Kinematics: Understanding Tension in Strings

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Understanding tension in strings involves recognizing the forces acting on each mass in a system. When a string holds a mass that in turn holds another mass, the tension in the first string (T1) must equal the sum of the weight of the first mass (m1g) and the tension from the second string (T2). The second mass's weight (m2g) also contributes to the tension in the system, necessitating separate equations for each mass to maintain equilibrium. Therefore, T1 must balance the forces acting on mass1, while T2 is determined solely by the weight of mass2. This approach clarifies the relationship between tensions and the weights of the masses involved.
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I am trying to self learn kinematics , but i don't understand a certain concept :-


If a string hold a mass which in turn holds another mass by a string.

by F.B.D to in forming the first equation , we take T1 = m1g +t2

but shouldn't the second mass be included as well.

eg. if we are hanging something with a thread and someone hangs another string and mass to it , the strain on the first string is increases .

I am sorry for the vague outline i could give , hope you can understand it .
 
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Wouldn't that be included in the expression for T2?

T1 is the force needed to keep mass1 in equilibrium.
The forces actually "attacking" mass1 are the two tensions and its own weight.

T1 must be equal to, and oppositely directed to the sum of the two other forces attacking mass1.
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Thus, when you do this problem, always keep in mind that we are tracking the forces attacking some material OBJECT, and we set up our equations for each object SEPARATELY.

Thus, you will ALSO have the equation:
T2=m2g, in order to keep mass2 in equilibrium.
 
For simple comparison, I think the same thought process can be followed as a block slides down a hill, - for block down hill, simple starting PE of mgh to final max KE 0.5mv^2 - comparing PE1 to max KE2 would result in finding the work friction did through the process. efficiency is just 100*KE2/PE1. If a mousetrap car travels along a flat surface, a starting PE of 0.5 k th^2 can be measured and maximum velocity of the car can also be measured. If energy efficiency is defined by...

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