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(A) Let the acceleration of block $A$ be $a_A$ towards the left and the acceleration of block $B$ be $a_B$ towards the left. From the constraint relat

Vedclass · Accepted Answer

$a_B = \frac{F}{10 m} 	ext{ m/s}^2$

Vedclass · Answer

(A) Let the acceleration of block $A$ be $a_A$ towards the left and the acceleration of block $B$ be $a_B$ towards the left. From the constraint relation,the length of the string is $L = x_A + x_B + x_B + x_B = x_A + 3x_B$ (considering the relative motion of the pulleys). Differentiating twice with respect to time,we get $a_A = 3 a_B$. For block $A$ (mass $2m$): $F - 2T = (2m) a_A = (2m)(3 a_B) = 6m a_B$  --- $(1)$ For block $B$ (mass $4m$): $2T = (4m) a_B$ --- $(2)$ Adding equations $(1)$ and $(2)$: $F = 6m a_B + 4m a_B = 10m a_B$ Therefore,$a_B = \frac{F}{10m} 	ext{ m/s}^2$.

Calculate the acceleration of the block $B$ in the figure,assuming the surfaces and the pulleys $P_1$ and $P_2$ are all smooth and the pulleys and string are massless.

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