Key Ideas What makes an object speed up, slow down, or change directions? What determines how much an object speeds up or slows down?

Bellringer The concept of force explains many occurrences in our everyday lives. From your own experience, state what will happen in the following situations. A marble is placed at the top of a smooth ramp. What will happen to the marble? What force causes this? A marble is rolling around in the back of a small toy wagon as the wagon is pulled along the sidewalk. When the wagon is stopped suddenly by a rock under one of the wheels, the marble rolls toward the front of the wagon. Why does the marble keep going when the wagon stops? (Hint: Consider what it takes to change the velocity of the wagon and the marble.)

Bellringer, continued 3. If you dropped a flat uncrumpled sheet of notebook paper and a similar piece of notebook paper that was crushed into a ball from the same height, which will reach the floor first? Why are the forces on these two pieces of paper different?

Newton’s First Law What makes an object speed up, slow down, or change directions? Objects change their state of motion only when a net force is applied. This principle is Newton’s first law.

“If I have ever made any valuable discoveries, it has been owing more to patient attention, than to any other talent.” -Sir Isaac Newton 5

Background Sir Isaac Newton ( ) an English scientist and mathematician famous for his discovery of the law of gravity also discovered the three laws of motion. He published them in his book Philosophiae Naturalis Principia Mathematica (mathematic principles of natural philosophy) in Today these laws are known as Newton’s Laws of Motion and describe the motion of all objects on the scale we experience in our everyday lives. 6

Visual Concept: Newton’s First Law
Pick up Visual Concepts: #70587, Newton’s First Law

Newton’s Laws of Motion
1. An object in motion tends to stay in motion and an object at rest tends to stay at rest unless acted upon by an unbalanced force. 2. Force equals mass times acceleration (F = ma). 3. For every action there is an equal and opposite reaction. 8

Newton’s First Law An object at rest tends to stay at rest and an object in motion tends to stay in motion unless acted upon by an unbalanced force. 9

What does this mean? Basically, an object will “keep doing what it was doing” unless acted on by an unbalanced force. If the object was sitting still, it will remain stationary. If it was moving at a constant velocity, it will keep moving. It takes force to change the motion of an object. 10

What is meant by unbalanced force?
If the forces on an object are equal and opposite, they are said to be balanced, and the object experiences no change in motion. If they are not equal and opposite, then the forces are unbalanced and the motion of the object changes. 11

Some Examples from Real Life
A soccer ball is sitting at rest. It takes an unbalanced force of a kick to change its motion. Two teams are playing tug of war. They are both exerting equal force on the rope in opposite directions. This balanced force results in no change of motion. 12

Newton’s First Law is also called the Law of Inertia
Inertia: the tendency of an object to resist changes in its state of motion The First Law states that all objects have inertia. The more mass an object has, the more inertia it has (and the harder it is to change its motion). 13

More Examples from Real Life
A powerful locomotive begins to pull a long line of boxcars that were sitting at rest. Since the boxcars are so massive, they have a great deal of inertia and it takes a large force to change their motion. Once they are moving, it takes a large force to stop them. On your way to school, a bug flies into your windshield. Since the bug is so small, it has very little inertia and exerts a very small force on your car (so small that you don’t even feel it). 14

If objects in motion tend to stay in motion, why don’t moving objects keep moving forever?
Things don’t keep moving forever because there’s almost always an unbalanced force acting upon it. A book sliding across a table slows down and stops because of the force of friction. If you throw a ball upwards it will eventually slow down and fall because of the force of gravity. 15

In outer space, away from gravity and any sources of friction, a rocket ship launched with a certain speed and direction would keep going in that same direction and at that same speed forever. 16

Newton’s First Law, continued
Objects tend to maintain their state of motion. Inertia is related to an object’s mass. inertia: the tendency of an object to resist a change in motion unless an outside force acts on the object Seat belts and car seats provide protection. When a car comes to a stop, your seat belt and the friction between you and the seat provide the unbalanced backward force that is needed to bring you to a stop as the car stops.

