Calculate the percent difference between your weight in...

Key Concepts

Percent Difference Calculation

The percent difference is a method of quantifying the relative change between two values, often using the formula (difference/average or initial value) × 100. This concept is used to compare varying measurements, such as the weight of an object under different gravitational conditions.

Gravitational Acceleration Variation

In classical mechanics, gravitational acceleration decreases with increasing altitude above the Earth's surface. This variation means that objects experience slightly less gravitational pull the higher they are, affecting measurements of weight since weight is the force exerted by gravity on an object’s mass.

Weight Calculation

Weight is calculated as the product of mass and gravitational acceleration. As such, changes in gravitational acceleration due to altitude differences (for example, near sea level versus high altitudes) directly influence the weight of the same object even though its mass remains constant.

Transcript

00:01 In this question, we are asked to calculate the percent difference between your weight in sacramento near sea level and at the top of mount everest, which is 8 ,800 meters above sea level.

00:16 So in this question, we are evaluating the difference between two values, the weight of a person in sacramento, which i'm going to label ws, and that's going to be equal to g.

00:33 Mm over r s squared.

00:36 And i'm taking r s to be the radius of the earth in sacramento.

00:41 And then the weight of a person on top of mount everest, which is going to be equal to gmm over rme, i'll call it.

01:02 And that's going to be the radius of the earth plus 8800 meters, for the additional height due to mount everest itself.

01:12 So we're comparing these two values and we want to know their percentage difference.

01:17 So percentage difference can be calculated like this.

01:20 So essentially you take the difference between the two values and then you divide by their average.

01:27 So since we have two values, we're going to add them and then divide by two and multiply by 100.

01:36 And that will give us the percentage difference.

01:39 Now, this is actually a lot easier than it looks because all of these terms in the question have gmm in them.

01:51 So the gmm is going to cancel out.

01:53 So let me just substitute everything in and i'll show you what i mean...

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