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 (16 g), a lamb (18 g), a little pony (22 g) and a bird (15 g). She also purchased three small wooden dowels, each 13 cm long and of mass 7 g, and thread of negligible mass. She wants to hang the bear and the pony from the ends of the first 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 middle dowel and hang the whole assembly from the ceiling. Find where the middle thread should be attached to the middle dowel and where the ends of the middle dowel should be attached to the first and second dowel so that the entire assembly will hang level.

A)What is the distance from the end from which the Little Pony is suspended to the point where the first dowel is attached to the middle dowel?

B)What is the distance from the end from which the Bird is suspended to the point where the second dowel is attached to the middle dowel?

C)What is the distance from the end from which the middle thread is attached to the point where the first dowel is attached to the middle dowel?

-If somone could break down the problem I would really appreciate it.

Explanation / Answer

From 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 = 16 g

Lamb = L = 18 g

Pony = P = 22 g

Bird = B = 15 g

Dowel = D = 7g

Length of dowel = l =13 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)

= 169 / 30 cm

a = 5.633 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)

= 559 / 80 cm

b = 6..9875 cm

C) Again , we assume "c"

Let total mass on first dowel =F = D+T+P = 45 g

  Let total mass on second dowel = S = D+L+B = 40 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)

= 1131/ 184 cm

c = 6.146 cm

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