Visual Concept: Mass and Inertia

Newton’s Second Law What determines how much an object speeds up or slows down? Net force is equal to mass times acceleration. The unbalanced force on an object determines how much an object speeds up or slows down. This principle is Newton’s second law. net force = mass × acceleration, or F = ma Force is measured in newtons (N): 1 N = 1 kg × 1 m/s2

Force equals mass times acceleration.
Newton’s Second Law Force equals mass times acceleration. F = ma Acceleration: a measurement of how quickly an object is changing speed. 20

What does F = ma mean? Force is directly proportional to mass and acceleration. Imagine a ball of a certain mass moving at a certain acceleration. This ball has a certain force. Now imagine we make the ball twice as big (double the mass) but keep the acceleration constant. F = ma says that this new ball has twice the force of the old ball. Now imagine the original ball moving at twice the original acceleration. F = ma says that the ball will again have twice the force of the ball at the original acceleration. 21

More about F = ma If you double the mass, you double the force. If you double the acceleration, you double the force. What if you double the mass and the acceleration? (2m)(2a) = 4F Doubling the mass and the acceleration quadruples the force. So what if you decrease the mass by half? How much force would the object have now? 22

What does F = ma say? F = ma basically means that the force of an object comes from its mass and its acceleration. Something very massive (high mass) that’s changing speed very slowly (low acceleration), like a glacier, can still have great force. Something very small (low mass) that’s changing speed very quickly (high acceleration), like a bullet, can still have a great force. Something very small changing speed very slowly will have a very weak force. 23

Newton’s Second Law, continued
For equal forces, a larger mass accelerates less.

For equal masses, a greater force produces a greater acceleration.

Visual Concept: Newton’s Second Law

Math Skills Newton’s Second Law
Zookeepers lift a stretcher that holds a sedated lion. The total mass of the lion and stretcher is 175 kg, and the upward acceleration of the lion and stretcher is m/s2. What force is needed to produce this acceleration of the lion and the stretcher? 1. List the given and unknown values. Given: mass, m = 175 kg acceleration, a = m/s2 Unknown: force, F = ? N

Math Skills, continued 2. Write the equation for Newton’s second law.
force = mass  acceleration F = ma 3. Insert the known values into the equation, and solve. F = 175 kg  m/s2 F = 115 kg  m/s2 F = 115 N

Newton’s second law can also be stated as follows: The acceleration of an object is proportional to the net force on the object and inversely proportional to the object’s mass. a c e l r t i o n = f m s F

Section 2: Gravity Preview Key Ideas Bellringer Weight and Mass
Law of Universal Gravitation Free Fall Projectile Motion

Key Ideas How are weight and mass related?
Why do objects fall to the ground when dropped? What is the relationship between free-fall acceleration and mass? Why does a projectile follow a curved path?

Bellringer Recall that weight is defined as a measure of the gravitational force exerted on an object. Use knowledge you have about gravity to answer the questions in the following situations. Elvis is a student whose mass is 70 kg. On Earth’s surface, Elvis weighs about 690 N. Suppose Elvis could stand on the surface of the following bodies in the solar system. In the blanks provided, match Elvis’s weight with the letter of the appropriate body. (Hint: Earth has a mass of 6.0 x 1024 kg.) Planet Elvis’s weight a. Jupiter (m = 1.9 x 1027 kg) 780 N _______ b. Venus (m = 4.9 x 1024 kg) 113 N _______ c. Neptune (m = 1.0 x 1026 kg) 260 N _______ d. Mercury (m = 3.3 x 1023 kg) N _______ e. Earth’s moon (m = 7.4 x 1022 kg) 620 N _______

Bellringer, continued 2. Suppose Elvis is in orbit around Venus at a distance twice as far from the planet’s center as the surface of Venus is. Would you expect his weight to be greater than, less than, or equal to his weight on the surface of the planet?

Weight and Mass How are weight and mass related?
Weight is equal to mass times free-fall acceleration. weight: a measure of the gravitational force exerted on an object weight = mass x free-fall acceleration, or w = mg

Weight and Mass, continued
Weight is measured in newtons. Weight is different from mass. mass = a measure of the amount of matter in an object weight = the gravitational force an object experiences because of its mass

Visual Concept: Comparing Mass and Weight

Law of Universal Gravitation
Why do objects fall to the ground when dropped? All objects in the universe attract each other through the force of gravity.

Law of Universal Gravitation, continued
Newton’s law of universal gravitation gives the size of the gravitational force between two objects: m1 and m2 are the masses of the two objects d is the distance between the two objects G is a constant

All matter is affected by gravity. Two objects, whether large or small, always have a gravitational force between them. When something is very large, like Earth, the force is easy to detect. Gravitational force increases as mass increases. Gravitational force decreases as distance increases.

Visual Concept: Law of Universal Gravitation

Free Fall What is the relationship between free-fall acceleration and mass? In the absence of air resistance, all objects falling near Earth’s surface accelerate at the same rate regardless of their mass. free fall: the motion of a body when only the force of gravity is acting on the body

Visual Concept: Free Fall

Free Fall, continued Air resistance can balance weight.
terminal velocity: the constant velocity of a falling object when the force of air resistance is equal in magnitude and opposite in direction to the force of gravity Astronauts in orbit are in free fall.

