the mass of an object and it’s weight are different things. here we’ll show you how mass,...
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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
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Mass is the amount of matter in an object.
Mass = The amount of matter in an object
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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
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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
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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.
Weight = Force of Gravity
Weig
ht
Weig
ht
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In other words, less mass means less weight and more mass means more weight, so the truck has a greater weight than the boy.
Weight = Force of Gravity
Weig
ht
Weig
ht
Less mass means
less weight
More mass means more
weight
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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
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Weight is equal to mass in kilograms
Weight(N)
= Mass(kg)
× Acceleration of Gravity(N/kg)
Mass in kilograms
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Times something called the acceleration of gravity, measured in Newtons per Kilogram.
Weight(N)
= Mass(kg)
× Acceleration of Gravity(N/kg)
Acceleration of Gravity inNewtons per Kilogram
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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)
× Acceleration of Gravity(N/kg)
Acceleration of Gravity inNewtons per Kilogram
Depends on the mass of the planet or moon the object is on
or near
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On Earth, the Acceleration of Gravity is equal to 9.8 newtons per kilogram
Weight(N)
= Mass(kg)
× Acceleration of Gravity(N/kg)
Acceleration of Gravity inNewtons per Kilogram
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
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We can use a capital W to stand for weight.
Weight(N)
= Mass(kg)
× Acceleration of Gravity(N/kg)
W m g
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A lower case m to stand for mass,
Weight(N)
= Mass(kg)
× Acceleration of Gravity(N/kg)
W m g
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And a lower case g to stand for acceleration of gravity.
Weight(N)
= Mass(kg)
× Acceleration of Gravity(N/kg)
W m g
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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
=
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The equation is W = m times g
= ×W m g
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Where W stands for the weight in newtons,
= ×W m g
Weight in Newtons
(N)
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M stands for the mass in kilograms,
= ×W m g
Weight in Newtons
(N)
Mass in kilograms
(kg)
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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)
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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?
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And we’re asked for its weight.
A black bear has a mass of 190 kg.
What is its weight?
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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.
A black bear has a mass of 190 kg.
What is its weight?
Unless otherwise told, assume that the object in question is on Earth’s surface.
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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)
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The question tells us that the bear has a mass of 190 kg.
A black bear has a mass of 190 kg.What is its weight?
= ×W(N)
m(kg)
g(N/kg)
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So we can substitute 190 kg in for mass
A black bear has a mass of 190 kg.What is its weight?
= ×W(N)
m(kg)
g(N/kg)
= ×W(N)
190 kg
g(N/kg)
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It is known that the value for g on Earth is 9.8 newtons per kilogram.
A black bear has a mass of 190 kg.What is its weight?
= ×W(N)
m(kg)
g(N/kg)
= ×W190 kg
g(N/kg)
“g” on Earth is 9.8 N/kg
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kg
So we can substitute 9.8 newtons per kilogram in for “g” in this equation.
A black bear has a mass of 190 kg.What is its weight?
= ×W(N)
m(kg)
g(N/kg)
= ×W190 kg
9.8 N
“g” on Earth is 9.8 N/kg
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kg
190 times 9.8 is equal to 1862,
A black bear has a mass of 190 kg.What is its weight?
= ×W(N)
m(kg)
g(N/kg)
= ×W190 kg
9.8 N
W 1862 N=
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kg
we see that the unit kilograms is in the numerator and the denominator.
A black bear has a mass of 190 kg.What is its weight?
= ×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
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kg
so they can be cancelled out,
A black bear has a mass of 190 kg.What is its weight?
= ×W(N)
m(kg)
g(N/kg)
= ×W190 kg
9.8 N
W 1862 N= Can be cancelled out
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kg
leaving us with only newtons as a unit.
A black bear has a mass of 190 kg.What is its weight?
= ×W(N)
m(kg)
g(N/kg)
= ×W190 kg
9.8 N
W 1862 N=
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kg
So the unit for our answer is newtons.
A black bear has a mass of 190 kg.What is its weight?
= ×W(N)
m(kg)
g(N/kg)
= ×W190 kg
9.8 N
W 1862 N=
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kg
So W is equal to 1862 newtons.
A black bear has a mass of 190 kg.What is its weight?
= ×W(N)
m(kg)
g(N/kg)
= ×W190 kg
9.8 N
W 1862 N=
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kg
And we can state the final answer as the weight of a 190 kg bear is 1862 newtons.
A black bear has a mass of 190 kg.What is its weight?
= ×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