Determine a formula for the magnitude of the force F exerted on the large block (Mc) so that the mass Ma does not move relative to Mc. Ignore all friction. Assume Mb does not make contact with Mc.

The magnitude of the force F is given by

F =  ( + + ) *(*g/())

Explanation:

Given there are three blocks of masses , and (ref image in attachment)

When all three masses move together at an acceleration a, the force F is given by

F =  ( + + ) *a    ................(equation 1)

Also it is given that does not move with respect to , which gives tension T  is exerted on pulley  by only, Hence tension T is

T = *a    ..........(equation 2)

There is also also tension exerted by . There are two components here: horizontal due to acceleration a and vertical component due to gravity g. Thus tension is given by

T =   ................(equation 3)

From equation 2 and 3, we get

*a  =  

Squaring both sides we get

* = * (+)

* = ( * )+ ( *)

(  -  ) * = *

= */(  -  )

Taking square root on both sides, we get acceleration a

a = *g/()

Hence substituting the value of a in equation 1, we get

F =  ( + + ) *(*g/())

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