# Deriving Expression for Block Configuration

See attached file.

Three blocks are configured as in the attachment. A string is attached from block #1 to block #2 (looped over a pulley), and the angle between the string going from mass #2 to the pulley, with respect to straight downward, is θ (block #2 is hanging there, not touching block #3). An external force F is pushing on block #3.

(a) Derive an expression for F such that θ does not change with time and block #1 does not move with respect to block #3 (in other words, the whole configuration remains the same as it accelerates to the right). Ignore friction throughout the problem.

(b) Is it possible for this configuration to remain if M2>M1? Explain your reasoning.

(c) Now suppose there is a friction between block #1 and block #2, given by F(f)=μ(s)M(1)g. Rederive an expression for F.

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#### Solution Preview

See attached file.

For three blocks together:

F = (m1+M2+M3)*a ..............(1)

where a is the acceleration to be calculated so that system acts as a single entity.

See free body diagram in attached jpg file.

For M1 block, along the horizontal direction:

T = M1*a ........(2)

For M2 block, in vertical direction:

T*cos(Q) = M2*g .............(3)

and in horizontal direction:

T*sin(Q) = M2*a ......(4)

From eqn(2) substitute the ...

#### Solution Summary

The problem shows all the workings to arrive at the solutions.