3.1 Force of Gravity

Words to Know for Chapter 3.1 A force Force Due to Gravity Gravitational Field Strength Gravity Inverse Square Law Mass Newton’s Law of Universal Gravitation Universal Gravitational Constant Weight

What causes an object to accelerate? What causes an object to change direction? What causes an object to accelerate? What causes an object to change its state?

FORCE A pull or a push exerted on an object which may change the object’s state of rest, motion, and its shape

What kind of force is the ball experiencing in each picture? Change of direction Change of velocity (stop moving) Change of velocity (moving from rest)

What kind of force is the ball experiencing in each picture? In each picture, how do you know the ball is experiencing at least one force? Change of direction Change of velocity (stop moving) Change of velocity (moving from rest)

The ball’s speed and directions change What kind of force is the ball experiencing in each picture? Change of direction Change of velocity (stop moving) The ball’s speed and directions change Change of velocity (moving from rest)

The ball’s speed and directions change In the each case: FORCE changes VELOCITY with respect to TIME Change of direction Change of velocity (stop moving) The ball’s speed and directions change Change of velocity (moving from rest)

Representation of FORCE SI unit: N (newton) = = kg ∙ m/s2 The amount of force that is acting on a 1 kg mass and producing acceleration of 1 m/s2

FORCE can act through contact or at a distance Contact Force Field Force Name 2 of examples of each! Physical contact between two objects No physical contact between two objects

FORCE can act through contact or at a distance Contact Force Field Force Pushing an object Pulling an object Gravitational Force Magnetic Force Electrical Force

WHAT FORCES ACT ON A TOY CAR? 1. What happened to the car before the collision (changes in motion?) 2. What happened to the car during the collision? 3. What happened to the car after the collision (changes in motion?) How can you describe the forces acting on the car without using words?

REMEMBER Diagrams will be studied in detailed in the next section FORCE DIAGRAMS Diagrams will be studied in detailed in the next section Effect of force depends on magnitude and direction = FORCE is a vector REMEMBER

FORCE can act through contact or at a distance Field Force No physical contact between two objects

Gravitational Force Any two bodies in the universe exert a gravitational force on each other

Gravitational Force The amount of force depends on how massive the bodies are and how apart they are!

Gravitational Force - IMPORTANT 1.It can’t be “shut off”

Gravitational Force - IMPORTANT 2. It is always an ATTRACTIVE force, never REPULSIVE

It creates gravitational field around an object Gravitational Force It creates gravitational field around an object

Force (gravitational) field is An area where force is exerted

Force (magnetic) field Example:

Depends on the mass of an object GRAVITATIONAL field Depends on the mass of an object The heavier the object, the bigger the gravitational field.

GRAVITATIONAL FIELD STRENGTH A smaller object is then attracted to the centre of the Earth because Earth has larger mass The force within the gravitational field is called GRAVITATIONAL FIELD STRENGTH

Gravitational Field How can you see it?

GRAVITATIONAL FIELD STRENGTH g = Fg m Fg = gravitational force m = mass g = gravitational field strength At Earth surface, g = 9.81 N/kg

Gravitational Force = Fg = WEIGHT Near the surface of Earth – objects fall with the same rate

Gravitational Force = Fg = WEIGHT Rearranging the equation… g = Fg m

Gravitational Force = Fg = WEIGHT Rearranging the equation… g·m = Fg

Mass is the amount of matter in an object WEIGHT vs. MASS Mass is the amount of matter in an object

The mass of an object is the same anywhere in the universe WEIGHT vs. MASS The mass of an object is the same anywhere in the universe = never changes for an object

WEIGHT of an object will change depending on: WEIGHT vs. MASS WEIGHT of an object will change depending on:

WEIGHT of an object will change depending on: the amount of the gravitational force that is exerted on the object

WEIGHT = Fg on Earth vs Moon

Weight units are: Newtons WEIGHT vs. MASS Mass units are: g or kg Weight units are: Newtons

QUICK Check page 77 882N 64.9 kg 1.7 N/kg

HOMEWORK Problems: worksheet #1 Page: 1

Measuring the Force of Gravity The usual way is to balance the force of gravity with another force acting upward (with springs or coils)

Newton’s Law of Universal Gravitation Sir Isaac Newton realized this…

Newton’s Law of Universal Gravitation The Force of Gravity is an universal force which is exerted by any two objects on each other

Newton’s Law of Universal Gravitation It’s the same for planets or apples...

