Solve Tension Problem: 2 Objects in 350N Rope, Answer 25s

[iwan97]

Homework Statement

Two objects (2kg and 3kg) are attached by a rope which can withstand maximum tension force of 350N. Forces acting on objects change with time (F=k*t) where k=10N/s.
After how many seconds will rope break. Solution is 25s.

3. Attempt at the solution:

I have tried everything but I can't figure it out. Only thing I was able to calculate was acceleration , a=F_T/m₁+m₂, a=70m/s² but I don't think it's correct.

P.S. Sorry for my english, its not my native language.

 

[haruspex]

Homework Statement

Two objects (2kg and 3kg) are attached by a rope which can withstand maximum tension force of 350N. Forces acting on objects change with time (F=k*t) where k=10N/s.
After how many seconds will rope break. Solution is 25s.
View attachment 112614

3. Attempt at the solution:

I have tried everything but I can't figure it out. Only thing I was able to calculate was acceleration , a=F_T/m₁+m₂, a=70m/s² but I don't think it's correct.

P.S. Sorry for my english, its not my native language.

I do not understand the problem description/diagram.
The diagram shows three forces (F). The middle and right ones have the same subscript, either 2 or z, but the left one looks different. The left and right ones have marked directions, left and right respectively, but the middle one does not.
Which are actual applied forces, and are they equal in magnitude at all times?

 

[iwan97]

I do not understand the problem description/diagram.
The diagram shows three forces (F). The middle and right ones have the same subscript, either 2 or z, but the left one looks different. The left and right ones have marked directions, left and right respectively, but the middle one does not.
Which are actual applied forces, and are they equal in magnitude at all times?

Middle one is F_z or tension force, left one is F₁, right one is F₂. In the middle there is an x sign which is just representing breaking I guess.

 

[haruspex]

Middle one is F_z or tension force, left one is F₁, right one is F₂. In the middle there is an x sign which is just representing breaking I guess.

Are F₁ and F₂ both =kt, same k? If so, why would there be any acceleration?

 

[iwan97]

Yes for both forces =kt. I have no idea really how to start. I know how to work out standard tension problems but this one is really difficult.

 

[TomHart]

Can you verify that the problem is stated correctly. Something doesn't seem right. At 25 seconds, if F = kt, where k = 10, the force(s) would only be 250 N. How could the rope break with 250 N of force?

P.S. Welcome to Physics Forums.
P.S.S. I think your english is very good.

 

[haruspex]

Yes for both forces =kt. I have no idea really how to start. I know how to work out standard tension problems but this one is really difficult.

If the two applied forces are equal and opposite then there is no acceleration. It will take 35 s to reach 350N.

 

[haruspex]

P.S.S. I think your english is very good.

pps. (Smiley)

 

[haruspex]

I can get the desired answer if F₁=kt and F₂=2kt.

 

[iwan97]

I'll try to translate the problem one more time.

Two objects (2kg and 3kg) are attached by a rope which can withstand maximum tension force of 350N. (I hope this part is clear)
Forces are acting on objects and their intensity change with time F=kt, where k is constant (10 N/s). Calculate the length of time from the beginning of the movement until rope breaks.

 

[haruspex]

I'll try to translate the problem one more time.

Two objects (2kg and 3kg) are attached by a rope which can withstand maximum tension force of 350N. (I hope this part is clear)
Forces are acting on objects and their intensity change with time F=kt, where k is constant (10 N/s). Calculate the length of time from the beginning of the movement until rope breaks.

As I indicated, it cannot be that the two forces are supposed to be the same. There would be no acceleration, so it becomes a trivial problem with a different answer.

 

[Chestermiller]

Are there two forces or three forces? Is that force shown between the two masses an externally applied force, or is it just a confusing way of showing that there is tension in the rope.

 

[iwan97]

There 2 forces and in the middle is tension force.

Is there any way you can get 25s ?

 

[gneill]

There 2 forces and in the middle is tension force.

Is there any way you can get 25s ?

There are two ways already mentioned:
1) There is an error in the problem statement where the maximum tension is actually 250 N instead of 350 N, and
2) There is an error in the problem statement where F₁ is not equal to F₂ but rather F₂ = 2F₁ where F₁ = kt.

Otherwise the problem does not have a solution that matches what is given.

 

[iwan97]

There are two ways already mentioned:
1) There is an error in the problem statement where the maximum tension is actually 250 N instead of 350 N, and
2) There is an error in the problem statement where F₁ is not equal to F₂ but rather F₂ = 2F₁ where F₁ = kt.

Otherwise the problem does not have a solution that matches what is given.

In that case thanks for help. I guess there's just something wrong with the problem then.