Projectile Motion Why does a projectile follow a curved path?
Projectile motion has two components—horizontal and vertical. When the two motions are combined, they form a curved path. projectile motion: the curved path that an object follows when thrown, launched, or otherwise projected near the surface of Earth

Projectile Motion, continued
Projectile motion has a horizontal component. After you have thrown a ball, no horizontal forces are acting on the ball (if air resistance is ignored). So, the horizontal component of velocity of the ball is constant after the ball leaves your hand. Projectile motion also has a vertical component. When you throw a ball, gravity pulls it downward, which gives the ball vertical motion. In the absence of air resistance, gravity on Earth pulls objects that are in projectile motion downward with an acceleration of 9.8 m/s2, just as it pulls down all falling objects.

Projectile Motion, continued
Orbiting is projectile motion.

Visual Concept: Projectile Motion

Section 3: Newton’s Third Law
Preview Key Ideas Bellringer Action and Reaction Forces Momentum Math Skills Conservation of Momentum

Key Ideas What happens when an object exerts a force on another object? How do you calculate the momentum of an object? What is the total momentum after objects collide?

Bellringer You have learned that forces account for changes in the motion of objects. Using what you have learned, explain what happens in the following situation. An ice skater holding a basketball is standing on the surface of a frozen pond. The skater throws the ball forward. At the same time, the skater slides on the ice in the opposite direction.

Bellringer, continued 1. Is the force on the ball greater than, less than, or equal to the opposite force on the skater? Explain your answer. 2. Is the acceleration of the ball greater than, less than, or equal to the acceleration of the skater? (Hint: Remember Newton’s Second Law.) Explain your answer.

Action and Reaction Forces
What happens when an object exerts a force on another object? When one object exerts a force on a second object, the second object exerts a force equal in size and opposite in direction on the first object. This is Newton’s third law.

For every action there is an equal and opposite reaction.
Newton’s Third Law For every action there is an equal and opposite reaction. 54

What does this mean? For every force acting on an object, there is an equal force acting in the opposite direction. Right now, gravity is pulling you down in your seat, but Newton’s Third Law says your seat is pushing up against you with equal force. This is why you are not moving. There is a balanced force acting on you– gravity pulling down, your seat pushing up. 55

Think about it . . . What happens if you are standing on a skateboard or a slippery floor and push against a wall? You slide in the opposite direction (away from the wall), because you pushed on the wall but the wall pushed back on you with equal and opposite force. Why does it hurt so much when you stub your toe? When your toe exerts a force on a rock, the rock exerts an equal force back on your toe. The harder you hit your toe against it, the more force the rock exerts back on your toe (and the more your toe hurts). 56

Force equals mass times acceleration (F = ma).
Newton’s First Law: Objects in motion tend to stay in motion and objects at rest tend to stay at rest unless acted upon by an unbalanced force. Newton’s Second Law: Force equals mass times acceleration (F = ma). Newton’s Third Law: For every action there is an equal and opposite reaction. 57

Vocabulary Inertia: the tendency of an object to resist changes in its state of motion Acceleration: •a change in velocity •a measurement of how quickly an object is changing speed, direction or both Velocity: The rate of change of a position along a straight line with respect to time Force: strength or energy 58

Action and Reaction Forces, continued
Forces always occur in pairs. For every action force, there is an equal and opposite reaction force. Forces in a force pair do not act on the same object. Equal forces don’t always have equal effects. Example: The action force of Earth pulling on an object and causing it to fall is much more obvious than the equal and opposite reaction force of the falling object pulling on Earth.

Visual Concept: Action and Reaction Forces

Momentum How do you calculate the momentum of an object?
For movement along a straight line, momentum is calculated by multiplying an object’s mass and velocity. momentum = mass x velocity, or p = mv

Momentum, continued momentum: quantity defined as the product of the mass and velocity of an object SI units of momentum = kilograms times meters per second (kg•m/s). Momentum and velocity are in the same direction. Momentum increases as mass and velocity increase. Force is related to change in momentum. As the period of time of the momentum’s change becomes longer, the force needed to cause this change in momentum becomes smaller.

Math Skills Momentum Calculate the momentum of a 6.00 kg bowling ball moving at 10.0 m/s down the alley toward the pins. 1. List the given and unknown values. Given: mass, m = 6.00 kg velocity, v = 10.0 m/s (toward the pins) Unknown: momentum, p = ? kg • m/s (and direction)

Math Skills, continued momentum = mass x velocity p = mv
2. Write the equation for momentum. momentum = mass x velocity p = mv 3. Insert the known values into the equation, and solve. p = mv = 6.00 kg  10.0 m/s p = 60.0 kg • m/s (toward the pins)

Conservation of Momentum
What is the total momentum after objects collide? The total momentum of two or more objects after a collision is the same as it was before the collision. In other words, the total amount of momentum in an isolated system is conserved. This principle is the law of conservation of momentum.