Newton’s Law of Universal Gravitation It’s a MUTUAL force between two objects

Newton’s Law of Universal Gravitation It varies as the inverse of the square of the distances between two objects G = Universal Gravitational Constant m1 and m2 = masses of bodies attracting each other r = the distance between the centres of the two bodies

Newton’s Law of Universal Gravitation DIRECTLY Proportional? INVERSELY Proportional? G = Universal Gravitational Constant m1 and m2 = masses of bodies attracting each other r = the distance between the centres of the two bodies

G = Universal Gravitational Constant 6.67 x 10-11 Nm2/kg2 determined by Henry Cavendish

HOMEWORK Problems: Read pages 79 - 80 Quick Check on pg 80

Earth’s Gravitational Field Strength This means... The Gravitational Field Strength of Earth, g, depends ONLY on the mass of Earth AND the distance, r, from the centre of Earth to the centre of mass of the object that has mass m

QUICK Check page 80 ¼ Fg 1/9 Fg 4Fg 9 Fg

QUICK Check page 80 9.80 x 102 N 1.62 x 102 N 1.4 x 10-11 N

Use MS Excel to draw the graphs 9.80 x 102 N 1.62 x 102 N 1.4 x 10-11 N

Which of the Graphs does your graph most resemble? Force of Gravity (N) Distance from Center of Earth (Mm) = r

Distance from Center of Earth (Mm) = r Force of Gravity (N) Distance from Center of Earth (Mm) = r

Distance from Center of Earth (Mm) = r 0.1570 0.0246 0.0785 6.16 x 10-3 0.0523 2.74 x 10-3 0.0392 1.54 x 10-3 0.0314 9.86 x 10-4 Force of Gravity (N) Distance from Center of Earth (Mm) = r

Distance from Center of Earth-1 (Mm) = r-1 0.1570 0.0246 0.0785 6.16 x 10-3 0.0523 2.74 x 10-3 0.0392 1.54 x 10-3 0.0314 9.86 x 10-4 Force of Gravity (N) Fg vs r-1 Force of Gravity (N) Distance from Center of Earth-1 (Mm) = r-1

Force of Gravity vs. INVERSE Distance from Centre (Mm-1) r-2 0.1570 0.0246 0.0785 6.16 x 10-3 0.0523 2.74 x 10-3 0.0392 1.54 x 10-3 0.0314 9.86 x 10-4 Force of Gravity (N) Force of Gravity vs. INVERSE Distance from Centre Fg vs r-2 Force of Gravity (N) Distance from Center of Earth-1 (Mm) = r-1

Fg vs r-2 Fg vs r-1 Force of Gravity (N) Force of Gravity (N) Distance from Center of Earth-1 (Mm) = r-2 Fg vs r-1 Force of Gravity (N) Distance from Center of Earth-1 (Mm) = r-1

Fg vs r-2 Fg = 400 x 1/r2 y = mx + b 1 a) Fg vs 1/r2 OR Fg vs r-2 1 b) Force of Gravity (N) Fg = 400 x 1/r2 Distance from Center of Earth-1 (Mm) = r-2 1 a) Fg vs 1/r2 OR Fg vs r-2 1 b) y = Fg x = 1/r2 m = 400 N·m2 b = 0 N y = mx + b

Fg vs r-2 Force of Gravity (N) Fg = 400 x 1/r2 4.90 = 400/r2 r = 9.04 Mm Distance from Center of Earth-1 (Mm) = r-2 G =6.67 x 10-11 Nm2/kg2 m1(Earth) = 5.98 x 10 24 kg m2(rock) = 1.00 kg r (radius) = 6.38 x 10 6 m Fg = 9.80 N 1. First calculate Fg of the rock on the Earth’s surface 2. Then, use that Fg/2 and the graph above to look up the distance

Fg vs r-2 Force of Gravity (N) Fg = 400 x 1/r2 Fg = 0.0983 N Distance from Center of Earth-1 (Mm) = r-2 G =6.67 x 10-11 Nm2/kg2 m1(Earth) = 5.98 x 10 24 kg m2(rock) = 1.00 kg r (radius) = 6.38 x 10 7 m

HOMEWORK Problems: worksheet #1 Page: 2 - 3

HOMEWORK Page: 83 (textbook) 3.1 Review Questions Problems: all even