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TRANSCRIPT
Forces
Section 3 • Using Newton’s Laws
Section 1 • Forces
Section 2 • Newton’s Laws of Motion
Table of Contents
Section
1Section
1 Forces
What is force?
• A force is a push or pull.
• Sometimes it is obvious that a force has been applied.
• But other forces aren’t as noticeable.
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1 Forces
Changing Motion
• A force can cause the motion of an object to change.
• If you have played billiards, you know that you can force a ball at rest to roll into a pocket by striking it with another ball.
Corbis/Punchstock
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1 Forces
Changing Motion
• The force of the moving ball causes the ball at rest to move in the direction of the force.
Corbis/Punchstock
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1 Forces
Balanced Forces
• Force does not always change velocity.
• When two or more forces act on an object at the same time, the forces combine to form the net force.
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1 Forces
Unbalanced Forces
• The students are pushing on the box in the same direction.
• These forces are combined, or added together, because they are exerted on the box in the same direction.
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Unbalanced Forces
• The net force that acts on this box is found by adding the two forces together.
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Unbalanced Forces
• They are considered to be unbalanced forces.
• The net force that moves the box will be the difference between the two forces because they are in opposite directions.
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Balanced Forces
• The net force on the box is zero because the two forces cancel each other.
• Forces on an object that are equal in size and opposite in direction are called balanced forces.
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1 Forces
• Suppose you give a skateboard a push with your hand.
Friction
• Does the skateboard keep moving with constant speed after it leaves your hand?
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• The force that slows the skateboard and brings it to a stop is friction.
Friction
• Friction is the force that opposes the sliding motion of two surfaces that are touching each other.
• The amount of friction between two surfaces depends on two factorsthe kinds of surfaces and the force pressing the surfaces together.
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• If two surfaces are in contact, welding or sticking occurs where the bumps touch each other.
What causes friction?
• These microwelds are the source of friction.
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• The larger the force pushing the two surfaces together is, the stronger these microwelds will be, because more of the surface bumps will come into contact.
What causes friction?
• To move one surface over the other, a force must be applied to break the microwelds.
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• Suppose you have filled a cardboard box with books and want to move it.
Static Friction
• It’s too heavy to lift, so you start pushing on it, but it doesn’t budge.
• If the box doesn’t move, then it has zero acceleration.
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• That force is the friction due to the microwelds that have formed between the bottom of the box and the floor.
Static Friction
• Static friction is the frictional force that prevents two surfaces from sliding past each other.
• Another force that cancels your push must be acting on the box.
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• You ask a friend to help you move the box.
Sliding Friction
• Pushing together, the box moves. Together you and your friend have exerted enough force to break the microwelds between the floor and the bottom of the box.
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• If you stop pushing, the box quickly comes to a stop.
Sliding Friction
• This is because as the box slides across the floor, another forcesliding frictionopposes the motion of the box.
• Sliding friction is the force that opposes the motion of two surfaces sliding past each other.
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Rolling Friction
• As a wheel rolls over a surface, static friction acts over the area where they wheel and the surface touch.
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• This special case of static friction is sometimes called rolling fiction.
Rolling Friction
• Rolling friction prevents wheels from slipping.
• When referring to tires on vehicles, the term traction is often used instead of friction.
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1 Forces
• Gravity is one of the four basic forces.
• The other basic forces are the electromagnetic force, the strong nuclear force, and the weak nuclear force.
Gravity
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What is gravity?
• Gravity is an attractive force between any two objects that depends on the masses of the objects and the distance between them.
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• Isaac Newton formulated the law of universal gravitation, which he published in 1687.
• This law can be written as the following equation.
The Law of Universal Gravitation
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• In this equation G is a constant called the universal gravitational constant, and d is the distance between the two masses, m1 and m2.
• The law of universal gravitation enables the force of gravity to be calculated between any two objects if their masses and the distance between them is known.
The Law of Universal Gravitation
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• According to the law of universal gravitation, the gravitational force between two masses decreases rapidly as the distance between the masses increases.
The Range of Gravity
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• No matter how far apart two objects are, the gravitational force between them never completely goes to zero.
The Range of Gravity
• Because the gravitational force between two objects never disappears, gravity is called a long-range force.
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• Because objects do not have to be in contact, gravity is sometimes discussed as a field.
The Gravitational Field
• A field is a region of space that has a physical quantity (such as force) at every point.
• The strength of the gravitational field is 9.8 N/kg near Earth’s surface and gets smaller as you move away from Earth.
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• The gravitational force exerted on an object is called the object’s weight.