Visual Concept: Momentum and Collisions

Forces Preview Understanding Concepts Reading Skills
Interpreting Graphics

Understanding Concepts
After a bank customer cashes a check, some of the money received accidentally slips from the customer’s hands. What force causes the bills to hit the ground later than the coins do? A. static friction B. gravity C. air resistance D. magnetism

Understanding Concepts, continued
If the nickel and iron at the Earth’s core were suddenly replaced with cotton candy, what would happen to the mass and weight of the objects on the Earth’s surface? F. Their mass and weight both increase. G. Their mass would stay the same and their weight would decrease. H. Their mass would decrease and their weight would increase. I. Neither their mass nor weight change.

3. A truck with a mass of 2,000 kg is traveling at a constant velocity of 40 m/s. What is the net force acting upon the truck? A. 0.0 N B N C. 50 N D 800 N

4. A high-altitude balloonist at an altitude of 15,000 m drops an instrument package. When does the package reach terminal velocity? F. as it begins to fall G. as it matches the speed of the plane H. as it stops accelerating from air resistance I. as it impacts the Earth’s surface

5. Explain why the moon does not fly off into space in a straight line nor plummet directly toward the Earth’s surface.

5. Explain why the moon does not fly off into space in a straight line nor plummet directly toward the Earth’s surface. Answer: The forward and downward motions combine to produce an orbit.

6. A racing motorcycle with a mass of 300 kg accelerates from 0 to 60 m/s in 5 seconds. How much force is acting on the motorcycle?

6. A racing motorcycle with a mass of 300 kg accelerates from 0 to 60 m/s in 5 seconds. How much force is acting on the motorcycle? Answer: 3,600 N

Reading Skills A REGULAR VISITOR A microgravity environment is one in which the apparent weight of an object is much less than its weight on Earth. The term microgravity is used instead of weightlessness because every object has some weight, though that weight may be so minuscule as to be undetectable. Because every object in the universe exerts a gravitational pull on every other object, every object possesses weight. Microgravity occurs whenever an object is in free fall. Scientists achieve microgravity environments in a number of ways. Drop towers and research aircraft provide it for up to 20 s. The Shuttle and the International Space Station can provide it for months.

Reading Skills, continued
A REGULAR VISITOR, continued A rocket ship that is accelerating by firing its rockets cannot provide microgravity. Even if the rocket is accelerating uniformly, force is applied to the rocket by the gas escaping out the back. This force must be transferred to each part of the ship through either pressure or tension, and thus weightlessness is not experienced.

When the Shuttle is orbiting, it is in constant motion around the Earth. Why isn’t this motion experienced as weight? A. There is no net force acting on the Shuttle. B. The Shuttle’s mass is not large enough to exert a measurable gravitational pull. C. The Earth is exerting the same pull on both the Shuttle and its passengers. D. The Earth is too far away to have a measurable gravitational effect.

8. Why can the Shuttle provide microgravity only after it achieves orbit?

8. Why can the Shuttle provide microgravity only after it achieves orbit? Answer: Because before that point and after it takes off, the Shuttle is accelerating, so there is a net force on it that is also experienced by the objects within it.

Interpreting Graphics
The following graph charts the speeds of three objects in motion. Use this graph to answer questions 9 and 10.

Interpreting Graphics, continued
At the 1 s mark, which objects have equal momentum? A. the bicycle and the rock B. the rock and the bowling ball C. the bowling ball and the bicycle D. All three objects have the same momentum.

10. At the 3 s mark, which object or objects have a net force acting on them? F. the bicycle H. the bowling ball G. the rock I. the bicycle and the bowling ball

The following graphic shows a long jumper making a jump from west to east. Use this graphic to answer questions 11 and 12.

11. In what direction or directions is the net force acting on the jumper between 0.5 s and 2 s? A. first up and to the east, then down and to the west B. first up and to the east, then down and to the east C. up and to the east D. down and to the west

12. When the long jumper jumps, Earth exerts a force that moves him up and to the east. Since there is a reaction force exerted on Earth, why doesn’t Earth move the same distance down and to the west?

12. When the long jumper jumps, Earth exerts a force that moves him up and to the east. Since there is a reaction force exerted on Earth, why doesn’t Earth move the same distance down and to the west? Answer: The acceleration of Earth is force divided by mass, and since Earth’s mass is so large, the resulting acceleration of Earth is very small.

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Key Ideas What makes an object speed up, slow down, or change directions? What determines how much an object speeds up or slows down?

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