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Anonymous asked in Science & MathematicsPhysics · 1 month ago

Two objects attract each other with a gravitational force of magnitude 1.01 10^-8 N when separated by 19.9 cm. ?

Two objects attract each other with a gravitational force of magnitude 1.01 10^-8 N when separated by 19.9 cm. If the total mass of the two objects is 5.02 kg, what is the mass of each?

I know that the heavier mass is 3 but I got 1.8 for the lighter mass and that was incorrect. Can someone please help?

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  • 1 month ago
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    1.01 10^-8 N ?? is that 1.01x10^-8 N

    F = G m₁m₂/r² = 1.01e-8

    (6.674e-11) m₁m₂/(0.199)² = 1.01e-8

    m₁ + m₂ = 5.02

    two eq is two unknowns

    m₁ = 5.02 –  m₂

    (6.674e-11) m₂(5.02 – m₂)/(0.199)² = 1.01e-8

    –(6.674e-11) m₂²/0.0396  + m₂(6.674e-11)(5.02)/0.0396 – 1.01e-8 = 0

    1.685e-9m₂² – 8.46e-9m₂ + 1.01e-8 = 0

    1.685m₂² – 8.46m₂ + 10.1 = 0

    m₂² – 5.02m₂ + 5.99 = 0

    m₂ = 3.07, 1.95

    1.95 is the answer...

    Gravitational attraction in newtons

    F = G m₁m₂/r²

    G = 6.674e-11 m³/kgs²

    m₁ and m₂ are the masses of the two objects in kg

    r is the distance in meters between their centers

  • 1 month ago

    "I know that the heavier mass is 3...".   3 what?  You need units for this to make any sense.

    The total mass is 5.02 kg.   If you know the mass of one of the objects, just subtract that amount from 5.02 kg to get the mass of the other object.

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