Robin is making a mobile to hang over her baby sister\'s crib. She purchased fou

Question

Robin is making a mobile to hang over her baby sister's crib. She purchased four stuffed animals: a teddy bear (18.9 g), a lamb (20.9 g), a little pony (25.7 g) and a bird (17.7 g). She also purchased three small wooden dowels, each 12.3 cm long and of mass 5.71 g, and thread of negligible mass. She wants to hang the bear and the pony from the ends of one dowel and the lamb and the bird from the ends of the second dowel. Then, she wants to suspend the two dowels from the ends of the third dowel and hang the whole assembly from the ceiling.

a) At what point on the third dowel (or center dowel) should the string (coming from the ceiling) be attached? Give your answer relative to the dowel with the teddy bear and the little pony.

b) At what point on the dowel holding the little pony and the teddy bear - relative to the teddy bear - should the center dowel be attached?

Robin is making a mobile to hang over her baby sister's crib. She purchased four stuffed animals: a teddy bear (18.9 g), a lamb (20.9 g), a little pony (25.7 g) and a bird (17.7 g). She also purchased three small wooden dowels, each 12.3 cm long and of mass 5.71 g, and thread of negligible mass. She wants to hang the bear and the pony from the ends of one dowel and the lamb and the bird from the ends of the second dowel. Then, she wants to suspend the two dowels from the ends of the third dowel and hang the whole assembly from the ceiling. a) At what point on the third dowel (or center dowel) should the string (coming from the ceiling) be attached? Give your answer relative to the dowel with the teddy bear and the little pony. b) At what point on the dowel holding the little pony and the teddy bear - relative to the teddy bear - should the center dowel be attached? c) At what point on the dowel holding the bird and the lamb - relative to the lamb - should the center dowel be attached?

Explanation / Answer

Given,

mass of pony = 25.7 g or 0.257 kg

mass of teddy bear = 18.9 g or 0.189 kg

mass of bird = 17.7 g or 0.177 kg

mass of lamb = 20.9 g or 0.209 kg

length of dowel = 12.3 cm or 0.123 m

mass of dowel = 5.71 g or 0.0571 kg

mass on each side of the center dowel

Mleft = mass of pony + mass of dowel + mass of teddy

Mleft = 0.257 + 0.189 + 0.0571

Mleft = 0.5031 kg

Mright = mass of lamb + mass of bird + mass of dowel

Mright = 0.177 + 0.209 + 0.0571

Mright = 0.4431 kg

equating the moment on both the sides on center dowel

Mleft * x = Mright * (0.123 -x) +Mdowel * (0.123/2 - x)

0.5031 * x = 0.4431 * (0.123 -x) + 0.0571 * (0.123/2 - x)

x = 0.05782 m

point on the third dowel should the string be attached = 0.05782 m

mass of teddy * x = mass of pony * (0.123 -x) + 0.0571 * (0.123/2 - x)

0.189 * x = 0.257 * (0.123 -x) + 0.0571 * (0.123/2 - x)

x = 0.06981 m

point on the dowel holding the little pony and the teddy bear = 0.06981 m

mass of bird * x = mass of lamb * (0.123 -x) + 0.0571 * (0.123/2 - x)

0.177 * x = 0.209 * (0.123 -x) + 0.0571 * (0.123/2 - x)

x = 0.06594 m

point on the dowel holding the bird and the lamb - relative to the lamb = 0.123 - 0.06594

point on the dowel holding the bird and the lamb - relative to the lamb = 0.05706 m

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