To better understand the concept of static equilibrium a laboratory procedure as
ID: 1356094 • Letter: T
Question
To better understand the concept of static equilibrium a laboratory procedure asks the student to make a calculation before performing the experiment. The apparatus consists of a round level table in the center of which is a massless ring. There are three strings tied to different spots on the ring. Each string passes parallel over the table and is individually strung over a frictionless pulley (there are three pulleys) where a mass is hung. The table is degree marked to indicate the position or angle of each string. There is a mass m1 = 0.157 kg located at 1 = 26.5° and a second mass m2 = 0.215 kg located at 2 = 275°. Calculate the mass m3, and location (in degrees), 3, which will balance the system and the ring will remain stationary.
Explanation / Answer
given ,
m1 = 0.157 kg
m2 = 0.215 kg
theta 1 = 26.5 degrees
theta 2 = 275 degrees
w1 = mass1*gravity
= 0.157*9.8
=1.539 N
w2 = mass2*gravity
= 0.215*9.8
= 2.107 N
m2 angle= (theta 2 - theta 1)
= (275 - 26.5)
= 248.5 degrees
South west = (248.5 - 180)
= 68.5 degrees
West component = (sin 68.5)*w2
= (sin 68.5) x 2.107
= 1.96N
South component of m2 = (cos 68.5) * w2
= (cos 68.5) * 2.107
= 0.772 N.
North = W1 - South component
= 1.539 - 0.772
= 0.767N.,
W3 = sqrt. (1.96^2 + 0.767^2),
= 2.105N
w3 / g = 2.105 / 9.8
= 215 g
theta = tan^-1 (0.767 / 1.96)
= 21.4 degrees (south of east)
theta 1 in clockwise, (26.5 + 21.4 + 90) = 137.9 degrees
m3 = 215g.
90 degrees from North
21.4 degrees from East
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