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Forces and the Laws of Motion Chapter 4

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4-1 Changes in Motion Objectives Describe how force affects the motion of an object Interpret and construct free-body diagrams

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Changes in Motion Dynamics is an area of mechanics which seeks to explain why objects move as they do This involves studying how forces affect motion force – an action exerted on an object that may change the object’s state of rest or motion

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Changes in Motion Often times a force acting on an object will cause the object’s velocity to change with respect to time – it’s accelerating Examples: throwing a baseball vs. catching a baseball

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Changes in Motion A newton is the SI unit of force newton (N) – the amount of force required to accelerate a 1 kg mass at 1 m/s 2 Therefore, 1 N = 1 kg x 1 m/s 2

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Changes in Motion Forces can act through contact or at a distance Contact forces are forces that result from the physical contact between objects (push/pulls) Examples: pushing a cart, kicking a football, etc. Field forces are force that do not involve the physical contact between objects Examples: gravitational force, electromagnetic force, etc.

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Force / Free-body Diagrams Force is a vector quantity Both the magnitude and the direction of the force will influence how it affects the motion of an object. The acceleration will be in the same direction as the force.

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Force / Free-body Diagrams

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Drawing Free-body Diagrams 1) Identify the forces acting on the object and the direction of the forces. 2) Draw a diagram to represent the isolated object. 3) Draw and label vector arrows for all external forces acting on the object.

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4-2 Newton’s First Law Objectives: Explain the relationship between the motion of the object and the net force acting on the object Determine the net force acting on an object Calculate the force required to bring an object to equilibrium

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Newton’s First Law It is a common misconception that if there are no forces acting on an object it will be at rest Consider what happens when push a book along a table vs. pushing it along a sheet of ice. What happens? Why?

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Newton’s First Law Galileo correctly concluded that it is an object’s nature to maintain its state of motion or rest Newton further developed this idea into what has come to be known Newton’s First Law of Motion

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Newton’s First Law Newton’s First Law of Motion: An object at rest remains at rest, and an object in motion continues in motion with constant velocity (constant speed in a straight line) unless the object experiences a net external force. Sometimes referred to as the law of inertia

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Newton’s First Law inertia – the tendency of an object to resist being moved or, if the object is moving, to resist a change in speed or direction Mass is a measure of inertia of a body The more mass that an object has, the harder it is to change its state of motion (requires a greater force) Pushing a car vs. a truck (starting from rest) Stopping a baseball vs. a bowling ball (same velocity)

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Newton’s First Law Any object that is accelerating has to have a net force acting on it net force (ΣF) – the vector sum of all of the forces acting on an object If the net force is equal to zero, the object will have a constant velocity (acceleration = 0) Example: a book being slid at a constant velocity – Why is it not accelerating?

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Newton’s First Law

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Objects that are either at rest or moving with a constant velocity are said to be in equilibrium equilibrium – the state in which the net force on an object is zero

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Newton’s First Law

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4-3 2 nd & 3 rd Laws of Motion Objectives: Describe an object’s acceleration in terms of its mass and the net force acting on it. Calculate the direction and magnitude of the acceleration caused by a known net force. Identify action-reaction pairs

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Newton’s Second Law Newton’s Second Law of Motion: The acceleration of an object is directly proportional to the net force acting on the object and inversely proportional to the object’s mass. Equation: ΣF = ma net force = mass x acceleration

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Newton’s Second Law Acceleration is inversely proportional to mass. If the same force is applied to objects of different masses: The object with the greater mass will experience a smaller acceleration. The object with less mass will experience a greater acceleration.

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Newton’s Second Law Acceleration is directly proportional to net force. When mass is constant: Increasing the force increases the acceleration by the same factor. Decreasing the force decreases the acceleration by the same factor.

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Newton’s Second Law Sample Problem C: Roberto and Laura are studying across from each other at a wide table. Laura slides a 2.2 kg book toward Roberto. If the net force acting on the book is 1.6 N to the right, what is the book’s acceleration?

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Newton’s Second Law U: a (m/s 2 ) K: m = 2.2 kg ΣF = 1.6 N to the right ΣF = ma 1.6 N = (2.2 kg)a a = 0.73 m/s 2 to the right

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Newton’s Third Law Newton recognized that a single isolated force cannot exist Consider what happens when a person wearing ice skates pushes on the wall of an ice rink… Forces always exist in pairs – Newton described this in his third law of motion

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Newton’s Third Law Newton’s Third Law of Motion: Whenever one object exerts a force on a second object, the second object exerts an equal and opposite force on the first object. Equal magnitude, opposite direction

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Newton’s Third Law Generally stated: For every action there is an equal and opposite reaction. The objects exerting the forces on each other are referred to as the action-reaction pair These forces occur at the same time and act on different objects

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Newton’s Third Law Consider the following examples: What are the action-reaction forces involved when a person hammers a nail into a piece of wood? How does a rocket work?

