1. Gravity and Motion Acceleration of falling objects due to gravity
Chapter 6, Section 1
Gravity and Motion
Acceleration of falling objects due to gravity
Air Resistance
Orbiting Objects
Projectile Motion

2. 1) Who did the first Gravity experiments?
In the late 1500's, everyone knew that heavy objects fall faster than lighter ones. Why? Aristotle said so and everyone believed him.
Galileo was the first scientist to question this the common knowledge.

3. Galileo’s experiment:
He dropped two different
canon balls, one heavy and
one light
from Pisa’s Leaning Tower.
Results:
They landed on
the ground at the same
time!

4. 2) Why do objects fall to the ground at the same rate?
Because Force depends on mass and acceleration so acceleration depends on force and mass.
Ping-Pong Ball 
 Golf Ball
This stop-action photo shows these 2 balls fall at the same rate even though they have different masses!

5. A heavier object experiences a greater gravitational force than a lighter object.
But a heavier object is also harder to accelerate because it has more mass.
So the extra mass balances the additional gravitational force.

6. YouTube myth busters clip

7. 3) How do we find acceleration due to gravity?
Acceleration is the rate at which velocity changes over time. The direction is DOWN
a = =
a = acceleration units : m/s2
= change in velocity t = time

8. All objects accelerate toward the Earth at a rate of 9.8 m/s2.
This means, for every second an object falls, the object’s downward velocity increases by 9.8 m/s2.

9. A falling object accelerates at a constant rate.
This means, the object falls faster and farther each second than it did the second before.

10. 4) How do we calculate change in velocity of a falling object?
= g X t
= change in velocity = difference between final and initial velocity
g = acceleration due to gravity = 9.8 m/s2
t = time spent falling V V t
g= 9.8m/s2

11. v = g X t v = 9.8 m/s2 X 2 s v = 19.6 m/s downward
Remember we can find the change in velocity of a falling object with this equation:
v = g X t
Problem: A penny at rest is dropped from the top of the Pit. What is the penny’s velocity after it has fallen for 2 seconds?
v = g X t
v = 9.8 m/s2 X 2 s
v = 19.6 m/s downward

12. The same penny hits the ground in 4 seconds
The same penny hits the ground in 4 seconds. What is the penny’s velocity as it hits the ground?

13. The same penny hits the ground in 4 seconds
The same penny hits the ground in 4 seconds. What is the penny’s velocity as it hits the ground?
v = g X t
v = 9.8 m/s2 X 4 s
v = 40 m/s downward

14. 5) How does air resistance affect falling objects?
Air resistance: is the force that opposes the motion of objects through air.

15. Terminal Velocity
As an object gains speed, it encounters an increasing amount of upward air resistance force.
Objects will continue to accelerate (gain speed) until the air resistance force increases to a large enough value to balance the downward force of gravity.
Since the elephant has more mass, weighs more and experiences a greater downward force of gravity, it will have to accelerate (gain speed) for a longer period of time before their is sufficient upward air resistance to balance the large downward force of gravity.
Once the upward force of air resistance upon an object is large enough to balance the downward force of gravity, the object is said to have reached a terminal velocity.

16. The amount of air resistance is dependent upon the size, shape, and speed of the falling object.
So, a parachute
increases the
surface area and
therefore the resistance
of a falling object.

