Everything is in balance. Let\'s say the right side block of the balance is equa

Question

Everything is in balance. Let's say the right side block of the balance is equal to the mass of both blocks on the left side of the balance. However, the left side of balance has a pulley system with a LATCH holding both blocks in place. In this pulley, one block is bigger than the other.

The question is If the latch were to be removed what will happen? Will the balance keep in balance or will it not, For either response please explain. If there is a physics equation to see this that would be helpful.

Explanation / Answer

once the latch is removed, the two blocks in the pulley will start moving.

let tension in the rope connecting the two masses is T and acceleration of the system is a .

let mass of smaller block is m kg and bigger block is M kg.

writing force balance equation for bigger block:

M*g-T=M*a...(1)

writing force balance equation for smaller block:

T-m*g=m*a...(2)

adding equation 1 and equation 2:

g*(M-m)=(M+m)*a

==>a=g*(M-m)/(M+m)

using this value of a in equation 1,

T=M*(g-a)

=M*g*(1-((M-m)/(M+m))

=2*m*M*g/(M+m)

total tension in the left side of the balance=T+T=2*T=4*m*M*g/(M+m)

weight of the right side balance is (M+m)*g

so left and right side will be balanced only when M=m which is not the case

hence the balance wont be balanced.

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