Weight
• Because the weight of an object on Earth is equal to the force of Earth’s gravity on the object, weight can be calculated from this equation:
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• Weight and mass are not the same.
Weight and Mass
• Weight is a force and mass is a measure of the amount of matter an object contains.
• Weight and mass are related. Weight increases as mass increases.
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• The weight of an object usually is the gravitational force between the object and Earth.
Weight and Mass
• The weight of an object can change, depending on the gravitational force on the object.
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• The table shows how various weights on Earth would be different on the Moon and some of the planets.
Weight and Mass
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• In the 1840s the most distant planet known was Uranus.
Finding Other Planets
• The motion of Uranus calculated from the law of universal gravitation disagreed slightly with its observed motion.
• Some astronomers suggested that there must be an undiscovered planet affecting the motion of Uranus.
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• Using the law of universal gravitation and Newton’s laws of motion, two astronomers independently calculated the orbit of this planet.
Finding Other Planets
• As a result of these calculations, the planet Neptune was found in 1846.
Elvele Images/Alamy
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A force is a push or pull. Forces, such as theforce of the atmosphere against a person’s body,are not always noticeable.
A force is a __________.
Answer
Question 1
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When are forces on an object balanced?
Answer
When forces are equal in size and opposite in direction, they are balanced forces, and the net force is zero.
Question 2
Section Check
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Question 3
Gravity is an attractive force between any twoobjects and depends on the masses of the objectsand the distance between them.
Gravity is an attractive force between any two objects and depends on __________.
Answer
Section Check
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2 Newton’s Laws of Motion
Newton's Laws of Motion
• The British scientist Sir Isaac Newton (1642–1727) was able to state rules that describe the effects of forces on the motion of objects.
• These rules are known as Newton's law's of motion.
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2 Newton’s Laws of Motion
Newton's First Law of Motion
• Newton's first law of motion states that an object moving at a constant velocity keeps moving at that velocity unless an unbalanced net force acts on it.
• If an object is at rest, it stays at rest unless an unbalanced net force acts on it.
• This law is sometimes called the law of inertia.
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2 Newton’s Laws of Motion
Inertia and Mass
• Inertia (ih NUR shuh) is the tendency of an object to resist any change in its motion.
• If an object is moving, it will have uniform motion.
• It will keep moving at the same speed and in the same direction unless an unbalanced force acts on it.
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2 Newton’s Laws of Motion
Inertia and Mass
• If an object is at rest, it tends to remain at rest. Its velocity is zero unless a force makes it move.
• The inertia of an object is related to its mass. The greater the mass of an object is, the greater its inertia.
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2 Newton’s Laws of Motion
• Newton’s second law of motion describes how the forces exerted on an object, its mass, and its acceleration are related.
Force, Mass, and Acceleration
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2 Newton’s Laws of Motion
• What’s different about throwing a ball horizontally as hard as you can and tossing it gently?
• When you throw hard, you exert a much greater force on the ball.
Force and Acceleration
Getty Images
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2 Newton’s Laws of Motion
Force and Acceleration
• The hard-thrown ball has a greater change in velocity, and the change occurs over a shorter period of time.
Getty Images
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2 Newton’s Laws of Motion
• Recall that acceleration is the change in velocity divided by the time it takes for the change to occur.
• So, a hard-thrown ball has a greater acceleration than a gently thrown ball.
Force and Acceleration
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2 Newton’s Laws of Motion
• If you throw a softball and a baseball as hard as you can, why don’t they have the same speed?
• The difference is due to their masses.
Mass and Acceleration
Getty Images/Lars A. Niki
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2 Newton’s Laws of Motion
• If it takes the same amount of time to throw both balls, the softball would have less acceleration.
Mass and Acceleration
• The acceleration of an object depends on its mass as well as the force exerted on it.
• Force, mass, and acceleration are related.
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2 Newton’s Laws of Motion
• Newton’s second law of motion states that the acceleration of an object is in the same direction as the net force on the object, and that the acceleration can be calculated from the following equation:
Newton’s Second Law
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2 Newton’s Laws of Motion
• Newton’s second law also can be used to calculate the net force if mass and acceleration are known.
Calculating Net Force with the Second Law
• To do this, the equation for Newton’s second law must be solved for the net force, F.
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2 Newton’s Laws of Motion
• To solve for the net force, multiply both sides of the equation by the mass:
Calculating Net Force with the Second Law
• The mass, m, on the left side cancels, giving the equation:
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2 Newton’s Laws of Motion
Newton’s Third Law
• Newton’s third law of motion states that when one object exerts a force on a second object, the second one exerts a force on the first that is equal in strength and opposite in direction.
