Question

A mobile is constructed of light rods, light strings, and beach souvenirs as shown in the figure below. If m4 = 12.0 g, find values for the following. (Let d1 = 3.60 cm, d2 = 5.10 cm, d3 = 1.80 cm, d4 = 5.20 cm, d5 = 3.70 cm, and d6 = 4.60 cm.)

(a)    m₁ =  

(b)    m₂ =  

(c)    m₃ =  

Answer 1

m₁ = ?

m₂ = ?

m₃ = ?

m₄ = 12 g

For the lowest rod,

Distance of m₁ from the support string of the lowest rod = d₆ = 4.6 cm

Distance of m₄ from the support string of the lowest rod = d₅ = 3.7 cm

Balancing the moment of the lowest rod about the point where the support string is attached,

m₁d₆ = m₄d₅

m₁(4.6) = (12)(3.7)

m₁ = 9.65 g

For the middle rod,

Distance of m₂ from the support string of the middle rod = d₃ = 1.8 cm

Distance of the string supporting the lowest rod from the support string of the middle rod = d₄ = 5.2 cm

Balancing the moment of the middle rod about the point where the support string is attached,

m₂d₃ = (m₁ + m₄)d₄

m₂(1.8) = (9.65 + 12)(5.2)

m₂ = 62.54 g

For the topmost rod,

Distance of m₃ from the support string of the topmost rod = d₂ = 5.1 cm

Distance of the string supporting the middle rod from the support string of the topmost rod = d₁ = 3.6 cm

Balancing the moment of the topmost rod about the point where the support string is attached,

m₃d₂ = (m₁ + m₂ + m₄)d₁

m₃(5.1) = (9.65 + 62.54 + 12)(3.6)

m₃ = 59.43 g

a) m₁ = 9.65 g

b) m₂ = 62.54 g

c) m₃ = 59.43 g