A light is hung from the ceiling with two ropes of unequal length. The ropes are

Question

A light is hung from the ceiling with two ropes of unequal length. The ropes are attached to a metal ring, and then the light is hung from the ring. The angles the ropes hang from the vertical direction are theta_1 = 10 degrees and theta_2 = 25 degrees. On the picture, these are the angles between the ropes and the vertical dashed line. The masses of the ropes and ring are very small so can be neglected. The tension in rope 1 is measured to be T_1 = 10.0 N. What is the mass of the light? Give your answer in kg. Give your results to at least three significant digits. The number of significant digits is not graded, this is just to avoid the answer being counted as incorrect because of rounding.

Explanation / Answer

Vertical components are T1sin [ heta] and T2sin [ heta]

Horizontal component T1cos [ heta] and T2cos [ heta]

By arrangement horizontal componenets are opposite to each other so

T1cos [ heta] = T2cos [ heta]

so, (10.0)cos10 = T2cos25

T2 = 10.85 N

Now equation of forces in vertical direction

T1sin [ heta] + T2sin [ heta] = mg

(10.0)sin10+ (10.85)sin25 = m(9.8)

6.73 = m(9.8)

m = 6.73/9.8 = 0.6867 kg

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