Why Isn't the String's Mass Included in Block B's Tension?

[516aldnsdhfl]

Homework Statement

In the diagram above, a massless string connects two blocks- of masses m1(left) and m2(right), respectively- on a flat frictionless tabletop. A force F pulls on Block A, as shown.

If the string connecting the blocks were not massless, but instead had a mass of m, figure out the acceleration of block B.

Homework Equations

F = ma
Ft for block B = ma
F-Ft for block A = ma

The Attempt at a Solution

I attempted to stick the string's mass to the Ft for block b, and got the right answer, but the concept is wrong. The answer key says that the F to the very right just pulls on the string's mass, block A's mass, and block B's mass all together.

Why is the mass of string not included in the block B's tension to the right?

 

[PhanthomJay]

Homework Statement

In the diagram above, a massless string connects two blocks- of masses m1(left) and m2(right), respectively- on a flat frictionless tabletop. A force F pulls on Block A, as shown.

If the string connecting the blocks were not massless, but instead had a mass of m, figure out the acceleration of block B.

Homework Equations

F = ma
Ft for block B = ma
F-Ft for block A = ma

The Attempt at a Solution

I attempted to stick the string's mass to the Ft for block b, and got the right answer, but the concept is wrong. The answer key says that the F to the very right just pulls on the string's mass, block A's mass, and block B's mass all together.

Why is the mass of string not included in the block B's tension to the right?

What you are calling Ft for block B and Ft for block A are not the same (there must be a tension change along the length of the string with mass). Draw a free body diagram of Block B alone. Does the mass of the string enter into Newton's 2nd law equation?