief..

I hope someone could help me out

 

[Redbelly98]

Have you drawn free-body diagrams, one for each kid?

What does the upward acceleration for kid #1 tell you about the net force, and therefore about the tension in the rope?

Use the fact that the tension is the same throughout the rope's length, and think about the net force on kid #2.

 

[I Like Pi]

Have you drawn free-body diagrams, one for each kid?

What does the upward acceleration for kid #1 tell you about the net force, and therefore about the tension in the rope?

Use the fact that the tension is the same throughout the rope's length, and think about the net force on kid #2.

Well.. I know for kid #1, his net force = force applied - force of gravity, while for the kid, his net force is basically the force of gravity, for that's the only force applied on him

I don't get how i can explain this

thanks so much for your time though

 

[Redbelly98]

Besides gravity, there is 1 other force acting on each kid.

The kids don't simply fall to the ground. Something prevents them from falling, and that thing is what provides a force other than gravity. What is that thing?

 

[I Like Pi]

Besides gravity, there is 1 other force acting on each kid.

The kids don't simply fall to the ground. Something prevents them from falling, and that thing is what provides a force other than gravity. What is that thing?

well its the them hanging on?

 

[jrab]

it starts with a n and ends with an l

and is also known as t*****n

 

[Redbelly98]

well its the them hanging on?

Yes. Both kids are hanging on to the rope. So, besides gravity, the rope tension also acts on each kid.

 

[I Like Pi]

yes, i know tension is acting on them. so since the second kid exerts a downward force, it results in an upward force on kid 2? Since both forces are the same, they would again result in equilibrium?

 

[Redbelly98]

Yes, the other force is the rope tension.

But, this is not a case of equilibrium, which would mean a net force of zero on each child. That is not what is going on here, they tell you one child is accelerating so the net force is definitely not zero for that child.

Have you drawn free-body diagrams, one for each kid?

If one child is accelerating upward while climbing up the rope, what does that say about the tension, in comparison to the force of gravity? (Tension and gravity are the 2 forces acting on the child.)

 

[I Like Pi]

Yes, the other force is the rope tension.

But, this is not a case of equilibrium, which would mean a net force of zero on each child. That is not what is going on here, they tell you one child is accelerating so the net force is definitely not zero for that child.

Have you drawn free-body diagrams, one for each kid?

If one child is accelerating upward while climbing up the rope, what does that say about the tension, in comparison to the force of gravity? (Tension and gravity are the 2 forces acting on the child.)

Well for kid 1 i got, FT-Fg1 = ma1, while for the other i got Ft-Fg+Fa = ma2, but this confuses me..

 

[Redbelly98]

Well for kid 1 i got, FT-Fg1 = ma1, while for the other i got Ft-Fg+Fa = ma2, but this confuses me..

What is Fa? There is only gravity and rope tension here.

 

[I Like Pi]

What is Fa? There is only gravity and rope tension here.

The applied force? Well, I know that when that kid exerts a downward force, it results in an upward force on the other kid.

 

[Redbelly98]

But the kids are not touching each other. The only way they can apply a force on each other is through the rope tension, which is already accounted for by the Ft terms.

Take the Fa out of your equation in Post #10, and compare ma1 and ma2.