Answer to Question #157195 in Mechanics | Relativity for Darren

Question

A particle of mass mkg lies on a smooth plane inclined at an angle 30^o to the horizontal. The particle is attached to a light inextensible string which passes over a smooth pulley fixed at the top of the plane. Anothet particle of mass 3mkg is attached to the other end of the string and hangs freely. The system is released from rest with the string taught and the hanging part vertical. Find in terms of m and g,
(a) the acceleration of the system and the tension in the string
(b) the magnitude of the reaction force exerted by the string on the pulley.

Answer 1

Answer

Equation for 3 kg mass can be written as

$3mg-T=ma$ ...

Eq. 1

And for m kg mass

$T-mgsin30°=ma$

By putting the value of Tension T from equation 1

$3mg-ma-mgsin30°=ma\\2ma=3.5mg\\a=\frac{7}{4}g \quad m/s^2$

(2)

Tention in string

$T=1.25mg$

Reaction on pully

$R=\sqrt{T^2+T^2+2T^2cos60°}\\R=\sqrt{3}T$

And

$R=2.16mg \quad N$