WEBVTT
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If the gravitational force between two masses was 10 newtons at a certain distance, what would the gravitational force become if that distance was doubled?
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Newtonβs law of universal gravitation states that for two masses π one and π two, the force of gravity πΉ between them will be given by the following relation: πΉ is equal to πΊ multiplied by π one multiplied by π two divided by π squared, where πΊ is the gravitational constant, π one and π two are the two masses, and π is the distance between them.
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In this case, we have that 10 is equal to πΊ multiplied by π one multiplied by π two divided by π squared.
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Our new force πΉ one when the distance has doubled is equal to πΊ multiplied by π one multiplied by π two divided by two π squared.
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As two π all squared is equal to four π squared, we can say that πΉ one is equal to πΊ multiplied by π one multiplied by π two divided by four π squared.
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This can be rewritten as πΉ one is equal to a quarter of πΊ multiplied by π one multiplied by π two divided by π squared.
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As the initial gravitational force was equal to 10 newtons, we can substitute 10 into this equation: πΊ multiplied by π one multiplied by π two divided by π squared is equal to 10.
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This means that πΉ one is equal to a quarter multiplied by 10.
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A quarter of 10 is five over two or five halves.
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This is equal to 2.5 newtons.
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Therefore, when the distance between the two masses is doubled, the gravitational force has quartered or we have divided it by four.