2. a.) An art student wants to make a mobile to hang from the ceiling, in which

Question

2. a.) An art student wants to make a mobile to hang from the ceiling, in which 3 unequal objects will balance each other. His first object weighs 120 grams. Calculate the 2 unknown weights, X and Y, so his mobile will just balance. Use the distances given in the diagram, and assume that the weight of connecting strings and wires can be neglected. 8 cm 5 cm 4 cm 6 cm 8 cm 1 cm cm gm 3 cm (Hint: taking torques about the point A, how much must X + Y weigh together?) b.) Is there more than one possible solution for the preceding problem? Answer yes or no, and explain with one or two sentences.

Explanation / Answer

a) The tension in the rope of 6 cm will be (Wx + Wy)*g

hence balancing torque about point A,

120*g*8 = (Wx + Wy)*g*5

Wx + Wy = 192 ----(i)

now balancing torque about the point connecting weights X and Y.

Wx*g*8 = Wy*g*2

Wy = 4 Wx ----(ii)

from equations i and ii,
Wx = 38.4 grams.

Wy = 4*38.4 = 153.6 grams.

b)

No, there is only one possible answer as all the above equations are linear and have only one solution.

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