Measuring Mass & Weight With Newton's Laws

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  • 0:01 Newton's Laws
  • 0:54 What Is Mass?
  • 1:29 Solving for Mass
  • 2:27 What Is Weight?
  • 3:14 Solving for Weight
  • 4:04 Lesson Summary
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Lesson Transcript
Instructor: Kevin Newton

Kevin has edited encyclopedias, taught middle and high school history, and has a master's degree in Islamic law.

If you thought that learning Newton's Laws of Motions was only useful to pass a physics test, think again! In this lesson, we'll learn how to use them to calculate mass and weight, two related but different concepts.

Review of Newton's Laws

Before we put Newton's Laws of Motion to use, let's make sure that we remember what they are. Newton's First Law is the idea of inertia, or that a body in motion stays in motion while an object at rest stays at rest. Newton's Second Law is the idea that force is equal to mass times acceleration. Finally, Newton's Third Law states that for every action there is an equal and opposite reaction.

So what do all these laws have to do with finding mass and weight? Everything. However, of the three laws of motion, by far, the most useful for our purposes is the second law. That said, keep those other two fresh in your head as well, as we may refer back to them to justify any statements we make.

What Is Mass?

Let's say that I have a car with a mass of 1,000 kilograms. What does that even mean? Couldn't I just say that the car weighs 1,000 kilograms? Actually, no. Mass is a measure of how much matter is present in an object. By saying that my car has a mass of 1,000 kilograms, I am saying that no matter where I take that car, there will always be the same amount of mass there. The only ways that I can change the mass of that car would be to put a custom body kit on it, adding to the mass, or taking a sledgehammer to the thing, reducing the mass.

Solving for Mass

Newton's Second Law of Motion makes it possible for us to solve for mass if we know the acceleration and force of the object. Remember, force is equal to mass times acceleration. Therefore, if we divide the force by acceleration, the resulting answer should give us the mass of the object in question. Let's give it a shot. Let's say that my car has a force of 9800 newtons (N), the unit used to measure force, on the ground. Remember that acceleration due to gravity is 9.8 meters per second squared. We know that it is having a force on the ground due to Newton's Third Law, the one about equal and opposite reactions, right?

So let's solve the math. 9800 newtons divided by 9.8 meters per second squared leaves 1000 kilograms. Remember that a newton is equal to a kilogram meter per second squared. See, it's just shorter to call them 'newtons.'

What Is Weight?

So what is weight, then? Simply put, weight is the force that we have due to gravity. This is why people can be weightless in space; they are subject to reduced amounts of gravity. On the Moon, someone weighs 1/6 of what they weigh on the Earth due to the fact that the gravity on the Moon is only 1/6 of the total on Earth.

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