Question

A laboratory on the concept of static equilibrium uses an apparatus called a force table. The force table consists of a round, level platform marked in degree increments about its circumference. In the center of the table sits a massless ring, to which three strings are tied. Each string is strung over a separate pulley clamped to the edge of the platform, and then tied to a freely-hanging mass, so that each string is under tension and the ring is suspended parallel to the table surface.

A mass of ?1=0.157 kg is located at ?1=22.5∘, and a second mass of ?2=0.211 kg is located at ?2=279∘ . Calculate the mass ?3 and the angular position ?3 (in degrees) that will balance the system and hold the ring stationary over the center of the platform.

Answer 1

|F1|= 0.157x9.8N

F1=1.5386cos22.5 i + 1.5386sin22.5j = 1.4215 i + 0.5888 j

|F2| = 0.211x9.8N

F2=-2.0678cos9 j + 2.0678sin9 i = -2.0423 j + 0.3235i

let F3 be p i+q j

For equilibrium, F1+F2+F3 =0

p= -(1.4214+0.3235) and q =(2.0423-0.5888)

F3= -1.745 i + 1.4535 j

|F3| = 2.271

m3 = 2.271/9.8 kg = 0.232kg

let the angle between -x axis and F3 be .

2.271cos = 1.745

cos= 0.76838397181

=39.8^o

So angle from the +x axis = 180-39.8 =140.2^o