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how do two different masses attract each other with an equal and opposite force? watch

    • Thread Starter

    this is in the gravitational fields sections and i thought objects of higher mass would create a larger force than a smaller test mass ??? thanks I'm probably misinterpreting the question.

    Remember that gravity is an interaction between two particles (in fact it acts between every single pair of particles in the universe, just that for small particles and particles far away, the force is so small, it's undetectable). It's not just this particle is big - it'll cause a large force on everything, this particle is small - it'll cause a small force on everything.
    The formula for the force of gravity as derived by Newton:
     F = G \dfrac{m_{1}m_{2}}{r^2}
    You see those m_1 and m_2? Those are the two masses. The force of gravity depends on BOTH of the masses of the two particles.

    And yes, according to Newton's 3rd Law, gravity doesn't just act on one of the particles, it acts on both, with the same magnitude, but opposite directions.

    Let's think about an example: The moon and the earth. You probably realise that earth's gravity provides the centripetal force for the moon's orbit, keeping the moon orbiting us instead of flying away. But realise, that the moon is also attracting the earth. Just as the earth pulls on the moons, the moon pulls on the earth, with equal magnitude and opposite direction.

    Don't believe me that it's the same magnitude? Look at Newton's formula for gravity. Switch around m_1 and m_2 (ie. change the situation from the earth attracting the moon to the moon attracting the earth). The F stays exactly the same.

    This is the reason things have a constant acceleration on earth (9.81m/s^2). This means that if you double the mass of the thing being attracted, you double the force, meaning the acceleration stays the same.

    (Original post by kibap)
    this is in the gravitational fields sections and i thought objects of higher mass would create a larger force than a smaller test mass ??? thanks I'm probably misinterpreting the question.
    Newton's third law says that it must be equal and opposite.

    All of the previous answers are correct and I know it may seem very weird that 2 masses attract each other with equal and opposite forces.

    Just imagine this: When you jump up from the ground, gravity of the Earth pulls you down. You experience a downward force that is equals to your weight ( = mg) and accelerates downward. According to Newton's 3rd Law, the Earth also experiences the same force but upward. But you don't really see the Earth moving, don't you? This is because the Earth so massive that force acted on barely has any effect on it. Since a = F/m, the Earth, in fact, does accelerate upward but by a very very tiny amount that we regard it as not moving.

    To sum up, 2 masses attract each other with equal and opposite forces but we are usually confused that the bigger mass experiences a smaller force because it is less 'affected' (smaller acceleration, movement) by the force because of its bigger mass.

    Hope this helps.
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