17. 6) When is terminal velocity reached?
Terminal velocity is reached when the upward force of air resistance is equal to the downward force of gravity.
When an object has
reached terminal
velocity, it looks like
it’s floating!
No more acceleration!
Skydiving is a great activity for experiencing some key laws of physics. Skydivers jump from planes flying high above the earth. Immediately, and in a rather dramatic way, they become keenly aware of the force of gravity. At a certain point, their parachutes open, giving them, on top of a tremendous feeling of relief, a sensation of deceleration caused by friction with the air, or drag.
Below is additional information to help understand how this works, along with some historical notes.
Why is Galileo wearing a space suit? Click on the picture to find out.
Galileo Drops the Ball – Drag
In around 1590 Galileo Galilei ( ) climbed up the Leaning Tower of Pisa and dropped some balls to the ground. Two balls of different masses, but of similar shape and density that were released together hit the ground at the same time. Until then it was commonly believed that heavy things fall faster than light things. Many people still believe this, and casual observation of everyday phenomena often does tend to confirm this view.
If you drop a brick and a feather at the same time the brick will probably hit the ground first. But this is because of differences in the amount of friction between these objects and the air around them, not because their masses are different. If there were no air, the feather and the brick would hit the ground at the same time.
Newton and the Apple – Gravity
According to legend, Isaac Newton ( ) learned about gravity when an apple fell on his head while he was sitting under a tree. He realized that there was a force -- the "force of gravity" -- that caused objects to accelerate toward earth.
Drag – the friction between an object and a fluid, such as air, that it is moving through – is a force that acts opposite to the direction that the object is moving, slowing it down. When an object is falling, drag is an upwards force. Unlike the force of gravity, drag increases with speed. When an object is not moving through the air drag is zero. As it moves faster, drag increases.
The mass of a skydiver is the same with the parachute folded up in the backpack as it is when it is open. But the open parachute causes much more drag. If you took a feather and squashed it into a small ball it would fall through the air with less drag and therefore fall faster.

18. YouTube Top Gear

19. 7) How can an object free fall?
Free fall- when only gravity is pulling it down on an object
There are no other forces acting on an object in free fall.
Free fall can occur only where there is no air, because air resistance is a force.

20. Two places where there is no air resistance: space and a vacuum

21. 8) When is an object orbiting?
Orbit: When an object is traveling around another object in space.
When a space shuttle orbits the Earth, it is moving forward (horizontal motion) but is also in free fall (vertical motion) toward the Earth.
Astronauts are always in free fall as well; this allows them to float!

23. YouTube Science Theater 1

24. 9) What is a centripetal force?
Centripetal force: the unbalanced force is needed to keep objects in circular motion and constantly changing direction
Why?
Any object in circular motion is constantly changing direction.
Objects is space orbit in a circular path.
Centripetal = “toward the center”
An unbalanced force is needed to keep them changing directions to make a circle.

25. The moon stays in orbit around the Earth because Earth’s gravitational force provides a centripetal force on the moon.

26. YouTube Science Theater

27. 10) What is projectile motion?
Projectile motion is the curved path that an object follows when throw or launched near the Earth’s surface.
The curved motion is the combination of horizontal motion and vertical motion.
Examples:
A frog leaping
Water sprayed by a sprinkler
Swimmer diving into water
Ballls being juggled
Arrow shot by an archer

29. Scissors

30. Tuesday, May 5, 2009 The Ball Drop Lab
Formula for finding the relationship between distance, gravity and acceleration:
x = ½ x g x t2
x = change in distance; height of the structure
g = acceleration due to gravity = 9.8m/s2
t2 = time squared (time x time)

31. Gravity and Falling Objects
Take the average number of seconds and use your formula to determine the height of the structure.
x = ½ x g x t2
What are sources of error?
Timing of stopwatch, dropping the ball at the same height
Do you think the use of this formula is more accurate for shorter or taller structures?
Shorter structures; air resistance will take effect as an object free falls for more time.

33. Newton’s Laws of Motion
“If I have seen farther than others, it is because I have stood on the shoulders of giants.”
Isaac Newton used the observations of Aristotle and Galileo to explain the relationship between force and motion using simple mathematics.

34. Newton’s First Law of Motion

35. An object at rest will remain at rest and an object in motion will remain in motion unless acted upon by an unbalanced force.