• These forces are sometimes called the action and reaction forces.
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2 Newton’s Laws of Motion
Newton’s Third Law
• But, the action force doesn’t cause the reaction force. They occur at the same time.
• When you jump on a trampoline, for example, you exert a downward force on the trampoline.
• Simultaneously, the trampoline exerts an equal force upward, sending you high into the air.
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2 Newton’s Laws of Motion
Action and Reaction Forces Don’t Cancel
• According to the third law of motion, action and reaction forces act on different objects.
• Thus, even though the forces are equal, they are not balanced because they act on different objects.
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2 Newton’s Laws of Motion
• For example, consider a student pushing on a box.
• The box pushes on the student, but the student remains in place because of the friction between her shoes and the floor.
Action and Reaction Forces Don’t Cancel
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2 Newton’s Laws of Motion
• The forces on the box include the student’s push to the right and sliding friction to the left.
• The net force on the box is not zero and the box accelerates to the right.
Newton’s Laws of Motion
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2 Newton’s Laws of Motion
• A force is an interaction between two objects.
• For example, it does not make sense to say, “The box has a force of 20 N.”
Newton’s Laws of Motion
• However, it does make sense to say, “The student pushes on the box with a force of 20 N.”
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Question 1
Inertia is __________.
A. the tendency of an object to resist any change in its motionB. the tendency of an object to have a positive accelerationC. The tendency of an object to have a net force of zero.D. The tendency of an object to change in speed or direction.
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Answer
Inertia is the tendency of an object to resist any change in its motion. An unbalanced force must act upon the object in order for its motion to change.
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Question 2
A. accelerationB. momentumC. speedD. velocity
Newton’s second law of motion states that _________ of an object is in the same direction as the net force on the object.
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Answer
The answer is A. Acceleration can be calculated by dividing the net force in newtons by the mass in kilograms.
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Question 3
According to Newton’s law, the second object exerts a force on the first that is equal in strength and opposite in direction.
According to Newton’s third law of motion, what happens when one object exerts a force on a second object?
Answer
Section Check
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What happens in a crash?
• The law of inertia can explain what happens in a car crash.
• When a car traveling about 50 km/h collides head-on with something solid, the car crumples, slows down, and stops within approximately 0.1 s.
The McGraw-Hill Companies, Inc./Andrew Resek, photographer
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What happens in a crash?
• Any passenger not wearing a safety belt continues to move forward at the same speed the car was traveling.
• Within about 0.02 s (1/50 of a second) after the car stops, unbelted passengers slam into the dashboard, steering wheel, windshield, or the backs of the front seats.
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Safety Belts
• The force needed to slow a person from 50 km/h to zero in 0.1 s is equal to 14 times the force that gravity exerts on the person.
• The belt loosens a little as it restrains the person, increasing the time it takes to slow the person down.
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Safety Belts
• This reduces the force exerted on the person.
• The safety belt also prevents the person from being thrown out of the car.
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Air bags
• Air bags also reduce injuries in car crashes by providing a cushion that reduces the force on the car's occupants.
• When impact occurs, a chemical reaction occurs in the air bag that produces nitrogen gas.
• The air bag expands rapidly and then deflates just as quickly as the nitrogen gas escapes out of tiny holes in the bag.
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Earth’s Gravitational Acceleration
• When all forces except gravity acting on a falling object can be ignored, the object is said to be in free fall.
• Close to Earth’s surface, the acceleration of a falling object in free fall is about 9.8 m/s2.
• This acceleration is given the symbol g and is sometimes called the acceleration of gravity.
• If an object is in free fall near Earth’s surface, the net force on it equals the force of gravity (Fnet = Fg).
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• Recall that g = 9.8 N/kg = 9.8 m/s2.
Earth’s Gravitational Acceleration
• This acceleration is given the symbol g and is sometimes called the acceleration of gravity.
• Therefore, Newton’s second law gives us the object’s acceleration:
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• When an object falls toward Earth, it is pulled downward by the force of gravity.
Air Resistance
• However, a friction-like force called air resistance opposes the motion of objects that move through the air.
• Air resistance causes objects to fall with different accelerations and different speeds.
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• Air resistance acts in the opposite direction to the motion of an object through air.
Air Resistance
• If the object is falling downward, air resistance acts upward on the object.
• The size of the air resistance force also depends on the size and shape of an object.
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• The amount of air resistance on an object depends on the speed, size, and shape of the object.
Air Resistance
• Air resistance, not the object’s mass, is why feathers, leaves, and pieces of paper fall more slowly than pennies, acorns, and apples.
