You are building a toy mobile with cups, copying the design shown in the figure

Question

You are building a toy mobile with cups, copying the design shown in the figure (Figure 1) . The bottom rod is 20 cm long, the middle rod is 15 cm long, and the top rod is 8 cm long. You put one penny in the bottom left cup, three pennies in the bottom right cup, eleven pennies in the middle right cup, and five pennies in the top left cup.

a) Determine the cord attachment point for the bottom rod. Ignore the masses of the rod and the cups. (x)

b) Determine the cord attachment point for the middle rod. Ignore the masses of the rod and the cups. (y)

c) Determine the cord attachment point for the top rod. Ignore the masses of the rod and the cups.

Explanation / Answer

the basic aim is to balance the whole structure so that it may not rotate about the attachment point.

consider first the bottom rod   one penny in the bottom left cup, three pennies in the bottom right cup,

therefore position of x is 3/4 of 20 cm from the bottom left cup which is equal to 15 cm from the bottom left cup.

consider middle rod   eleven pennies in the middle right cup,

therefore position of y is 11/15 of 15 cm from the left portion of middle rod which is equal to 11 cm from the left portion of middle rod.

consider top rod . five pennies in the top left cup.

therefore position of z is 15/20 of 8 cm from the top left cup which is equal to 6 cm from the top left cup.

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