Calculating Tension on Strings: Results & Confusion

In summary: After I posted what I did above, I realized that I was assuming too much. The best you can do is solve for how the relative tensions change as ##M_2## increases.
  • #1
Saptarshi Sarkar
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13
Homework Statement
The question is added below
Relevant Equations
##T_1=\frac{(M_1+M_2)}{2}g##
##T_2=\frac{\sqrt 3(M_1+M_2)}{2}g##
##T_3=M_2g##
Screenshot_2020-09-16-21-46-07-11_f541918c7893c52dbd1ee5d319333948.jpg


Attempt:

By drawing the Free Body diagrams and calculating the different tensions, I got the following results

##T_1=\frac{(M_1+M_2)}{2}g##
##T_2=\frac{\sqrt 3(M_1+M_2)}{2}g##
##T_3=M_2g##

But, I am not sure what the answer is as although ##T_2>T_1## but ##T_3## does not depend on ##M_1##. So, I am not able to relate the different tensions to each other.

I guess I can ignore ##M_1## and get the result ##T_3>T_2>T_1##. But, I am not sure about that.
 
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  • #2
Saptarshi Sarkar said:
So, I am not able to relate the different tensions to each other.
Sure you can.

Make use of the fact that ##M_2## > ##M_1## to prove what you already suspect.
 
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  • #3
FYI: I took the statement that the wires are "very strong" to imply that you'll really have to increase ##M_2## >> ##M_1##, so in a sense you are "ignoring" ##M_1##.
 
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  • #4
Doc Al said:
FYI: I took the statement that the wires are "very strong" to imply that you'll really have to increase ##M_2## >> ##M_1##, so in a sense you are "ignoring" ##M_1##.
That may be the thinking behind the question, but it does not really work.
We are not told that ##M_1## is particularly light. Despite the strength of the wires, it could already be the case that the system is close to breaking and ##M_2<(3+2\sqrt 3)M_1## by a sufficient margin that ##W_2## will break first.
 
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  • #5
haruspex said:
That may be the thinking behind the question, but it does not really work.
We are not told that ##M_1## is particularly light. Despite the strength of the wires, it could already be the case that the system is close to breaking and ##M_2<(3+2\sqrt 3)M_1## by a sufficient margin that ##W_2## will break first.
After I posted what I did above, I realized that I was assuming too much. The best you can do is solve for how the relative tensions change as ##M_2## increases.

As always, thanks for your post.
 

Related to Calculating Tension on Strings: Results & Confusion

1. What is tension in a string?

Tension is the amount of force applied to a string, which causes it to stretch or compress. It is measured in units of newtons (N) and is dependent on the mass of the object attached to the string and the acceleration due to gravity.

2. How do you calculate tension in a string?

Tension can be calculated using the formula T = mg, where T is tension, m is the mass of the object, and g is the acceleration due to gravity. In some cases, the formula may need to be adjusted to account for the angle of the string or other external forces.

3. What factors can affect the tension on a string?

The tension on a string can be affected by the mass of the object attached to it, the acceleration due to gravity, the angle of the string, and any external forces acting on the string.

4. Why are there sometimes discrepancies in tension calculations?

Discrepancies in tension calculations can occur due to human error, variations in measurements, or not accounting for all factors that can affect tension. It is important to double-check calculations and consider all possible factors to ensure accuracy.

5. How can we reduce confusion when calculating tension on strings?

To reduce confusion when calculating tension on strings, it is important to carefully follow the steps of the calculation, double-check all measurements and calculations, and consider all possible factors that can affect tension. It may also be helpful to have a second person check the calculations for accuracy.

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