a boy and a girl are at rest on separate skis 12 m apart on a horizontal icy surface. the boy and his skis have twice the inertia of the girl and her skis. determine the location of the center of mass in meters measured from the position of the girl.

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21-10-2022
Physics

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a boy and a girl are at rest on separate skis 12 m apart on a horizontal icy surface. the boy and his skis have twice the inertia of the girl and her skis. determine the location of the center of mass in meters measured from the position of the girl.

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ayune ayune · Answer 1 · 2022-10-29T23:17:27-04:00

With the position of the girl as a reference point, the center of mass is 8 m from the girl position.

If there are two objects as shown on the attached picture, the center of mass is:

xc = m₁ / (m₁ + m₂) . x₁ + m₂ / (m₁ + m₂) . x₂

From the problem, we know that the boy and his skis have twice the inertia of the girl and her skis. We can replace the mass in the equation with inertia, hence:

xc = I₁ / (I₁ + I₂) . x₁ + I₂ / (I₁ + I₂) . x₂

Let:

I₁ = the girl's inertia

I₂ = the boy's inertia

Hence,

I₂ = 2 I₁

Let make the position of the girl as a reference point, then,

x₁ = 0

x₂ = 12

Plug these parameters into the formula:

xc = I₁ / (I₁ + I₂) . 0 + 2 I₁ / (I₁ + 2 I₁) . 12

xc = 2/3 . 12 = 8 m

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