36. Unbalanced forces cause an object to:
Increase speed
Decrease speed
Change direction 36

37. Inertia: The tendency of objects to resist change in motion.

38. An object with more mass has more inertia.

39. Newton’s First Law in Real Life!
Hitting a ball that is not moving
Bumper cars
Seat belts
Table Cloth Trick

40. Newton’s Second Law of Motion

41. Force equals mass multiplied by acceleration F = m X a

42. Newton’s Second Law Terms to know:

43. Force: a push or a pull on an object.

44. An unbalanced force accelerates an object in the direction of that force.

45. The larger the force, the greater the acceleration.

46. Mass: how much matter is in an object.

47. Acceleration: a change in speed or direction.

48. Remember, acceleration is a change in speed or direction.

49. Force can be calculated! Force = mass x acceleration F = m X a

50. Examples:
Tug of war

51. Football defensive players.

52. Any thing where you have a big or fast object verses a small or slow object

53. Newton’s Third Law of Motion

54. For every action, there is an equal and opposite reaction.

55. All forces come in pairs.

56. Examples:
The book pushes down on the table, the table pushes up on the book

57. Did you know that when you take a step, you push the Earth away with the same force that it pushes you away? The Earth moves!

58. Examples:
For all of these, there are two objects involved

59. Examples:
A rocket engine – gas is squirted out of the engine, moving both gas and engine

60. Examples:
Release a balloon! 60

62. Momentum Notes
2/22/12

63. Momentum: is used to describe “how much” motion an object has.

64. momentum = mass x velocity p = m X v

65. Units for momentum
Kg x m/s

66. The letter “p” is used for momentum because “m” is used for mass.

67. The more momentum an object has, the more force is required to stop it.

68. A bullet has a small mass but a very high velocity, so it has a high momentum.

69. A train has a low velocity but a huge mass, so it has a large momentum.

70. A falling leaf has a small mass and a small velocity, so it has a small momentum.

71. Law of the Conservation of Momentum:

72. The total momentum of any group of objects remains the same unless acted upon by an outside force.

73. This is how billiards works:
The cue ball’s momentum is transferred to the numbered ball.

74. This is how billiards works:
The cue ball slows or stops.

75. This is how billiards works:
The numbered ball starts moving.

76. It is also how the Newton’s Cradle works!

77. What observations do you make when playing with the Newton’s Cradle?

78. The balls eventually stop. Why?

79. The end of Chapter 6!

81. Thursday, May 7, 2009
1. Use Newton’s first law to explain why airbags in cars are important during a head on collision.
2. How does Newton’s second law explain why it is easier to push a bike than to push a car with the same acceleration.
3. Newton’s third law to explain how a rocket accelerates.

82. Answers
1. Newton’s First Law: During a collision, an unbalanced force stops the motion of the car, but no unbalanced force acts on the people inside the car (unless they are wearing seat belts!) People continue to move forward. Airbags provide an unbalanced force to stop the motion of the people in the car. The airbags prevent people from hitting the dashboard or windshield.
2. Newton’s Second Law: The bike has a smaller mass, so a smaller force is required to give it the same acceleration as the car.
3. Newton’s Third Law: The hot gases expelled from the back of the rocket produce a reaction force on the rocket that accelerates it.

83. Newton’s Mini Labs

84. Velocity: the rate at which an object changes its position; speed with direction!
Suppose that during your trip, you traveled a distance of 5 miles
and the trip lasted 0.2 hours (12 minutes).
The average speed of your car could be determined as:
                                                                                                                                                 

85. Study each car individually in order to determine the answer.
Acceleration: the rate at which an object changes its velocity.
Which car or cars (red, green, and/or blue) are undergoing an acceleration?
Study each car individually in order to determine the answer.
The red car moves at a constant velocity, covering the same distance each second of the animation.
The green and blue cars are speeding up, thus covering an increased distance in each second.

