Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 month ago

The ratios of the weights of two objects on the Moon and on Earth are in proportion. A rock weighing 3 N on the Moon weighs 18 N on Earth. How much would a rock that weighs 5 N on the Moon weigh on Earth?

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• The ratios of the weights of two objects on the Moon and on Earth are in proportion.

A rock weighing 3 N on the Moon weighs 18 N on Earth.

A rock that weighs 5 N on the Moon would weigh 30 N on Earth.

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• I won't do your homework for you

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• Anonymous
1 month ago

You have to be at least 13 to be on this site, kid.

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• A rock weighing x on the moon weighs 6x on earth. Therefore a rock that

weighs 5 N n the moon weighs 6(5 N) on earth, ie., 30 N on earth.

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• Intuitively, we are shown an example where a 3 N object in the moon weighs *6* times as much on the Earth (18 N).

So clearly a 5 N object on the moon would weigh 30 N on Earth.

Here it's very easy to figure out the constant of proportionally in your head. But if you wanted to be a little more mathematically formal, you would solve it as follows:

Write an equation for the direct variation:

e = km

e : weight on Earth (in Newtons)

m : weight on the Moon (in Newtons)

k : constant of proportionally

Plug in what you know about the first object:

18 = 3k

Solve for k:

k = 18/3

k = 6

So now you have an equation you can use for other objects:

e = 6m

Now when you are told an item weighs 5 N on the moon, you can figure its weight on Earth:

e = 6*5

e = 30

30 N

Got it?

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• E ∝ M, so E = kM

Now, when E = 18, M = 3

so, 18 = 3k

i.e. k = 6

=> E = 6M

Hence, when M = 5, E = 30

i.e. 5 Newtons on the moon will be 30 Newtons on earth.

Note: This is true as the force due to gravity on the Earth compared to the moon is 6 : 1

:)>

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• A newton is how much force is required to make a mass of one kilogram

accelerate at a rate of one meter per second squared.

The ratios of the weights of two objects on the Moon and on Earth are in proportion.

A rock weighing 3 N on the Moon weighs 18 N on Earth.

A rock that weighs 5 N on the Moon would weigh 30 N on Earth.

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• 18 : 3 as x : 5

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• 5 x 6 = 30N

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