Answer:
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/(
))
