A body of mass 543 grams is at a height of 22 meters above the surface of the ground. Determine its gravitational potential energy relative to the ground, rounding your answer to two decimal places. Take 𝑔 to be equal to 9.8 meters per square second.
Remember, gravitational potential energy represents the potential an object has to do work as a result of being located at a particular position in a gravitational field. In this specific case, we’re interested in the potential that the object of mass 543 grams has to do work as a result of being located at a height of 22 meters above the ground. Specifically, the gravitational potential energy 𝐸 sub 𝐺 of an object with mass 𝑚 that is at height ℎ above some reference point is given by 𝑚𝑔ℎ, where 𝑔 is acceleration due to gravity. Now, in this case, that’s roughly 9.8 meters per square second.
Now, when we work with gravitational potential energy, we tend to work with kilograms, meters, and meters per square second. Now, kilograms square meters per square second is actually equivalent to joules. So this means we can calculate the gravitational potential energy of the body by converting its mass from grams to kilograms and then working with its height in meters and gravity in meters per square second. Specifically, we know that to convert from grams to kilograms, we divide by 1000. So the mass of the body in kilograms is 0.543 kilograms.
We’re therefore able to define 𝑚 to be equal to 0.543 kilograms, ℎ to be equal to 22 meters, and 𝑔 to be equal to 9.8 meters per square second. Substituting all of these into the formula for gravitational potential energy, and we get 0.543 times 9.8 times 22. That gives us a value of 117.0708, which correct to two decimal places is 117.07. So we can say that the gravitational potential energy of the body relative to the ground is 117.07 joules.