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Forces Chapter 3

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3-1 Force and Acceleration The acceleration experienced by an object is directly proportional to the force exerted on it. The acceleration experienced by an object is directly proportional to the force exerted on it. A large force causes a large acceleration. A large force causes a large acceleration. A small force causes a small acceleration. A small force causes a small acceleration.

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3-1 Mass and Acceleration The acceleration experienced by an object is inversely proportional to the mass of the object. The acceleration experienced by an object is inversely proportional to the mass of the object. Imagine exerting equal forces on a baseball and a softball. Imagine exerting equal forces on a baseball and a softball. The softball accelerates less because its mass is greater. The softball accelerates less because its mass is greater.

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3-1 Newton’s Second Law Newton expressed the relationship between force, mass, and acceleration mathematically. Newton expressed the relationship between force, mass, and acceleration mathematically. Newton’s Second Law of Motion – acceleration of an object is in same direction as net force, is directly proportional to net force, and is inversely proportional to object’s mass. Newton’s Second Law of Motion – acceleration of an object is in same direction as net force, is directly proportional to net force, and is inversely proportional to object’s mass. acceleration (m/s 2 ) = net force (N)/mass (kg) acceleration (m/s 2 ) = net force (N)/mass (kg) a = F/m F = m x a a = F/m F = m x a

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3-1 Example: Newton’s Second Law You push a wagon that has a mass of 8 kg. If the net force on the wagon is 4 N, what is the wagon’s acceleration? You push a wagon that has a mass of 8 kg. If the net force on the wagon is 4 N, what is the wagon’s acceleration?

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3-1 Example: Newton’s Second Law If the mass of a helicopter is 4,500 kg, and the net force on it is 18,000 N, what is the helicopter’s acceleration. If the mass of a helicopter is 4,500 kg, and the net force on it is 18,000 N, what is the helicopter’s acceleration.

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3-1 Example: Newton’s Second Law What is the net force on a race car with a mass of 900 kg if its acceleration is 32.0 m/s 2 ? What is the net force on a race car with a mass of 900 kg if its acceleration is 32.0 m/s 2 ?

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3-1 Example: Newton’s Second Law A car pulled by a tow truck has an acceleration of 2.0 m/s 2. What is the mass of the car if the net force on the car is 3000 N? A car pulled by a tow truck has an acceleration of 2.0 m/s 2. What is the mass of the car if the net force on the car is 3000 N?

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3-1 Example: Newton’s Second Law What is the net force on a skydiver falling with a constant velocity of 10 m/s downward? What is the net force on a skydiver falling with a constant velocity of 10 m/s downward?

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3-1 Friction Friction is a force that opposes motion. Friction is a force that opposes motion. The amount of friction between two objects depends on the kinds of surfaces, the force pushing the surfaces together, and the surface area in contact. The amount of friction between two objects depends on the kinds of surfaces, the force pushing the surfaces together, and the surface area in contact.

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3-1 What causes friction? Even surfaces that seem smooth may be rough at the microscopic level. Even surfaces that seem smooth may be rough at the microscopic level. Microwelds form where bumps come into contact. Microwelds form where bumps come into contact. The larger the force pushing surfaces together, the more surface area in contact, and the stronger the microwelds. The larger the force pushing surfaces together, the more surface area in contact, and the stronger the microwelds.

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3-1 Static Friction Imagine you try to push a heavy box, but it doesn’t move. Imagine you try to push a heavy box, but it doesn’t move. Since acceleration is zero, the net force on the object is zero. Since acceleration is zero, the net force on the object is zero. Another force must cancel your applied force. What is this force? Another force must cancel your applied force. What is this force? Static friction is the frictional force that prevents two surfaces from sliding past each other. Static friction is the frictional force that prevents two surfaces from sliding past each other.

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3-1 Sliding Friction Sliding friction is the force that opposes the motion of two surfaces sliding past each other. Sliding friction is the force that opposes the motion of two surfaces sliding past each other. To move the box, you must apply enough force to break the microwelds (static friction). To move the box, you must apply enough force to break the microwelds (static friction). To keep the box moving, you must continually apply force to overcome sliding friction. To keep the box moving, you must continually apply force to overcome sliding friction.

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3-1 Rolling Friction Rolling friction is the frictional force between a rolling object and the surface with which it is in contact. Rolling friction is the frictional force between a rolling object and the surface with which it is in contact. Changing sliding friction to rolling friction is one way to reduce friction. Changing sliding friction to rolling friction is one way to reduce friction.