86. Force A push or a pull that causes a change in motion.
Net Force: The sum of all forces (magnitude and direction) acting on an object.
Balanced force: The object will be at equilibrium; it will not accelerate Two forces are of equal magnitude and in opposite directions, they balance each other. Net force = 0 N
Unbalanced force: causes motion

87. Newton’s First Law “Law of Inertia."
An object at rest tends to stay at rest and an object in motion tends to stay in motion with the constant speed and in the same direction unless acted upon by an unbalanced force.
Example: The car and the wall

88. Inertia: The tendency of objects to resist change in motion.
Mass is a measure of inertia.
A smaller mass has a smaller inertia and requires less force to move than a larger mass.

89. Newton’s Second Law
The acceleration (change in velocity) of an object depends on the mass of the object and the amount of force applied.

90. Sponge: Thursday, April 26, 2007
According to Newton’s Second Law,
Force = Mass X Acceleration
What is the acceleration of a 3 kg mass if a force of 14.4 N is used to move the mass?
(NOTE: 1 N is equal to 1 kg X m/s2)
Step 1- Write the equation
Step 2- Replace the letters with the values and units
Step 3- Solve the problem and include units!

91. 2nd Law of Motion: Acceleration is produced when a force acts on a mass. The greater the mass (of the object being accelerated) the greater the amount of force needed to accelerate the object)
An object accelerates in the direction the force is applied.
Acceleration is directly related to force:
If you push twice as hard, It will accelerate twice as much.
Acceleration is inversely proportional to the mass of the object.
If it gains twice that mass it will accelerate half as much. #2
a = F ÷ m
2a  = 2F ÷ m
a = 2F / 2m

92. Force = Mass X Acceleration
The Second Law of Motion can be expressed as a mathematical equation:
F=M X A or FORCE (Newtons) = MASS (kg) times ACCELERATION (m/s2 )
Using what we know lets say that on the way to work my car breaks down.
My car weighs 1000 kg.
As I am pushing my truck I am able to make it roll at 0.05 m/s2.
Since you know Newton's Second Law of Motion you can calculate how much force (NEWTONS) I am pushing (applying to) on my car.
F= M X A
F= 1000 kg x .05 m/s2
F= 50 NEWTONS #6
What force is necessary to accelerate a 70 kg object at a rate of 4.2 m/s2 ?

94. Newton’s 2nd Law explains why a rock and a feather accelerate at the same rate due to gravity.

95. The third law states that for every force there is an equal and opposite force. For example, if you push on a wall, it will push back on you as hard as you are pushing on it. If you push on the object (mass) it pushes back on you.
Newton’s Third Law

96. Action-reaction force must occur in pairs!
Note:  each of the two forces in the pair acts on a different object.
Hammer pushes on stake.
Stake pushes on hammer.
The hammer acts,
the stake re-acts.       #3

98. All forces act in pairs: for every action there is an equal and opposite reaction. *Forces are equal is size and opposite in direction. #9 #7

99. Gravity pulls the ball toward the Earth.
Action Force:
Gravity pulls the ball toward the Earth.
Reaction Force:
Gravity pulls the Earth toward the Earth.
We can’t see the Earth accelerating towards the ball!
Why?
Newton’s 2nd Law:
The mass of the Earth is much larger than the ball.
Acceleration of the Earth is much smaller than the acceleration of the ball.

100. Let's study how a rocket works to understand Newton's Third Law.
                                                                                                                   
The rocket's action is to push down on the ground with the force of its powerful engines, and the reaction is that the ground pushes the rocket upwards with an equal force.

