Value of frictional forces in a 3-block system

[Physics lover]

Homework Statement

Find the values of f1 and f2 in the given figure.

Relevant Equations

Free body Diagram

So I started by checking the options.I substituted the value of friction in the equations I got by making free body diagrams.I got different value of Tensions.For 1 and 3 Tension came to be 38 N.For 2 Tension came out to be 42N and for 4 Tension came out to be 40 N.
Now I think that I will take 1 and 3.As tension is minimum there.And since we get same value of acceleration of block 3 downwards,we will go with option 3.Because friction will be less than its maximum value.
Is my explanation correct?Please tell.

 

[haruspex]

What are these 1, 2, 3 and 4 you refer to? Do you mean A, B, C and D?
What equations are you plugging the values of friction into?
How did you arrive at the tensions you calculated?
Have you tested your solution in respect of each of the three masses?

 

[nrqed]

Homework Statement:: Find the values of f1 and f2 in the given figure.
Relevant Equations:: Free body Diagram

View attachment 260813

So I started by checking the options.I substituted the value of friction in the equations I got by making free body diagrams.I got different value of Tensions.For 1 and 3 Tension came to be 38 N.For 2 Tension came out to be 42N and for 4 Tension came out to be 40 N.
Now I think that I will take 1 and 3.As tension is minimum there.And since we get same value of acceleration of block 3 downwards,we will go with option 3.Because friction will be less than its maximum value.
Is my explanation correct?Please tell.

It is not correct. There is no physical reason to base an answer on the "minimum tension", this is not a valid criterion.

Note that to answer the question, it turns out that you do not need to calculate the tension in the rope at all. You don't need the acceleration either. Look carefully at the information provided.

 

[Physics lover]

What are these 1, 2, 3 and 4 you refer to? Do you mean A, B, C and D?
What equations are you plugging the values of friction into?
How did you arrive at the tensions you calculated?
Have you tested your solution in respect of each of the three masses?

Yes I was referring to Option a,b,c,d.

 

[Physics lover]

It is not correct. There is no physical reason to base an answer on the "minimum tension", this is not a valid criterion.

Note that to answer the question, it turns out that you do not need to calculate the tension in the rope at all. You don't need the acceleration either. Look carefully at the information provided.

So we should go with friction.
If both f1 and f2 are 20 N they can stop the motion.So I will go with option d).As if friction can stop the motion at its value less than or equal to static friction,it takes that value.Am i correct?

 

[haruspex]

So we should go with friction.
If both f1 and f2 are 20 N they can stop the motion.So I will go with option d).As if friction can stop the motion at its value less than or equal to static friction,it takes that value.Am i correct?

As I sort of hinted at the end of post #4, it is worth looking at each of the bodies. In particular, consider the suspended mass. What is the maximum possible tension according to the forces on that?

 

[Physics lover]

As I sort of hinted at the end of post #4, it is worth looking at each of the bodies. In particular, consider the suspended mass. What is the maximum possible tension according to the forces on that?

Maximum Possible tension I got by solving the equations was 42 N.
The equations were-:
For the suspended block-:40-T=4a
For left block-:T/2-20=4a₁
For right block-:T/2-28=4a₂
And a=(a₁-a₂)/2

 

[haruspex]

Maximum Possible tension I got by solving the equations was 42 N.

No, I said to consider just the suspended mass. What would happen to that if the tension were 42N?

 

[Physics lover]

No, I said to consider just the suspended mass. What would happen to that if the tension were 42N?

It will move upwards.But is that possible?

 

[haruspex]

It will move upwards.But is that possible?

Clearly it is not, so what, on that basis, is the maximum possible tension?

 

[Physics lover]

Clearly it is not, so what, on that basis, is the maximum possible tension?

40 N!

 

[Physics lover]

40 N!

So my answer would be f2=f2=20N.Is that correct?

 

[haruspex]

So my answer would be f2=f2=20N.Is that correct?

I think you mean the max upward force on the suspended mass is 40N, so the max tension is 20N. But yes, that's the quickest way to the answer.

 

[Physics lover]

I think you mean the max upward force on the suspended mass is 40N, so the max tension is 20N. But yes, that's the quickest way to the answer.

yes i meant that only.So tension in strings attached left and right block will be 20N.So f1=f2=20N.

 

[SammyS]

yes i meant that only.So tension in strings attached left and right block will be 20N.So f1=f2=20N.

Yes.