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Relative Velocity

Two blocks ar...

Question

Two blocks are connected by a string as shown in the figure. The upper block is hung by another string.
1) What will be the tension in the upper string due to the two blocks suspended in rest position?
2) What force F will have to be applied on the upper string to produce an acceleration.

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Solution

We have,

Two blocks $m_{1} = 2 k g, m_{2} = 4 k g$

Let the two blocks like one.

So force equation for the motion of the combination is given as:

$F - (m_{1} + m_{2}) g = (m_{1} + m_{2}) a$

$T = (m_{1} + m_{2}) (g + a)$ Where T is the tension and g is the acceleration due to gravity.

Bu putting the values

$T = (2 + 4) (9.8 + 2)$

$T = 70.8 N$

Now, consider the motion of the lower block

$T^{'} - m_{1} g = m_{1} a$

$T^{'} = m_{1} (g + a)$

By putting the values

$T^{'} = 4 (9.8 + 2)$

$T^{'} = 47.2 N$

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