A block with mass M lies on a slippery horizontal surface. On top of it there is another block with mass m which in turn is attached to an identical block by a string. The string has been pulled acros

Question

A block with mass M lies on a slippery horizontal surface. On top of it there is another block with mass m which in turn is attached to an identical block by a string. The string has been pulled across a pulley situated at the corner of the big block and the second small block is hanging vertically. Initially, the system is held at rest. Find the acceleration of the big block immediately after the system is released. You may neglect friction, as well as masses of the string and the pulley. (Take $m = 1 kg, M = 2 kg$ )

Answer:

2

Solution:

String constraint: $(M + m) a = m a_{1} \Rightarrow 3 a = a_{1}$ .

For the hanging block: $m g - T = m (a_{1} - a)$ ... combining with the block on top: $m g + ma = 2 m a_{1}$ .

$10 + a = 2 a_{1} = 6 a \Rightarrow 10 = 5 a$

$a = 2$ m/s $^{2}$

TestHub · Accepted Answer

String constraint: ( M + m ) a = m a 1 ​ ⇒ 3 a = a 1 ​ . For the hanging block: m g − T = m ( a 1 ​ − a ) ... combining with the block on top: m g + ma = 2 m a 1 ​ . 10 + a = 2 a 1 ​ = 6 a ⇒ 10 = 5 a a = 2 m/s 2

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