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March 29, 2017

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four uniform spheres, with masses MA= 100kg, MB= 650 kg, MC= 1800 kg, and MD = 100 kg, have (x,y) coordinates of (0, 50 cm), (O,O), (-80 cm, 0), and (40,0) respectively. What is the net gravitational force F2 on spere B due to the other spheres?

  • physics - ,

    F = G M1 m/r^2 direction attractive
    let M1 = 650. the mass of B
    then G M1 = 6.67*10^-11 *650
    = 4.34* 10^-8
    so I will call
    k = 4.34*10^-8 and do the arithmetic later
    now each force = k m/r^2
    now let's do forces in the X direction
    no x force from A on B
    x force C on B = k(1800/80^2) = -2812 k
    x force D on B = k (100/.4^2) = +625 k
    total x force Fx = - 2187 k

    The only y force is from A in + y direction
    Fy = k (100/.5^2) = k 100/.25 = 400 k
    so
    Fx = -2187(4.34*10^-8)
    Fy = + 400 (4.34*10^-8)
    You can multiply that out
    if magnitude and direction are asked then
    F = sqrt(Fx^2+Fy^2)
    tan angle to - x axis in quadrant 2 = Fy/|Fx|

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