Mass, Mass, Weight and Weight and GravityGravity

PhysicsMr. Maloney

© 2002 Mike Maloney

ObjectivesObjectivesStudents will be able to explain how mass and weight are related to each

other. explain where gravitational forces arise from. develop and use a universal and local model of

gravity apply the local model of gravity to describe a

model of freefall

© 2002 Mike Maloney

Mass and weightMass and weight

Mass and weight are different from each other.

Mass is how much stuff (matter) you are made out of.

Weight is the gravitational force exerted by a large body (Earth)

© 2002 Mike Maloney

Mass and WeightMass and Weight

When you get on a scale what are you measuring … mass or weight?

Right WEIGHTWhat about when you put an object on

a triple beam balance?MASS it is.

© 2002 Mike Maloney

What is Weight?What is Weight?

1 22G

m mF G

r

The full model for the force of gravitational attraction between two objects as discovered by Newton looks like:

© 2002 Mike Maloney

2E

G

m MF G

r

What is Weight?What is Weight?

The full use is saved for AP, but we can use an approximation of it if we are near the surface of the Earth. At the surface of the Earth, what is constant in this equation?

The full model for the force of gravitational attraction between to objects as discovered by Newton looks like:

© 2002 Mike Maloney

What is Weight?What is Weight?

What is the value of a constant created by combining the three constant values here?

9.8 m/s2

We will call this little g (g = 9.8 N/kg)

2E

G

m MF G

r

G = 6.67428 x 10-11 m3 / (kg∙s2)] ME = 5.9742 × 1024 kg r = 6378000 m

NOTE

G is a UNIVERSAL constant, it is the same everywhere you go in the universe.

g is a LOCAL constant. It is only good at the surface of the Earth. Other planets have their own g, based on their size and mass. As you move father away from the surface of the Earth, g changes.

© 2002 Mike Maloney

Mass and WeightMass and Weight

So what is the weight of a 2 kg mass? Fg = m∙g = 2 kg ∙ 9.8 N/kg Right 19.6 N

What is the mass of a 1000 N person? Fg = m∙g m = Fg/g = 1000 N / 9.8 N/kg Right again, about 102 kg

© 2002 Mike Maloney

Let’s look at Newton’s Law of Gravitation one last time.

We used it to find the Force of the Earth on you, or anything near the Earth.

But we learned from Newton’s 3rd Law that forces are the way things interact.

What does that really mean? WE ALSO PULL ON THE EARTH! So, why do we fall to the Earth if we are

supposedly pulling it towards us?

Mass and WeightMass and Weight

2E

G

m MF G

r

© 2002 Mike Maloney

Other local g’sOther local g’s

Local gravitational constants

gEarth: 10 N/kg.

gMoon: 1.6 N/kg

gJupiter: 26 N/kg

gyou: ~0.000000005 N/kg

GF m g

FG,green

FG,red

FG,green

FG,red

FG,orange

FG,blue

© 2002 Mike Maloney

Consequence (freefall)Consequence (freefall) Let’s now apply

Newton’s 2nd law and our understanding of gravity to an object in freefall.

What is the acceleration of an object in freefall?

gF F ma

mg ma

g a

Fg

© 2002 Mike Maloney

Consequence (freefall)Consequence (freefall)

So even though ag and g are the same, they are really different.

g is the local gravitational constant.ag is the acceleration of an object when the

only force acting on it is gravity. It is better to say g = 10 N / kg

and ag = 10 m/s2.

© 2002 Mike Maloney

ObjectivesObjectivesAre you able to explain how mass and weight are related to each

other. explain where gravitational forces arise from. develop and use a universal and local model of

gravity apply the local model of gravity to describe a

model of freefall