Reference no: EM132306084

Question - A thin plank of mass M is placed centrally across two solid cylindrical rollers each of mass m, and the system is allowed to move freely from rest without slip down a slope of angle θ as shown in the figure below.

(a) Derive expressions for the initial accelerations of the plank and the roller. Your solution should include the following in a systematic way:

(i) Identification of the types of ensuing motions of the plank and the rollers,

(ii) Free-body, kinematic and kinetic diagrams with an appropriate global axes system clearly shown

(iii) Statements of relevant kinematic and kinetic relationships with reference to your chosen global axes system in (ii)

(iv) Clear, logical and systematic manipulations of the relationships you have stated in (iii) above to arrive at the desired results.

(b) Using the results you have obtained in part (a) (iv) above, explain whether the acceleration of the plank changes as the system moves so that the plank is no longer in the central position.