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 (20.3 g), a lamb (22.9 g), a little pony (27.3 g) and a bird (17.7 g). She also purchased three small wooden dowels, each 15.5 cm long and of mass 3.75 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

rom the given problem, it is understood that the entire dowel system is in the shape of a letter "H" roughly , when seen from top.

Each line corresponds to a dowel, the horizontal line is the middle dowel. and at 4 ends , 4 toys are hung.

For solving this problem, we use "net torque = 0" , because is at rest and in level.

From here, we indicate mass of Teddy bear = T = 20.3 g

Lamb = L = 22.9 g

Pony = P = 27.3 g

Bird = B = 17.7 g

Dowel = D = 3.75g

Length of dowel = l =15.5 cm

A) Let our required distance be "a".

Now , we apply "net torque = 0 " about the joint. Here , torque is caused by only masses. "m*g*d".

(Mass of dowel should also be included. COM of dowel should be considered seperately for either sides.)

So, we get P*g*a + D*(a/l) *(a/2)*g = T*g*(l-a) + D*(l-a/l) *(l-a)/2 *g (cancel "g" on both sides and solve for "a".)

(P+T+D)*a = (T + D/2)*l

So, a = l*(T + D/2) / (P+T+D)

a = 6.69 cm

B) Similaly, we calculate "b".

B*g*b + D*(b/l) *(b/2)*g = L*g*(l-b) + D* (l-b/l) *(l-b)/2 *g (cancel "g" on both sides and solve for "b".)

(B+L+D)*b = (L + D/2)*l

So, b = l*(L + D/2) / (B+L+D)

b = 8.66 cm

C) Again , we assume "c"

Let total mass on first dowel =F = D+T+P =51.35 g

Let total mass on second dowel = S = D+L+B = 44.35 g

SO we get, F*g*c + D*(c/l) *(c/2)*g = S*g*(l-c) + D*(l-c/l) *(l-c)/2 *g (cancel "g" on both sides and solve for "c" ).

(F+S+D)*c = (S + D/2)*l

So, c = l*(S + D/2) / (F+S+D)

c = 7.21 cm

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