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splitwheel | 2 years ago

1kg mass and a 2kg mass do not fall at the same rate. The Gravitational force is (G*m1*m2)/r^2. You are observing that m1 (the earth) is much much greater than m2 (the 1 or 2 kg masses), and you are simplifying to (G*m1)/d^2 because of the precision of the measuring device. Also, d is the same for both masses.

discuss

order

evanb|2 years ago

They do fall at the same rate, even with Newtonian gravity. For,

    F = m a
    F_gravity = GMm/r^2
so that

    ma = GMm/r^2.
Now cancel m from both sides and get

    a = GM/r^2
If you plug in G=6.674e-11 m^3 kg^-1 s^-2, M = M_Earth = 5.972e+24 kg and r = R_earth = 6.378e+6 m you get

    a = 9.79... m/s^2
which ought to be familiar.

splitwheel|2 years ago

The force is on both objects at the same time. The force in F = ma is a function of the mass of both and their distance. If the mass is different in the two scenarios, then the force is different. On earth with small weights, they seem the same because of the precision of the measurement.

This is why you _weigh_ less on the moon.

hllooo|2 years ago

what no they do fall at the same rate. acceleration is F/m so the mass of the object cancels out

stbede|2 years ago

The mass of the earth dictates the acceleration of the individual masses towards the earth. However the acceleration of the earth itself towards the masses are dependent on how much mass is falling towards the earth. When more mass is falling to the earth, the earth accelerates towards the masses faster. So the thought experiment is flawed because with only one 1 kg weight falling towards earth, the gap between the weight closes slower than when there are three 1 kg weights spaced 1 m apart and dropped simultaneously.