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• As an object falls, the downward force of gravity causes the object to accelerate.
Terminal Velocity
• However, as an object falls faster, the upward force of air resistance increases.
• This causes the net force on a sky diver to decrease as the sky diver falls.
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• Finally, the upward air resistance force becomes large enough to balance the downward force of gravity.
Terminal Velocity
• This means the net force on the object is zero.
• Then the acceleration of the object is also zero, and the object falls with a constant speed called the terminal velocity.
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• The terminal velocity is the highest speed a falling object will reach.
Terminal Velocity
• The terminal velocity depends on the size, shape, and mass of a falling object.
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• You’ve probably seen pictures of astronauts and equipment floating inside the space shuttle.
Weightlessness and Free Fall
• They are said to be experiencing the sensation of weightlessness.
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• However, for a typical mission, the shuttle orbits Earth at an altitude of about 400 km.
Weightlessness and Free Fall
• According to the law of universal gravitation, at 400-km altitude the force of Earth’s gravity is about 90 percent as strong as it is at Earth’s surface.
• So an astronaut with a mass of 80 kg still would weigh about 700 N in orbit, compared with a weight of about 780 N at Earth’s surface.
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• So what does it mean to say that something is weightless in orbit?
Floating in Space
• When you stand on a scale you are at rest and the net force on you is zero.
• The scale supports you and balances your weight by exerting an upward force.
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• The dial on the scale shows the upward force exerted by the scale, which is your weight.
Floating in Space
• Now suppose you stand on the scale in an elevator that is falling.
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• If you and the scale were in free fall, then you no longer would push down on the scale at all.
Floating in Space
• The scale dial would say you have zero weight, even though the force of gravity on you hasn’t changed.
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• A space shuttle in orbit is in free fall, but it is falling around Earth, rather than straight downward.
Floating in Space
• Everything in the orbiting space shuttle is falling around Earth at the same rate, in the same way you and the scale were falling in the elevator.
• Objects in the shuttle seem to be floating because they are all falling with the same acceleration.
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• According to the second law of motion, when a ball has centripetal acceleration, the direction of the net force on the ball also must be toward the center of the curved path.
Centripetal Force
• The net force exerted toward the center of a curved path is called a centripetal force.
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• When a car rounds a curve on a highway, a centripetal force must be acting on the car to keep it moving in a curved path.
Centripetal Force and Traction
• This centripetal force is the frictional force, or the traction, between the tires and the road surface.
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• Anything that moves in a circle is doing so because a centripetal force is accelerating it toward the center.
Centripetal Force and Traction
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• Imagine whirling an object tied to a string above your head.
Gravity Can Be a Centripetal Force
• The string exerts a centripetal force on the object that keeps it moving in a circular path.
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Gravity Can Be a Centripetal Force
• In the same way, Earth’s gravity exerts a centripetal force on the Moon that keeps it moving in a nearly circular orbit.
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Force and Changing Momentum
• Recall that acceleration is the difference between the initial and final velocity, divided by the time.
• Also, from Newton’s second law, the net force on an object equals its mass times its acceleration.
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Force and Changing Momentum
• By combining these two relationships, Newton’s second law can be written in this way:
• In this equation mvf is the final momentum and mvi is the initial momentum.
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Law of Conservation of Momentum
• The momentum of an object doesn’t change unless its mass, velocity, or both change.
• Momentum, however, can be transferred from one object to another.
• The law of conservation of momentum states that if a group of objects exerts forces only on each other, their total momentum doesn’t change.
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When Objects Collide
• The results of a collision depend on the momentum of each object.
• When the first puck hits the second puck from behind, it gives the second puck momentum in the same direction.
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When Objects Collide
• If the pucks are speeding toward each other with the same speed, the total momentum is zero.
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Rocket Propulsion
• In a rocket engine, burning fuel produces hot gases. The rocket engine exerts a force on these gases and causes them to escape out the back of the rocket.
• By Newton’s third law, the gases exert a force on the rocket and push it forward.
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Question 1
When two objects collide, what happens to their momentum?
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Answer
According to the law of conservation of momentum, if the objects in a collision exert forces only on each other, their total momentum doesn’t change, even when momentum is transferred from one object to another.
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Question 2
What is terminal velocity?
A. The fastest speed an object in free fall will reach.B. The final velocity of an object.C. The change in an object’s speed.D. The last direction an object is moving.
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Answer
The answer is A. Terminal velocity is the fastest speed an object will reach in free fall.
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Question 3
Why is it important to wear a safety belt?
