Video: Calculating the Weight of an Object from Its Mass

What is the weight of a 3.0-kilogram mass on the surface of Earth? [A] 29.4 N [B] 58.8 N [C] 29.4 kg [D] 3.0 kg [E] 9.0 N.

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Video Transcript

What is the weight of a 3.0-kilogram mass on the surface of Earth? a) 29.4 newtons, b) 58.8 newtons, c) 29.4 kilograms, d) 3.0 kilograms, e) 9.0 newtons.

To answer this question, we need to understand the difference between two key terms, weight and mass. Mass is a measure of how much matter is in an object. The SI base unit for mass is kilograms. Mass is also independent of external interactions and forces. So a 10-kilogram mass is still a 10-kilogram mass, whether it’s on the surface of Earth or floating out in the vacuum of space or in the presence of some strong electromagnetic field.

Weight, on the other hand, is the gravitational force acting on an object. Since weight is a force, it’s measured in newtons. Also, because weight is a measure of gravitational force, it depends on the local gravitational field. To illustrate the difference between mass and weight, let’s imagine that we have two similarly sized planets, one that is more massive than the other.

Since the planets are of similar size, the gravitational field at the surface of the more massive planet will be stronger than the gravitational field at the surface of the less massive planet. Now, we’d see what happens if we introduce a box with a mass of 10 kilograms. Let’s put a copy of this box on the surface of both planets. Remember that mass is independent of external interactions and forces. So even though both boxes are in different environments, their mass is still the same 10 kilograms.

What about the weight, the gravitational force acting on these objects? Recall that the gravitational force acting on an object is equal to the mass times the local gravitational acceleration, which is the same thing as saying the mass times the local gravitational field. With this in mind, we can clearly see that the box on the more massive planet has a larger weight than that of the box on the less massive planet. This is because 𝑚 is the same in both cases. But 𝑔 is larger for the more massive planet, where the gravitational field at the surface is stronger.

From this example, we clearly see the difference between mass and weight. The two objects on two different planets have the same mass. But 𝑚 times 𝑔, the force of gravity acting on these objects, is different. So let’s go back to the question. The question is asking us for the weight of a 3.0-kilogram mass. We now know how to find this. The way is just the force of gravity as given by 𝑚 times 𝑔. We were given 𝑚. It’s 3.0 kilograms. What we need to know is 𝑔.

The 𝑔 that we’re looking for is the gravitational acceleration at the surface of the Earth. And this is a number that we should have memorized. It’s 9.8 meters per second squared. So the force of gravity is 𝑚𝑔. It’s 3.0 kilograms times 9.8 meters per second squared. Counting out the multiplication, we get 29.4 kilogram meters per second squared. And recall that the unit kilogram meters per second squared is precisely one newton, exactly the units we would expect for weight. So our final answer is that the weight of a 3.0-kilogram mass on the surface of the Earth is 29.4 newtons. And this matches up with answer choice a, 29.4 newtons.

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