Together with a friend, you are carrying a ladder that weighs 130 N. You have cleverly convinced your friend to hold the ladder 0.1 m from the center of gravity, while you yourself are 1.5 m from the center of gravity. How much of the weight of the ladder are you yourself supporting?

W₁ = 8.12 N

Explanation:

Consider the weight supported by the person and friend to be:

W₁ = Weight supported by person

W₂ = Weight supported by Friend

Now, their sum must be equal to total weight of ladder. Hence,

W₁ + W₂ = 130 N

W₂ = 130 N - W₁   equation (1)

Now, to carry the ladder, the moment due to both person's forces must be equal:

Moment due to person 1 = Moment due to friend

W₁ d₁ = W₂ d₂

where,

d₁ = distance between person and center of gravity = 1.5 m

d₂ =  distance between friend and center of gravity = 0.1 m

W₁(1.5 m) = W₂(0.1 m)

W₁ = W₂ (0.1 m/1.5 m)

W₁ = W₂(0.06667)

using equation (1):

W₁ = (130 N - W₁)(0.06667)

W₁ + 0.06667W₁ = 8.6667 N

W₁ = 8.12 N

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