Table of Contents Forces Section 1 • Forces Section 2 • Newton’s Laws of Motion Section 3 • Using Newton’s Laws

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.

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

Changing Motion The force of the moving ball causes the ball at rest to move in the direction of the force. Corbis/Punchstock

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.

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.

Unbalanced Forces The net force that acts on this box is found by adding the two forces together.

Unbalanced Forces The net force that moves the box will be the difference between the two forces because they are in opposite directions. They are considered to be unbalanced forces.

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.

Friction Suppose you give a skateboard a push with your hand. Does the skateboard keep moving with constant speed after it leaves your hand?

Friction The force that slows the skateboard and brings it to a stop is 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 factorsthe kinds of surfaces and the force pressing the surfaces together.

What causes friction? If two surfaces are in contact, welding or sticking occurs where the bumps touch each other. These microwelds are the source of friction.

What causes friction? 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. To move one surface over the other, a force must be applied to break the microwelds.

Static Friction Suppose you have filled a cardboard box with books and want to move it. 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.

Static Friction That force is the friction due to the microwelds that have formed between the bottom of the box and the floor. 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.

Sliding Friction You ask a friend to help you move the box. 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.

Sliding Friction If you stop pushing, the box quickly comes to a stop. This is because as the box slides across the floor, another forcesliding frictionopposes the motion of the box. Sliding friction is the force that opposes the motion of two surfaces sliding past each other.

Rolling Friction As a wheel rolls over a surface, static friction acts over the area where they wheel and the surface touch.

Rolling Friction This special case of static friction is sometimes called rolling fiction. Rolling friction prevents wheels from slipping. When referring to tires on vehicles, the term traction is often used instead of friction.

Gravity 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.

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.

The Law of Universal Gravitation 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 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 Range of Gravity 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 No matter how far apart two objects are, the gravitational force between them never completely goes to zero. Because the gravitational force between two objects never disappears, gravity is called a long-range force.

The Gravitational Field Because objects do not have to be in contact, gravity is sometimes discussed as a 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.

Weight The gravitational force exerted on an object is called the object’s 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:

Weight and Mass Weight and mass are not the same. 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.

Weight and Mass The weight of an object usually is the gravitational force between the object and Earth. The weight of an object can change, depending on the gravitational force on the object.

Weight and Mass The table shows how various weights on Earth would be different on the Moon and some of the planets.

Finding Other Planets In the 1840s the most distant planet known was Uranus. 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.

Finding Other Planets Using the law of universal gravitation and Newton’s laws of motion, two astronomers independently calculated the orbit of this planet. As a result of these calculations, the planet Neptune was found in 1846. Elvele Images/Alamy

Section Check Question 1 A force is a __________. Answer A force is a push or pull. Forces, such as the force of the atmosphere against a person’s body, are not always noticeable.

Section Check Question 2 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.

Section Check Question 3 Gravity is an attractive force between any two objects and depends on __________. Answer Gravity is an attractive force between any two objects and depends on the masses of the objects and the distance between them.

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.

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.

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.

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.

Force, Mass, and Acceleration Newton’s second law of motion describes how the forces exerted on an object, its mass, and its acceleration are related.

Force and Acceleration 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. Getty Images

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

Force and Acceleration 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.

Getty Images/Lars A. Niki Mass and Acceleration 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. Getty Images/Lars A. Niki

Mass and Acceleration If it takes the same amount of time to throw both balls, the softball would have less acceleration. The acceleration of an object depends on its mass as well as the force exerted on it. Force, mass, and acceleration are related.

Newton’s Second Law 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:

Calculating Net Force with the Second Law Newton’s second law also can be used to calculate the net force if mass and acceleration are known. To do this, the equation for Newton’s second law must be solved for the net force, F.

Calculating Net Force with the Second Law To solve for the net force, multiply both sides of the equation by the mass: The mass, m, on the left side cancels, giving the equation:

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.

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.

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.

Action and Reaction Forces Don’t Cancel 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.

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 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.” However, it does make sense to say, “The student pushes on the box with a force of 20 N.”

Section Check Question 1 Inertia is __________. A. the tendency of an object to resist any change in its motion B. the tendency of an object to have a positive acceleration C. The tendency of an object to have a net force of zero. D. The tendency of an object to change in speed or direction.

Section Check 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.

Section Check Question 2 Newton’s second law of motion states that _________ of an object is in the same direction as the net force on the object. A. acceleration B. momentum C. speed D. velocity

Section Check Answer The answer is A. Acceleration can be calculated by dividing the net force in newtons by the mass in kilograms.

Section Check Question 3 According to Newton’s third law of motion, what happens when one object exerts a force on a second object? Answer According to Newton’s law, the second object exerts a force on the first that is equal in strength and opposite in direction.

The McGraw-Hill Companies, Inc./Andrew Resek, photographer 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

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.

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.

Safety Belts This reduces the force exerted on the person. The safety belt also prevents the person from being thrown out of the car.

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.

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).

Earth’s Gravitational Acceleration Therefore, Newton’s second law gives us the object’s acceleration: Recall that g = 9.8 N/kg = 9.8 m/s2. This acceleration is given the symbol g and is sometimes called the acceleration of gravity.

Air Resistance When an object falls toward Earth, it is pulled downward by the force of gravity. 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.

Air Resistance Air resistance acts in the opposite direction to the motion of an object through air. 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.

Air Resistance The amount of air resistance on an object depends on the speed, size, and shape of the object. Air resistance, not the object’s mass, is why feathers, leaves, and pieces of paper fall more slowly than pennies, acorns, and apples.

Terminal Velocity As an object falls, the downward force of gravity causes the object to accelerate. 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.

Terminal Velocity Finally, the upward air resistance force becomes large enough to balance the downward force of gravity. 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.

Terminal Velocity The terminal velocity is the highest speed a falling object will reach. The terminal velocity depends on the size, shape, and mass of a falling object.

Weightlessness and Free Fall You’ve probably seen pictures of astronauts and equipment floating inside the space shuttle. They are said to be experiencing the sensation of weightlessness.

Weightlessness and Free Fall However, for a typical mission, the shuttle orbits Earth at an altitude of about 400 km. 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.

Floating in Space So what does it mean to say that something is weightless in orbit? 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.

Floating in Space The dial on the scale shows the upward force exerted by the scale, which is your weight. Now suppose you stand on the scale in an elevator that is falling.

Floating in Space If you and the scale were in free fall, then you no longer would push down on the scale at all. The scale dial would say you have zero weight, even though the force of gravity on you hasn’t changed.

Floating in Space A space shuttle in orbit is in free fall, but it is falling around Earth, rather than straight downward. 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.

Centripetal Force 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. The net force exerted toward the center of a curved path is called a centripetal force.

Centripetal Force and Traction 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. This centripetal force is the frictional force, or the traction, between the tires and the road surface.

Centripetal Force and Traction Anything that moves in a circle is doing so because a centripetal force is accelerating it toward the center.

Gravity Can Be a Centripetal Force Imagine whirling an object tied to a string above your head. The string exerts a centripetal force on the object that keeps it moving in a circular path.

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.

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.

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.

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.

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.

When Objects Collide If the pucks are speeding toward each other with the same speed, the total momentum is zero.

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.

Section Check Question 1 When two objects collide, what happens to their momentum?

Section Check 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.

Section Check Question 2 What is terminal velocity? The fastest speed an object in free fall will reach. The final velocity of an object. The change in an object’s speed. The last direction an object is moving.

Section Check Answer The answer is A. Terminal velocity is the fastest speed an object will reach in free fall.

Section Check Question 3 Why is it important to wear a safety belt?

Section Check 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.