(Solved): QUESTION 2 (COMPULSORY, 20 marks) A rigid uniform slender rod AB of length lm and mass mkg is suppo ...

QUESTION 2 (COMPULSORY, 20 marks) A rigid uniform slender rod

of length

and mass

is supported by a second rigid massless

of length

, and a string

, also of length

.

and string

are initially at an angle

to rod

, which is horizontal and stationary, when string

snaps. (a) Draw fully annotated free-body and kinetic diagrams of rod

for the instant immediately after the string snaps, indicating all the relevant forces and moments. (4 marks) (b) Using a rigid body motion analysis: relative acceleration, derive an algebraic expression for the acceleration of the mass centre

relative to the acceleration of pin

, as a function of the angular acceleration

of rod

and angle

. Present the result in vector form. Hint: at the instant that the string snaps,

. (c) Using Newton's laws, derive three additional algebraic equations of motion of the rod

for the instant shown, in terms of the system variables (geometry, mass etc.). (d) Use the equations derived in parts (b) and (c) and the following parameter data:

,

, to determine (i) the force experienced by pin

, (ii) the angular acceleration of the

(i.e.

), (iii) the magnitude of the acceleration experienced by

. (8 marks) (e) Bonus marks: Is the force experienced in rod

tensile or compressive immediately after the string snaps? Give a reason why this is so. The reason needs to be logical otherwise the mark for the tension or compression answer will not be awarded. (Bonus: 2 marks)