An art student wants to make a mobile to hang from the ceiling, in which 3 unequ

Question

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. (Hint: taking torques about the point A, how much must X+Y weigh together?) Please show all work! 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. (Hint: taking torques about the point A, how much must X+Y weigh together?) Please show all work!

Explanation / Answer

From the given figure, when the system is under equilibrium the net torque and force becomes zero so about B the net force and torque is zero so x(8cm ) = Y(2cm ) x/y = 1/4 y = 4x and X+Y + W = 0 W = X+Y = x+4x = 5x Now about A 8cm (120g) = 5cm (W) 120*8 = 5*5x therefore x = 120*8 / 25 = 38.4 g and y = 4(38.4) = 153.6g then W = x+y = 192g

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