Your friend, Bill, has built a \"mobile\" to hang over his infant daughter\'s cr

Question

Your friend, Bill, has built a "mobile" to hang over his infant daughter's crib. He has built it as instructed -- he thinks, but it won't hang properly. (He purchased the decoration from Ikea.)

Here's what it looks like.

It is 60.0 cm long and is supposed to be able to hang with the connector located at the mid-point -- the 30.0 cm mark. All the bears are equally spaced apart.

mLarge = 0.300 kg, the mass of the two larger bears

mSmall = 0.150 kg, the mass of the two smaller bears

The suspending bar is made of Photonium, which is infinitely strong and has no mass.

(A) You notice that it is possible to adjust the position of the hanger. Determine the horizontal location of the center of mass of the system.

xCM = _____cm

(B) In the assembly instructions, you noticed that Bill could have purchased the Platinum Upgrade, where the suspension bar is actually made out of platinum, which is nearly twice as dense as lead. How would changing the suspension bar in that manner affect the location of the connection point?

Please show work.

Explanation / Answer

let

m1 = 0.15 kg, x1 = 0

m2 = 0.3 kg, x2 = 0.15 m

m3 = 0.15 kg, x3 = 0.45 m

m4 = 0.3 kg, x4 = 0.6 m

A) Xcm = (m1*x1 + m2*x2 + m3*x3 + m4*x4)/(m1+m2m3+m4)

= (0.15*0 + 0.3*0.15 + 0.15*0.45 + 0.3*0.6)/(0.15 + 0.3+0.15 + 0.3)

= 0.325 m

= 32.5 cm

B) The center of mass would be in between 30 cm and 32.5 cm

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