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28 January, 01:41

You are holding a shopping basket at the grocery store with two 0.55-kg cartons of cereal at the left end of the basket. the basket is 0.78 m long. where should you place a 1.8-kg half gallon of milk, relative to the left end of the basket, so that the center of mass of your groceries is at the center of the basket?

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  1. 28 January, 02:06
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    Refer to the diagram shown below.

    The basket is represented by a weightless rigid beam of length 0.78 m.

    The x-coordinate is measured from the left end of the basket.

    The mass at x=0 is 2*0.55 = 1.1 kg.

    The weight acting at x = 0 is W₁ = 1.1*9.8 = 10.78 N

    The mass near the right end is 1.8 kg.

    Its weight is W₂ = 1.8*9.8 = 17.64 N

    The fulcrum is in the middle of the basket, therefore its location is

    x = 0.78/2 = 0.39 m.

    For equilibrium, the sum of moments about the fulcrum is zero.

    Therefore

    (10.78 N) * (0.39 m) - (17.64 N) * (x-0.39 m) = 0

    4.2042 - 17.64x + 6.8796 = 0

    -17.64x = - 11.0838

    x = 0.6283 m

    Answer: 0.63 m from the left end.
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