prob_033

# prob_033 - 33. REASONING We place the third particle (mass...

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33. REASONING We place the third particle (mass = m 3 ) as shown in the following drawing: m 2 m m 3 L D The magnitude of the gravitational force that one particle exerts on another is given by Newton’s law of gravitation as F = Gm 1 m 2 / r 2 . Before the third particle is in place, this law indicates that the force on each particle has a magnitude F before = Gm 2 m / L 2 . After the third particle is in place, each of the first two particles experiences a greater net force, because the third particle also exerts a gravitational force on them. SOLUTION For the particle of mass m , we have 3 2 22 after 3 2 before 2 2 1 2 2 Gmm Gm m FL m DL Gm m F mD L + == + For the particle of mass 2 m , we have () 3 2 after 3 2

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## This note was uploaded on 01/29/2010 for the course CALC 01:640:135 taught by Professor Soffer during the Spring '08 term at Rutgers.

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prob_033 - 33. REASONING We place the third particle (mass...

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