I know this may sound strange, but we need to discuss the difference between mass and weight.

• In everyday language these two words mean the same thing… maybe “mass” just sounds a little more technical.
• In physics they mean two entirely different things.

Think of the following three situations…

1. Kick an empty pop can and it moves easily.
   This makes sense, since aluminum cans are very light and easy to move around.
2. Kick one filled with pop and it moves less.
   You would probably even stub your toe a bit kicking this one. It’s the same can, but now there’s more stuff inside.
3. Kick one filled with lead and it hardly moves at all.
   Now we are driving you to the hospital with a broken toe! Same can, but filled with a lot of dense stuff. It is the one that has the most matter inside it.

The lead can has more inertia (it “wants” to stay at rest more).

more matter = more mass = more inertia

So a greater force is required to move a greater mass.

• It is possible to measure mass by applying a force to it and seeing how much it accelerates.
• This is known as inertial mass.

Mass is not the same as weight!

• Floating in space, you could hold a car in your hand… it’s easy because it has no weight.
• Throw it at someone and it hits them with its inertia… it hurts!
  • This is because it has still has mass, so it will tend to keep doing what it is already doing a lot.
• The amount of material that makes up the car is the same in space as it is on Earth, so they have the same mass.
  • The mass of an object is like asking “How many atoms are in that object?”… this number will always be the same, no matter where you are in the universe.

But weight is different depending on where you weigh something.

• It depends on how much gravity is pulling on the object.

Example 1: I have a 5.00kg rock.

1. Determine how much it weighs on the Earth and on the Moon.
   Mass is measured in kilograms, weight is measured in Newtons! Weight is really the force due to gravity acting on an object.
   
   On Earth...
   F_g= mg = 5.00kg (9.81m/s²) = 49.1N
   
   On the Moon...
   F_g= mg = 5.00kg (1.67m/s²) = 8.35N
   
2. Determine its mass on the Earth and on the Moon?
   What is the mass of the object on the Earth? 5kg!
   What is its mass on the moon? 5kg!
   The object has the same matter making it up even if I take it to a different place.

Although it might sound weird, if you are ever asked for the weight of an object, you must calculate the force due to gravity acting on the object and give your answer in Newtons!

• You can only give an answer in kilograms if you are asked the mass of an object.

Example 2: If a book weighs 20.5N and has a mass of 2.10kg, determine gravity in that area.

F_g=mg

g = F_g / m

= (20.5N) / (2.10kg)

g = 9.76m/s²