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3-1 Air Resistance Objects fall toward earth because of the force of gravity. Objects fall toward earth because of the force of gravity. Air resistance opposes the downward motion. Air resistance opposes the downward motion. Without air resistance (in a vacuum), all objects fall with the same acceleration. Without air resistance (in a vacuum), all objects fall with the same acceleration.

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3-1 Air Resistance Air resistance causes objects to fall with different accelerations. Air resistance causes objects to fall with different accelerations. Air resistance acts in the opposite direction to the motion of the object. Air resistance acts in the opposite direction to the motion of the object. The amount of air resistance on an object depends on the speed, size, and shape of the object. The amount of air resistance on an object depends on the speed, size, and shape of the object.

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3-1 Terminal Velocity As an object falls, gravity causes it to accelerate. As an object falls, gravity causes it to accelerate. Acceleration due to gravity is 9.8 m/s 2 on earth. Acceleration due to gravity is 9.8 m/s 2 on earth. However, air resistance increases as objects fall faster. However, air resistance increases as objects fall faster. When the upward force of air resistance is equal to the downward force of gravity, the object no longer accelerates. It falls at a constant velocity. When the upward force of air resistance is equal to the downward force of gravity, the object no longer accelerates. It falls at a constant velocity. This is called terminal velocity. This is called terminal velocity.

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3-1 Terminal Velocity Terminal velocity depends on size, shape, and mass of falling object. Terminal velocity depends on size, shape, and mass of falling object.

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3-2 Gravity Gravity is a force of attraction that exists between any two objects due to their mass. Gravity is a force of attraction that exists between any two objects due to their mass. Gravity depends on the masses of the objects and the distance between them. Gravity depends on the masses of the objects and the distance between them. Gravity increases as the mass of either object increases. Gravity increases as the mass of either object increases. Gravity decreases as the distance between the two objects increases. Gravity decreases as the distance between the two objects increases.

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3-2 Gravity Why don’t you feel the gravitational pull of your desk? Your notebook? Your neighbor? Why don’t you feel the gravitational pull of your desk? Your notebook? Your neighbor? Only Earth is close enough and has enough mass that you can feel its gravitational attraction. Only Earth is close enough and has enough mass that you can feel its gravitational attraction.

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3-2 Gravity One of the basic forces of the universe! One of the basic forces of the universe! Gravity Gravity Electromagnetic force Electromagnetic force Strong nuclear force Strong nuclear force Weak nuclear force Weak nuclear force

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3-2 The Law of Universal Gravitation Sir Isaac Newton, 1687 Sir Isaac Newton, 1687 F = Gm 1 m 2 F = Gm 1 m 2 d 2 F – gravitational force G – a constant m 1, m 2 – masses of the two objects d – distance between centers of mass

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3-2 Universal Gravitation Gravitational force between two objects decreases rapidly as distance between them increases. Gravitational force between two objects decreases rapidly as distance between them increases. If distance increases from 1m to 2m, force of gravity decreases by factor of 4. If distance increases from 1m to 2m, force of gravity decreases by factor of 4. Can force of gravity between two objects ever go to zero? Can force of gravity between two objects ever go to zero?

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3-2 Earth’s Gravitational Acceleration When all forces except gravity acting on a falling object can be ignored, to object is in free fall. When all forces except gravity acting on a falling object can be ignored, to object is in free fall. In free fall, all objects fall with the same acceleration. In free fall, all objects fall with the same acceleration. Near earth’s surface, acceleration is about 9.8 m/s 2. (g) Near earth’s surface, acceleration is about 9.8 m/s 2. (g) The downward force on a falling object is equal to mass x g. The downward force on a falling object is equal to mass x g.

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3-2 Weight Even if you’re not falling, earth exerts force on you, pulling you downward. Even if you’re not falling, earth exerts force on you, pulling you downward. weight = mass x g weight = mass x g Weight and mass are directly proportional but not the same. Weight and mass are directly proportional but not the same. Mass will not change with location, but weight can. Mass will not change with location, but weight can.

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3-2 Weightlessness Is an astronaut in space really weightless? Is an astronaut in space really weightless? Space shuttles orbit earth at an altitude of around 400 km. Space shuttles orbit earth at an altitude of around 400 km. At this position, the force of gravity is still about 90% as strong as on earth. At this position, the force of gravity is still about 90% as strong as on earth. The astronaut isn’t weightless, but feels weightless. The astronaut isn’t weightless, but feels weightless.