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Answer
In a crash, safety belts prevent passengers from continuing forward into the windshield, dashboard, or seats in front of them. Safety belts also increase the time it takes the passengers to slow down. This smaller acceleration means that the force acting on them is smaller. Thus, passengers are less likely to be injured in the crash.
Section Check
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• A force is a push or pull.
Forces
• The net force acting on an object is the combination of all the forces acting on the object.
• The forces on an object are balanced if the net force is zero.
Reviewing Main Ideas
Forces
• Friction is a force opposing the sliding motion of two surfaces in contact. Friction is caused by microwelds that form where the surfaces are in contact.
• Gravity is an attractive force between any two objects with mass. The gravitational force depends on the masses of the objects and the distance between them.
Reviewing Main Ideas
• Inertia is the resistance of an object to a change in motion.
Newton’s Law of Motion
• According to Newton’s first law of motion, the motion of an object does not change unless an unbalanced net force acts on the object.
• Newton’s second law of motion states that a net force causes an object to accelerate in the direction of the net force and that the acceleration is given by
Reviewing Main Ideas
Newton’s Laws of Motion
• Friction is a force opposing the sliding motion of two surfaces in contact. Friction is caused by microwelds that form where the surfaces are in contact.
• Air resistance opposes the motion of objects moving through the air.
• Newton’s third law of motion states that for every action there is an equal and opposite reaction.
Reviewing Main Ideas
Using Newton’s Laws
• The centripetal force is the net force on an object in circular motion and is directed toward the center of the circular path.
• When two objects collide, momentum can be conserved. Some of the momentum from one object is transferred to the other.
Reviewing Main Ideas
Question 1
Friction is the force that opposes __________ of two surfaces that are touching each other.
Answer
Friction opposes the sliding motion of two surfaces that are touching each other.
Chapter Review
Question 2
Air resistance is similar to __________.
A. accelerationB. frictionC. gravityD. net force
Chapter Review
Answer
The answer is B. Air resistance is a friction like force that opposes the motion of objects that move through the air.
Chapter Review
Question 3
You are moving a dresser that has a mass of 36 kg; its acceleration is 0.5 m/s2. What is the force being applied?
A. 8 NB. 18 NC. 35.5 ND. 72 N
Chapter Review
Answer
The answer is B. According to Newton's second law of motion, acceleration is calculated by dividing the force exerted on an object by the mass of the object. Rearrange the equation and find force by multiplying the mass of the object by its acceleration.
Chapter Review
Question 4
What is the gravitational force exerted on an object called?
Answer
The gravitational force exerted on an object is called the object’s weight
Chapter Review
Question 1
You are moving an object that has a mass of 25 kg; its acceleration is 0.25 m/s2. What is the force being applied?
A. 6.25 NB. 6.70 NC. 18.5 ND. 23.5 N
Standardized Test Practice
Answer
The answer is A. Acceleration is calculated by dividing the force exerted on an object by the mass of the object. Rearrange the equation and find force by multiplying the mass of the object by its acceleration.
Standardized Test Practice
Question 2
What is the gravitational force on a skydiver with a mass of 75 kg?
A. 8 NB. 667 NC. 588 ND. 735 N
Standardized Test Practice
Answer
The answer is D. Multiply the mass by the strength of gravity, 9.8 N/kg.
Standardized Test Practice
Question 3
On which planet is the acceleration due to gravity approximately 25 m/s2?
Standardized Test Practice
A. MarsB. JupiterC. SaturnD. Venus
Standardized Test Practice
Answer
The answer is B. Find the mass of an object by dividing its weight on Earth by the strength of gravity on Earth. Then use the object’s mass and the values in the table to determine the strength of gravity on each planet.
Standardized Test Practice
Question 4
On Earth, what is the weight of a car that has a mass of 4,000 kg?
A. 39, 200 NB. 17, 818 NC. 3, 920 ND. 186 N
Standardized Test Practice
Answer
The answer is A. The weight of an object on Earth is equal to its mass multiplied by gravitational strength.
Standardized Test Practice
Question 5
A. 39, 200 NB. 17, 818 N
C. 3, 920 ND. 186 N
Two balls roll toward each other and collide. Ball A has a momentum of 11 kg • m/s east and Ball B has a momentum of 88 kg • m/s west. If there are no external forces acting on the balls, what is the total momentum after the collision?
Standardized Test Practice
Answer
The answer is C. Momentum of the system is the same before and after the collision. Before the collision, the total momentum is p = 11 kg • m/s east and 88 kg • m/s west = 77 kg • m/s west. Momentum is conserved, so the final momentum of the system is 77 kg • m/s west.
Standardized Test Practice
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