Mathematical Methods and Mechanics

Question 4

A particle of mass z lies on a frictionless plane which is inclined at an angle of f r to the horizontal as shown in Figure Q4. The particle is connected by a light inextensible string, passing over a small light frictionless pulley at the top of the inclined plme, to a second particle of mass rc, which is hanging freely. When release from rest, the hanging particle moves downwards.

(a)

(b)

(c)

Fisure 04

Drawtwo force diagrams showing all the forces acting on each of the two particles.

(4 marks)

Write down the equations of motion of each of the two particles. (5 marks)

Find the coflrmon acceleration ofthe two particles and the tension in the string in terms of m andg, the magnitude of the acceleration due to gravity.

(4 marks)