Relation between Tension and net force

AI Thread Summary
Understanding the relationship between tension and net force involves analyzing the forces acting on connected masses. When a force K Newtons is applied to mass A, it affects both masses A and B through the tension in the rope. The tension can be determined by setting up the equation K - T = F(AR), where T is the tension and F(AR) is the force exerted by mass A on the rope. This equation illustrates that the net force acting on the system is equal to the applied force minus the tension. Physically, the rope transmits the force applied to mass A to mass B, creating an equal and opposite reaction, which is fundamental to Newton's third law.
Mr.Y
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I am having a lot of difficulty understanding this concept.

Suppose you have two objects A,B of mass A',B' connected by a massless rope. Let K Newtons be the force applied on object A .What is now the tension along the rope ?


-My reasoning:

K Newtons is the force applied to the combination of masses A'+B' ,now to find the tension along the rope we have to find the forces acting on the rope.

Applying a force to object A we have by Newton's third that F (AR)=-F(RA) where AR denotes the force of A on the rope and viceversa.

Similarly, F(BR)=-F(RB) .

So the forces acting on the ropes are -F(RA)-F(RB)=F(BR)+F(AR) ,since the rope is massless I have that F(BR)=F(AR) so I just need to find one of these two forces to find the tension.

Now this is the part that's really confusing to me :we could have also found the tension by setting up the equation K-T=F(AR) ,where T denotes the tension. So solving the last equation we find the tension along the rope,but why ?
Can you give me both an intuitive argument and also show me where this follows from just mathematical formalism ? (I hope I am not asking too much )
 
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The question is poorly defined but let us assume that masses are sitting on a level plane and that there are no friction forces acting .

When the force is applied to mass A what do you expect to happen physically ?
 
I would expect the rope to exert the same force to object A in the opposite direction.
(Yes sorry I have forgot to define if there's friction and the direction of the forces,bear with me !)
 
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