101. The Balloon Rocket Lab Materials: Meter stick Drinking straw Scissors
Purpose: To demonstrate how unbalanced forces cause motion and Newton’s Third Law of Motion.
(Also, create the fastest balloon!)
Materials: Meter stick
Drinking straw
Scissors
String
Balloon (23 cm. in circumference)
2 desks
Masking tape
Stopwatch
Clothespin

102. V= D / T (distance = 4 meters or when balloon deflates)
Procedure
Cut a 10 cm piece of drinking straw.
Cut 4.5 m of string.
Thread the end of the string through the straw piece.
Position the chairs 4 m apart.
Tie the string to the backs of the desk chairs. Make the string as tight as possible.
Inflate the balloon and twist the open end; clamp with a clothespin.
Move the straw to one end of the string.
Tape the inflated balloon to the straw.
Begin the timer and release the balloon at the same time.
Repeat the “race” 3 times and find your average time.
Use this time to calculate the velocity of the balloon.
V= D / T (distance = 4 meters or when balloon deflates)

103. What’s going on?

104. Results
The straw with the attached balloon jets across the string.
The movement stops at the end of the string or when the balloon totally deflates.
Why?
Newton’s Third Law of Action and Reaction states that when an object is pushed, it pushes back.
When the balloon was opened, the walls of the balloon pushed the air out.
When the balloon pushed agains the air, the air pushed back and the baloon moved forward, dragging the attached straw.
The string and the straw keep the balloon on a straight course!

105. Discussion Questions
1. Which type of balloon (round, long, etc.) makes the rocket go the farthest?
2. Does the size of the straw affect how long the rocket travels?
3. Does the type of string affect how far the rocket travels? (try fishing line, nylon string, cotton string, etc.)
4. Does the angle of the string affect how far the rocket travels?

106. Whiz Bang Demo: several massive books are placed upon the physics teacher's head. A wooden board is placed on top of the books and a hammer is used to drive a nail into the board. Due to the large mass of the books, the force of the hammer is sufficiently resisted (inertia). This is demonstrated by the fact that the blow of the hammer is not felt by the teacher. A common variation of this demonstration involves smashing a brick over the teacher's hand using a swift blow of the hammer. The massive brick resists the force and the hand is not hurt at all.
blood rushes from your head to your feet when riding on a descending elevator which suddenly stops.
the head of a hammer can be tightened onto the wooden handle by banging the bottom of the handle against a hard surface.
a brick is painlessly broken over the hand of a physics teacher by slamming the brick with a hammer. (CAUTION: Do not attempt this at home!)
to dislodge ketchup from the bottom of a ketchup bottle, the bottle is often turned upside down, thrust downward at a high speed and then abruptly halted.
headrests are placed in cars to prevent whiplash injuries during rear-end collisions.
while riding a skateboard (or wagon or bicycle), you fly forward off the board when hitting a curb, a rock or another object which abruptly halts the motion of the skateboard.

107. Momentum Depends on the mass and velocity of an object.
The more momentum an object has, the more difficult it is to change motion or direction.

108. Calculating Momentum p = m X v m: mass of the object (kg)
v: velocity of the object (m/s)
p: momentum (kg X m/s)
Momentum has a direction; an object’s momentum is the same direction of it’s velocity.

109. Law of Conservation of Momentum
When an object hits another object, some or all of the momentum of the first object is transferred to the object that it hit.
Any time objects collide, the total amount of momentum stays the same.
This applies as long as no other forces act on the colliding objects.
This applies whether objects stick together or bounce off each other after they collide.

110. Objects sticking together…
When football players tackle each other, they stick together. The velocity of each player changes after the collision because of conservation of momentum.
Dog leaping and catching a ball, teenager jumping on a skateboard.
The mass of the combined objects is equal to masses of the two objects together.
The objects move in the direction of the object who had greater momentum before the collision.

111. Objects bouncing off each other….
Although the bowling ball and bowling pins bounce off each other and move in different direction after a collion, momentum is neither gained nor lost.
The transfer of momentum causes objects to move in different direction at different speeds; but the total momentum of all objects will remain the same before and after the collision.
Examples: Billiards balls (pool), bumper cars.

112. Conservation of Momentum and Newton’s Third Law
Conservation of Momentum is explained by the action and reaction forces of Newton’s 3rd Law.