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Newton’s Third Law Field forces also exist in pairs When an apple falls from a tree it accelerates toward the Earth because the Earth exerts a gravitational force on the apple. If this is the action force, what is the reaction force?

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4-4 Everyday Forces Objectives: Explain the difference between mass and weight. Find the direction and magnitude of normal forces. Describe air resistance as a form of friction. Use coefficients of friction to calculate frictional force.

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Weight weight (F g ) – a measure of the magnitude of the gravitational force exerted on an object Since weight is the magnitude of the gravitational force acting on an object, it is a scalar quantity Will the weight of an object be constant?

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Weight vs. Mass Since the gravitational force between objects varies by location, weight will vary by an object’s location. Mass does not vary by location - it is an inherent property of the object. Example: A 1.5 kg hammer will have a weight of 14.7 N near the Earth’s surface, but it will weigh 2.4 N on the Moon (it’s mass is 1.5 kg in both locations)

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Weight The force of gravity can be calculated by the following equation: F g = ma g a g represents the acceleration due to gravity Near Earth’s surface a g = g = 9.8 m/s 2, so: F g = mg

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Weight What is the weight of an astronaut on Earth (g = 9.8 m/s 2 ) and on the Moon (a g = 1.6 m/s 2 ) if the astronaut’s mass is 81.6 kg?

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The Normal Force A television set is at rest on a table. The force of gravity is constantly acting on the TV. Is the TV in equilibrium? If so, how is it in equilibrium?

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The Normal Force normal force (F n ) – a force that occurs when objects come in contact with each other and acts perpendicular to the shared surface In the absence of other forces, F n is equal and opposite to the component of F g that is perpendicular to the contact surface. F n = mg cos θ

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The Normal Force

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The Force of Friction Friction is a force that resists motion (static friction) or opposes the motion of objects that are in contact (kinetic friction) Is there any friction acting on the jug of orange juice pictured to the right?

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The Force of Friction static friction (F s ) – the force that resists the initiation of sliding motion between two surfaces that are in contact and at rest

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The Force of Friction When a force is applied to an object that remains at rest, the F s is always equal an opposite to the component of the applied force that is parallel to the surface If the applied force increases, F s increases If the applied force decreases, F s decreases

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The Force of Friction Once the applied force is as great as it can be without causing the object to move, the static friction is at its maximum value (F s,max ) Increasing the applied force further will cause the object to move and it then be experiencing kinetic friction

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The Force of Friction kinetic friction (F k ) – the force that opposes the movement of two surfaces that are in contact and are sliding over each other The force of F k is less than F s,max The net force acting on the object is equal to the difference between the applied force and the force of kinetic friction ΣF = F applied - F k

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The Force of Friction The force of friction is approximately proportional to the normal force Example: It is easier to push a chair across the floor at a constant speed than it is to push a heavier desk at the same speed

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The Force of Friction The force of friction can only be approximately calculated This is because it is a macroscopic effect caused by a complex interaction of forces at the microscopic level.

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The Force of Friction In addition to the F n, the force of friction also depends on the surfaces in contact The quantity that expresses this concept is the coefficient of friction coefficient of friction (μ) – the ratio of the magnitude of the force of friction between two objects in contact to the magnitude of the normal force acting on the objects

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The Force of Friction The force of friction can be calculated with the following equations: Static Friction: F s ≤ μ s F n Kinetic Friction: F k = μ k F n

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The Force of Friction

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Air Resistance Whenever an object moves through a fluid substance, such as air or water, the fluid provides a force that opposes the objects motion Air resistance will increase on an object in free fall as the objects speed increases When the upward force of air resistance is equal in magnitude to the downward force of gravity the object reaches terminal velocity

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Fundamental Forces The four fundamental forces are all field forces Electromagnetic Force Gravitational Force Strong Nuclear Force Weak Nuclear Force

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Fundamental Forces The strong and weak nuclear forces have very small ranges and are not directly observable The electromagnetic and gravitational forces act over long ranges The strong nuclear force is the strongest of the fundamental forces; gravity is the weakest

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