Physics
Fox

### Summary

• All matter has mass.

• Mass is always positive. The SI unit of mass is kilograms (kg). • The gravitational force (aka. weight) acting on an object is given by: $W = m g$ where m = mass of object, g = gravitational field strength (= 10 N/kg on Earth). Rocky has a mass of 5kg.
His weight is:
W = mg = 5kg × 10N/kg = 50N

• g is different on different planets/moons. Therefore, objects with the same mass have different weights on other planets.

Let's learn about our first fundamental force. It's the one you see all around you; it's what pulls everything towards the ground — it's the gravitational force. All matter has mass, in the same way that all matter has a height and a width. We can think of mass as being 'how much stuff' is inside an object — so mass is always a positive value. Your mass is what you measure when you stand on some weighing scales. There are many different units for mass, such as pounds (lbs) and ounces (oz). In science, the unit that we use for mass is the kilogram (kg). A person might have a mass of 70 kg. A car might have a mass of 1000 kg. The Earth has a mass of 6 million billion billion kg. It's literally massive. For things with smaller masses, we use grams (g). 1 kilogram is the same as 1000 grams. (Remember: "kilo" means 1000). For example, an apple has a mass of around 100 g (= 0.1 kg).

If there's one thing you know about gravity, it's that gravity pulls things down. Of course, any pull must be a force! So there must be some kind of gravitational force that pulls objects downwards. How does this force behave? Are all objects pulled down equally? Let's answer these questions with another question; would you rather lift 2kg, or 200kg? You would probably prefer to lift the 2kg mass, as the 200kg mass would pull down on you much more than the 2kg mass.

From this we can deduce that the gravitational force must be bigger for bigger masses! Does the gravitational force depend on anything else? There is one more thing: it depends on where you are.

On Earth, most people would find a 35kg sofa too heavy to lift by themselves. On the moon, however, you could lift it with one arm! Gravity is stronger on the Earth because the Earth has more mass than the moon. We say that the Earth has a larger gravitational field strength than the Moon. We represent gravitational field strength with the symbol g, and it has units of Newtons per kilogram (N/kg). On Earth, g = 10 N/kg, and on the moon, g = 1.6 N/kg. This means the gravity is about 6× weaker on the moon than on the Earth.

In summary, the gravitational force is bigger for bigger masses (m), and is bigger for bigger gravitational field strengths (g). We can neatly write this as an equation: $W = m g$

Where W is the gravitational force (also known as weight).

We can also write this equation as a formula triangle: Mass and weight are often confused for each other, but they are two different things! Mass is something that objects have, but weight is a force (that acts on objects). Your mass is the same wherever you are, but your weight changes depending on which planet/moon you are on.

(A big reason people get them confused: to find your mass, you "weigh" yourself on some "weighing" scales.)

How much does a 35kg ‘KLÏPPÄN’ sofa weigh on Earth? We can sum up this question as:

Weight = ?
Mass = 35 kg
g = 10 N/kg (because this is g on Earth)

The equation relating weight, mass and gravitational field strength is: W = mg. Alternatively, we could find this by covering W on the formula triangle.

Therefore, the sofa has a weight W = 35 kg × 10 N/kg = 350 N.

A grand piano weights 800N on the moon. On the moon, g=1.6 N/kg. What is the mass of the piano? We can succinctly write this question as:

Weight = 800 N
Mass = ?
g = 1.6 N/kg

We need a formula to get mass from weight and gravitational field strength. Covering up m on the formula triangle shows W on top of g. Therefore, m = W/g is the equation we need.

Using a calculator, we find that the piano has a mass = (800 / 1.6) kg = 500 kg.

A great big 3kg bag of rice weighs 810N on the Sun. What is the gravitational field strength (g) on the Sun? We can more succinctly write this question as:

Weight = 810 N
Mass = 3 kg
g = ?

We need a formula to get gravitational field strength from weight and mass. Covering up g on the formula triangle shows W on top of m. Therefore, g = W/m is the equation we need.

Using a calculator, we find that the Sun has g = (810 / 3) N/kg = 270 N/kg.

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