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.

Tu

A mass of m1=0.157 kgm1=0.157 kg is located at θ1=24.5∘θ1=24.5∘ , and a second mass of m2=0.215 kgm2=0.215 kg is located at θ2=283∘θ2=283∘ . Calculate the mass m3 and the angular position θ3(in degrees) that will balance the system and hold the ring stationary over the center of the platform.

m3: ____kg

theta3: _____degrees

Answer 1

Fx + m1g cos(theta_1) + m2g cos(theta_2) = 0

Fx + (0.157 x 9.8 cos(24.5)) + (0.215 x 9.8 cos(283)) = 0

Fx = - 1.87 N

Similarly,

Fy + (0.157 x 9.8 sin(24.5)) + (0.215 x 9.8 sin(283)) = 0

Fy = 1.41 N

F = sqrt(Fx^2 + Fy^2) = 2.34 N

Mass, m = 2.34/9.8 = 0.24 kg

B)

Theta = 180 - arctan(Fy/Fx) = 142.9°

Comment in case any doubt please rate my answer....