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An object held at a point above the ground has 2352 joules of gravitational potential energy.
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The object’s mass is 20 kilograms.
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How far above the ground is the object?
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Okay, let’s make a quick sketch of this scenario.
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Let’s say this is our object.
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And here’s the ground.
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We’re told that our object has a mass of 20 kilograms and also that it has a particular given amount of gravitational potential energy.
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Based on this information, we want to solve for how far above the ground, we can call this distance ℎ, the object is.
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To start figuring this out, let’s recall a mathematical relationship for gravitational potential energy.
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We can abbreviate this as capital GPE.
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And it’s equal to the mass of an object multiplied by the acceleration due to gravity on the gravitational field that’s in multiplied by its height ℎ above some reference level.
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In this equation, the values of 𝑚 and ℎ are situation dependent.
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𝑔, on the other hand, so long as we’re at or near the surface for the Earth, is a constant value.
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We’ll treat it as exactly 9.8 metres per second squared.
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Now, if we write out this equation for our scenario, we can say that we know GPE that’s given to us in the problem statement.
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We know 𝑚 that’s also given.
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And it’s ℎ, the height above ground, that we want to solve for.
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We can algebraically rearrange this equation so that it reads ℎ is equal to the gravitational potential energy of our object divided by its mass times gravity.
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And it’s at this point that we can start substituting in for these terms.
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For GPE, we’ll substitute in 2352 joules.
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And then, for 𝑚, the object’s mass, we’ll substitute 20 kilograms and for 𝑔, the acceleration due to gravity, 9.8 metres per second squared.
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When we enter this expression on our calculator, to two significant figures, we find a result of 12 metres.
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This then is the height of the object above ground.