The Law of Universal Gravitation

https://www.youtube.com/watch?v=dplIZUX7tyU

Today you need to know…

1. The difference between the acceleration of gravity and the force of gravity.

2. How to calculate the force of gravity between two objects.

3. Fully understand that forces are not alone – they always act in pairs.

4. All unbalanced forces are caused by acceleration.

LAW OF UNIVERSAL GRAVITATION

Gravity is universal – everything is attracted to everything else – forces come in pairs. This attraction can be measured and is based on two things:

1. Mass2. Distance

221

r

mGmF

G = 6.67 x 10-11 Nm2/kg2

Gravitational Constant

The Force of Attraction (N)

mass of object one (kg) mass of object

two (kg)

distance between the centers of the two objects (m)

Understanding relationships between

variables

221

r

mGmF

The greater the mass the greater the forceThe force decreases as the square of the distance increases

DIRECTLY

INVERSELY ? The force of gravity on you is greatest when you are standing _____.a. On the earth’s surfaceb. Just above the Earth’s surfacec. Far above the Earth’s surface

As the distance between two objects increases then force INCREASES/DECREASES

Understanding relationships between variables

221

r

mGmF

The greater the mass the greater the forceThe force decreases as the square of the distance increases

How to solve problems regarding relationships between variables.

1. IGNORE G – it is always the same

2. Set up an original problem where everything is equal to 1

ex. 1= 1 x 1 12

3. Change only what the problem says.

EXAMPLE PROBLEM:

Two objects gravitationally attract each other with a force of 2 N. IF the distance between their centers is tripled, the new force of attraction is _______________ N. solution 1= 1 x 1 = 1 32 9So the force is reduced by a factor of 9. 2/9 =

Directly Proportional: force and mass•Two objects gravitationally attract each other with a force of 1N. IF the mass of one of the objects doubles, the new force of attraction is _______________ N.

•Two objects gravitationally attract each other with a force of 1N. IF the mass of both of the objects doubles, the new force of attraction is _______________ N.

•Two objects gravitationally attract each other with a force of 1N. IF the distance between their centers is decreased by a factor of four, the new force of attraction is _______________ N.

4. Two objects gravitationally attract each other with a force of 3 N. IF the distance between their centers is tripled, the new force of attraction is _______________ N.

5. Two objects gravitationally attract each other with a force of 4 N. IF the distance between their centers is doubled, the new force of attraction is _______________ N.

 

6. Two objects gravitationally attract each other with a force of 2 N. IF the distance between their centers is halved, the new force of attraction is _______________ N.

7. Two objects gravitationally attract each other with a force of 4 N. IF the distance between their centers is doubled and one mass is doubled, the new force of attraction is _______________ N. 8. Two objects gravitationally attract each other with a force of 6 N. IF the masses of both objects doubles and the distance between their centers doubled, the new force of attraction is _______________ N.

• Two objects gravitationally attract each other with a force of 10 N. IF the distance between their centers is halved and one mass is doubled, the new force of attraction is _______________ N.

• Two objects gravitationally attract each other with a force of 6 N. IF the masses of both objects doubles and the distance between their centers quadruples, the new force of attraction is _______________ N.

• Two objects gravitationally attract each other with a force of 4 N. IF the distance between their centers is doubled and one mass is doubled, the new force of attraction is _______________ N.

 • Two objects gravitationally

attract each other with a force of 1 N. IF the masses of both objects doubles and the distance between their centers doubled, the new force of attraction is _______________ N.

Constants – will be given to you

• G = 6.67 x 10-11 Nm2/kg2 This is the Gravitational Constant

• me = mass of the Earth (5.98 x 1024 kg)

• re = radius of the Earth (6.37 x 106 m)IMPORTANT

WHEN TOLD SOMETHING IS ON THE SURFACE OF THE EARTH… USE THIS!

• EXAMPLE :Find the force between two objects 6371 km apart. The first object has mass 70 kg, the second object has mass 6 x 1024 kg.

F = (6.67 x 10-11 ) (70) (6 x 1024 ) =63712

2.8 x1016

4.06 x 10 7

F= 6.90 X 10 8 NEXAMPLE: Two objects each have a mass of 1x10-3 kg. The force between the objects is 400 N. What is the distance between them?

r = (6.67 x 10-11 ) (1x10-3) (1x10-3) =400

6.67 x10-17

400

• EXAMPLE 3 :Find the force between the earth and an object with a mass of 75 kg., the object is on the surface of the earth.

F = (6.67 x 10-11 ) (75) (5.98 x1024 ) =(6.37 x 10 6) 2

EXAMPLE: Two objects of equal mass are seperated by a distance of 10 m and have a gravitational force of 20 N. What is the mass of each object?

m2 = 20 (10 2) = 6.67 x 10-11

2000 6.67 x 10 -

11

2.9 x1016

4.06 x 10 13

7.14 x 10 2

N

m2= 2.9 x 10 13

m= 2.9 x 10 13

• The more massive an object, the (more/less) that the object will be attracted to Earth.

• The further away from the Earth’s surface, the (more/less) another object will be attracted to Earth.

• 1.

5. Two objects each have a mass of 1 x 10-3 kg. The force between the objects is 200 N. What is the distance between them?

6. Two objects of equal mass experience a gravitational force of 1000N. They are separated by a distance of 1 m. What is the mass of each object?

7. What is the force between the earth and a mass of 1200 kg if the mass is on the surface of the earth? 

9. What is the force between the Earth and a mass of 1200 kg if the mass is 35000 meters above the Earth’s surface.

Newton had the insight to see that the force on the _______________ has the same nature as the force on an _______________.Force is ______________ proportional to the square of the distance between the masses. Force is ________________ proportional to the mass of each object. The law states that as two objects move toward each other because of gravitational attraction and the distance between them decreases, the force between them _____________________. As the distance between the two objects _________________, the force between them decreases. Mass also effects the force between the objects, as mass increases in either object, the force between them ___________________, Regardless of each objects mass the force between the two objects is ____________, a mutual interaction based on Newton’s 3rd Law.

MOONAPPLE INVE

RSELY

DIRECTLY

INCREASES INCRE

ASESINCREASESEQU

AL

• Since the object is accelerating, an invisible force must be present.

• The force is acting at a distance. • The force is not limited to earth.• Newton wondered if the force extended as far out as

the moon. He was aware that the moon always moved in a curved path. If a force is not acting on an object how do they move?

Newton reasoned that the moon is falling toward Earth for the same reason an apple falls from a tree—they are both pulled by Earth’s gravity.

The Falling Apple

Newton discovered that gravity is universal. Everything pulls on everything else in a way that involves only mass and distance.

Newton’s Law of Universal Gravitation

The Mass of the Earth

• https://www.youtube.com/watch?v=9yMQM5AN8mc

• Khan academyhttps://www.youtube.com/watch?

v=Xcel427Ezl0

When will I ever use this? https://www.youtube.com/watch?

v=iZWIUyXIhfQ