A force table is a circular table with a small ring that is to be balanced in th

Question

A force table is a circular table with a small ring that is to be balanced in the center of the table. The ring is attached to three hanging masses by strings of negligible mass that pass over frictionless pulleys mounted on the edge of the table. The magnitude and direction of each of the three horizontal forces acting on the ring can be adjusted by changing the amount of each hanging mass and the position of each pulley, respectively. Given a mass m1 = 0.038 kg pulling in the positive x-direction, and a mass m2 = 0.056 kg pulling in the positive y-direction, find the mass (m3) and the angle that will balance the ring in the center of the table.

Explanation / Answer

net force along X-axis is Fx = m1*a = m3*a*cos(theta)

m1 = m3*cos(theta).....(1)

net force along the Y-axis is Fy = m2*a = m3*a*sin(theta)...

m2 = m3*sin(theta).......(2)

(2)/(1)

tan(theta) = (m2/m1) = 0.056/0.038 = 1.47

theta = atan(1.47) = 55.84 degrees above the +x-axis

m3 = m1/cos(55.84) = 0.038/cos(55.84) = 0.0676 kg

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