Question

How to solve the 31st question?

Answer 1

See below.

Explanation:

Supposing that the B rod end glides without detaching from the wall, we have

`x_A = l cos theta`
`y_B = l sin theta`

and deriving

`dot x_A = v_A = -l sin theta dot theta`
`dot y_B = v_B = l cos theta dot theta`

and also

`ddot x_A = a_A = -l(dot theta)^2cos theta -lsin theta ddot theta`
`ddot y_B = a_B = -l (dot theta)^2sin theta+ l cos theta ddot theta`

Solving after eliminating `dot theta` we have

`a_B =-(a_A Cot theta + (v_A^2 Csc^3 theta)/l)`

`ddot theta = -1/l^2(a_A l csc theta+ v_A^2 cot thetaCsc^2 theta)`