Three identical blocks connected by ideal strings are being pulled along a horiz

Question

Three identical blocks connected by ideal strings are being pulled along a horizontal frictionless surface by a horizontal force F? . (Figure 1) The magnitude of the tension in the string between blocks B and C is T. Assume that each block has mass m.

Three identical blocks connected by ideal strings are being pulled along a horizontal frictionless surface by a horizontal force F? . (Figure 1) The magnitude of the tension in the string between blocks B and C is T. Assume that each block has mass m. What is the magnitude F of the force? Express the magnitude of the force in terms of T.

Explanation / Answer

Based on your description of the set up, the tension "T" accelerates just the block B and C.
therefore the acceleration of the blocks is a = T / (2M)
The pulling force "F", accelerates all three blocks: A and B, and C. therefore their acceleration
a = F / (3M).

Obviously, the acceleration of the two blocks (B and C0 is the same as the acceleration of the all three block, therefore

T/(2M) = F/(3M)

=> F = (3/2)T

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