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ISAAC NEWTON AND THE FORCE Dynamics

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Kinematics vs Dynamics Kinematics – the study of how stuff move Velocity, acceleration, displacement, vector analysis Started with Galileo around the year 1600 Describes how things move and how to predict their movements, but does not explain the movements Dynamics – the study of why stuff move Started with Isaac Newton and his three laws (1687) Explains why things move the way they do by using forces and relating the force to acceleration

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Newton and Galileo Galileo is considered by many to be the first real physicist (perhaps the first real scientist) because he was the first to experimentally test and describe the movement of objects (kinematics) Newton took this to another level, not only describing but also explaining why objects move the way they do (dynamics) The result is the Newton’s Laws (textbook chapter 5) The discoveries of Galileo and Newton form the basis of the topic of Classical Mechanics

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Force A force is defined as a push or pull Forces occur when objects touch each other Forces cause objects to accelerate Forces are vectors and therefore we have to use vector analysis There are 4 fundamental forces: Gravitational (attractive force between all objects) Electromagnetic (force resulting from electric charge) Strong Nuclear (attractive force inside atoms) Weak Force (a different form of electromagnetic force)

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Newton’s First Law An object with no net force acting on it remains at rest or moves in a straight line with constant velocity Object at rest will stay at rest and moving objects will continue to move unless acted upon by a force Also known as the law of inertia Inertia - resistance of any physical object to a change in its state of motion or rest

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Newton’s Second Law The acceleration of a body is directly proportional to the net force on it and inversely proportional to its mass The larger the mass of an object, the more force needed to make it accelerate We say that the massive object has more inertia than a less massive object F = ma F is force, measured in newtons (N)

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Newton’s Third Law When one object exerts a force on a second object, the second object exerts a force on the first that is equal in magnitude but opposite in direction These forces are called action-reaction force pairs An action produces an equal and opposite reaction Only the forces acting ON an object determine its acceleration

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Examples of Newton’s Second Law 1. What force is required to accelerated a 1200. kg car at 2.40 m/s 2 ? 2. How much force must be applied to a car travelling with velocity of 25.0 m/s if we want to stop it in 10.0 s? The mass of the car is 1100. kg

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Practice Problems Page 163 #1, 3 Page 168 #7, 8

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Mass and Weight Mass refers to the quantity of matter in an object Weight is the gravitational force of an object The weight is dependent on the mass and the gravitational force exerted on the object Astronauts in space are weightless (and even this isn’t exactly true), but they are not massless

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Weight The force of gravity is F = mg On Earth, g ≈ -9.81 m/s 2 Therefore, W = mg Weight is a vector, so pay attention to the direction Weight is usually referred to as the gravitational force, F g

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Calculating You Weight The bathrooms scales you may or may not own does not directly measure your mass It measures your weight as a force, then estimates your mass from that measurement The bathroom scale tells Mr. Lee that his mass is 84.6 kg. What is the weight measured by the scale?

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Practice Problems Page 137, #1~4 Please refer to page 132 and 133 for a table of values used in questions 2 and 3

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Free Body Diagrams A simple diagram used to depict an object and all forces acting on it

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Friction Friction is a force that inhibit relative motion between objects that are in contact with each other Friction slows things down, they are why objects tend to stop if we stop pushing/pulling them F f = μ*F n

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Normal Force (F N ) The force exerted by a surface on a object that prevents the object from penetrating the surface The force that prevents you from falling through the floor (awesome) or walking through a closed door (not so awesome) ALWAYS normal (perpendicular) to the surface Often (but not always) equal to the weight

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Coefficient of Friction (μ) This is a “stickiness” value for two objects Dependent on the surface-to-surface contact of the two objects The coefficient of friction has no unit Two types: μ s for Static Friction and μ k for Kinetic Friction Generally, μ k < μ s for any two materials

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Static Friction Static friction is friction that keep stationary objects stationary It only applies when we are trying to move an object from rest Its direction will be where it can prevent the object from accelerating

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Kinetic Friction Kinetic friction only applies to moving objects A force that tries to make moving objects stop ALWAYS points in the opposite direction of the object’s movement (opposite the velocity vector) Smaller in magnitude than static friction

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Net Force Newton’s second law: F net = ma F net is the sum of all forces acting on the object Remember that forces are vectors, and to add them we must use vector addition

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Example Problems A cart with a mass of 50.0 kg is being pushed along a rough sidewalk with an applied horizontal force of 200. N and has a constant velocity of 3.00 m/s a. What other horizontal force is acting on the cart and what is the magnitude and direction of that force? b. What value of applied horizontal force would be required to accelerate the carriage from rest to 6.00 m/s in 3.00 s?

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Another Example Problem An 5.00 kg block of metal is being pulled across a wooden desk at a uniform velocity. If the block is being pulled with a horizontal force of 50.0 N, what is the coefficient of kinetic friction?

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Practice Problems

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