The mass of an object and it’s weight are different things. Here we’ll show you how mass,...

The mass of an object and it’s weight are different things. Here we’ll show you how mass, weight, and gravity are all related.

Mass, Weight, and

Gravity

Mass is the amount of matter in an object.

Mass = The amount of matter in an object

If we compare a small boy and a semi truck, the truck contains more matter than the boy, so the truck has a larger mass than the boy.

Mass = The amount of matter in an object

Smaller MassLarger Mass

Weight is the pull of gravity or force of gravity on an object. For an object on or near Earth, it is the force pulling the object toward Earth.

Weight = Force of Gravity

Weig

ht

If we compare objects on Earth, the more mass an object has, the greater the force of gravity on it, or the greater weight it has.


Weig

ht

Weig

ht

In other words, less mass means less weight and more mass means more weight, so the truck has a greater weight than the boy.


Weig

ht

Weig

ht

Less mass means

less weight

More mass means more

weight

Because weight is a force, it is measured in units of force called newtons, abbreviated with a capital N.

Weight(N)

= Mass(kg)

× Acceleration of Gravity(N/kg)

Weight, or Force of

Gravity, in Newtons

Weight is equal to mass in kilograms

Weight(N)

= Mass(kg)


Mass in kilograms

Times something called the acceleration of gravity, measured in Newtons per Kilogram.

Weight(N)

= Mass(kg)


Acceleration of Gravity inNewtons per Kilogram

The value for the acceleration of gravity depends on the mass of the planet or moon the object is on or near.

Weight(N)

= Mass(kg)



Depends on the mass of the planet or moon the object is on

or near

On Earth, the Acceleration of Gravity is equal to 9.8 newtons per kilogram

Weight(N)

= Mass(kg)



Depends on the mass of the planet or moon the object is on

or near

On Earth, the Acceleration of Gravity = 9.8 N/kg

We can use a capital W to stand for weight.

Weight(N)

= Mass(kg)


W m g

A lower case m to stand for mass,

Weight(N)

= Mass(kg)


W m g

And a lower case g to stand for acceleration of gravity.

Weight(N)

= Mass(kg)


W m g

Mass(kg)

So now, we can just use these letters to give us an abbreviated form of this equation (click)

Weight(N)

= × Acceleration of Gravity(N/kg)

=

W m g

=

The equation is W = m times g

= ×W m g

Where W stands for the weight in newtons,

= ×W m g

Weight in Newtons

(N)

M stands for the mass in kilograms,

= ×W m g

Weight in Newtons

(N)

Mass in kilograms

(kg)

And g stands for the acceleration of gravity in newtons per kilogram.

= ×W m g

Weight in Newtons

(N)

Mass in kilograms

(kg)

Acceleration of Gravity (N/kg)

Here’s an example question. We’re given that a black bear has a mass of 190 kg.

A black bear has a mass of 190 kg.

What is its weight?

And we’re asked for its weight.


What is its weight?

It is important to know that for any questions involving mass and weight, if you are not told otherwise, assume that the object in question in on the surface of Earth.


What is its weight?

Unless otherwise told, assume that the object in question is on Earth’s surface.

We’re asked to calculate weight and we’re given mass, so we use the equation W = m times g, where W is the weight in newtons, m is the mass in kg, and g is the acceleration of gravity in N/kg.

A black bear has a mass of 190 kg.What is its weight?

= ×W(N)

m(kg)

g(N/kg)

The question tells us that the bear has a mass of 190 kg.


= ×W(N)

m(kg)

g(N/kg)

So we can substitute 190 kg in for mass


= ×W(N)

m(kg)

g(N/kg)

= ×W(N)

190 kg

g(N/kg)

It is known that the value for g on Earth is 9.8 newtons per kilogram.


= ×W(N)

m(kg)

g(N/kg)

= ×W190 kg

g(N/kg)

“g” on Earth is 9.8 N/kg

kg

So we can substitute 9.8 newtons per kilogram in for “g” in this equation.


= ×W(N)

m(kg)

g(N/kg)

= ×W190 kg

9.8 N

“g” on Earth is 9.8 N/kg

kg

190 times 9.8 is equal to 1862,


= ×W(N)

m(kg)

g(N/kg)

= ×W190 kg

9.8 N

W 1862 N=

kg

we see that the unit kilograms is in the numerator and the denominator.


= ×W(N)

m(kg)

g(N/kg)

= ×W190 kg

9.8 N

W 1862 N=The unit kg is in the numerator and the

denominator

kg

so they can be cancelled out,


= ×W(N)

m(kg)

g(N/kg)

= ×W190 kg

9.8 N

W 1862 N= Can be cancelled out

kg

leaving us with only newtons as a unit.


= ×W(N)

m(kg)

g(N/kg)

= ×W190 kg

9.8 N

W 1862 N=

kg

So the unit for our answer is newtons.


= ×W(N)

m(kg)

g(N/kg)

= ×W190 kg

9.8 N

W 1862 N=

kg

So W is equal to 1862 newtons.


= ×W(N)

m(kg)

g(N/kg)

= ×W190 kg

9.8 N

W 1862 N=

kg

And we can state the final answer as the weight of a 190 kg bear is 1862 newtons.


= ×W(N)

m(kg)

g(N/kg)

= ×W190 kg

9.8 N

W 1862 N=

The weight of a 190 kg bear is 1862 N

The mass of an object and it’s weight are different things. Here we’ll show you how mass,...

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