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3-2 Weightlessness Think about weighing yourself on a scale. Think about weighing yourself on a scale. You push down on the scale, the scale pushes back up on you and registers your weight. You push down on the scale, the scale pushes back up on you and registers your weight. What if you stood on a scale in a falling elevator? What if you stood on a scale in a falling elevator? What would the scale read? What would the scale read? If you and the scale are in free fall, the scale reads zero. If you and the scale are in free fall, the scale reads zero.

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3-2 Weightlessness A space shuttle in orbit is in free fall. A space shuttle in orbit is in free fall. Instead of falling down, it is falling around earth in a circular path. Instead of falling down, it is falling around earth in a circular path. Everything in the shuttle is also in free fall around the earth. Everything in the shuttle is also in free fall around the earth. Everything seems to be floating – everything is falling with the same acceleration. Everything seems to be floating – everything is falling with the same acceleration.

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3-2 Projectile Motion Objects that are thrown curve downward. Objects that are thrown curve downward. You must aim a bit above your target in order to hit it. You must aim a bit above your target in order to hit it. A projectile is anything thrown or shot through the air. A projectile is anything thrown or shot through the air. Because of gravity, projectiles follow curved paths. Because of gravity, projectiles follow curved paths.

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3-2 Projectile Motion Projectile motion has horizontal and vertical components. Projectile motion has horizontal and vertical components. Vertical velocity vectors are red. Vertical velocity vectors are red. Horizontal velocity vectors are blue. Horizontal velocity vectors are blue.

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3-2 Centripetal Force Acceleration toward the center of a curved or circular path is called centripetal acceleration. Acceleration toward the center of a curved or circular path is called centripetal acceleration. When an object goes around a curve, its acceleration is toward the center of the curve. When an object goes around a curve, its acceleration is toward the center of the curve. If acceleration is toward the center of the curve, then force is also toward the center (F = m x a). If acceleration is toward the center of the curve, then force is also toward the center (F = m x a). Net force toward the center of a curved path is centripetal force. Net force toward the center of a curved path is centripetal force.

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3-2 Centripetal Force When a car rounds a curve, centripetal force makes it move in a curved path. When a car rounds a curve, centripetal force makes it move in a curved path. The centripetal force is the traction (or friction) between the tires and the road. The centripetal force is the traction (or friction) between the tires and the road. If the road is slippery and frictional force is small, what will happen? If the road is slippery and frictional force is small, what will happen?

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3-2 Gravity as a Centripetal Force The Sun’s gravity exerts a centripetal force on the Earth. The Sun’s gravity exerts a centripetal force on the Earth. The Earth’s gravity exerts a centripetal force on the moon. The Earth’s gravity exerts a centripetal force on the moon.

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3-3 The Third Law of Motion Newton’s 3 rd Law of Motion – 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. Newton’s 3 rd Law of Motion – 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.

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3-3 Action and Reaction A pair of forces A pair of forces Act on different objects Act on different objects Equal in magnitude Equal in magnitude Opposite in direction Opposite in direction NOT BALANCED, DON’T CANCEL NOT BALANCED, DON’T CANCEL Examples: Examples:

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3-3 Rocket Propulsion How does Newton’s 3 rd Law explain how rockets work? How does Newton’s 3 rd Law explain how rockets work?

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3-3 Momentum Moving objects have a property called momentum. Moving objects have a property called momentum. “Inertia in motion” “Inertia in motion” Related to how much force it takes to change object’s motion Related to how much force it takes to change object’s motion p = m x v p = m x v Unit is kg m/s Unit is kg m/s Momentum has magnitude and direction Momentum has magnitude and direction

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3-3 Force and Changing Momentum To find the net force exerted on an object, divide the change in momentum by the time over which the change occurs: To find the net force exerted on an object, divide the change in momentum by the time over which the change occurs: F = (mv f – mv i )/t

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3-3 Momentum Problem What is the momentum of a car with a mass of 1300 kg traveling at a speed of 28 m/s? What is the momentum of a car with a mass of 1300 kg traveling at a speed of 28 m/s?

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3-3 Momentum Problem What is the force exerted by a catcher’s glove on a 0.15-kg baseball moving at 35 m/s that is stopped in 0.02 s? What is the force exerted by a catcher’s glove on a 0.15-kg baseball moving at 35 m/s that is stopped in 0.02 s?

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