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Energy

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Which has more energy? Explain. Work

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Work ( W ) - a force acting upon an object to cause a change in position and a change of energy. Units Nm = Joules (J) W = Fd = ∆ E t

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If a box lifted 5m gains 100J of energy, 1) What force was used? F d = ∆E T 2) What was the work done on the box? w = ∆E T

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If a box lifted 5m gains 100J of energy, 1) What force was used? F 5m = 100J 2) What was the work done on the box? w = 100J

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If a box lifted 5m gains 100J of energy, 1) What force was used? F = 20N 2) What was the work done on the box? w = 100J

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Are the following scenarios examples of work? Explain why or why not.

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Can vertical forces produce horizontal work? Explain. NO! A vertical force can never cause a horizontal displacement; a vertical force does not do work on a horizontally displaced object!! Independence of perpendicular vectors.

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Positive WorkNegative Work Force is in the same direction as motion. Increases energy of object. Force opposes motion. Decreases energy of object.

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When the force causing a change in position is acting at an angle compared to the direction of movement, you must: Resolve the force into components. Use the force that is acting in the same direction as the displacement. Work at Angles

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Work on Incline

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Force vs. Distance Graphs Find work done:

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Power

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Power ( P ) - The rate at which work is performed. (scalar) Units – J / s = Watt

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Work vs time Work time

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Work vs time Work time P = w t

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Work vs time Work time P = w t The slope of a work vs time graph is equal to the power.

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a)car speedingb) dripping faucet c) cork shot off bottle d) mass on string e)boy runningf) archer about to shoot g) falling dominos h) man on ladder Classifying Mechanical Energy

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Mechanical Energy - is the energy which is possessed by an object due to its motion or its stored energy of position. (scalar) Gravitational Potential, Kinetic, & Elastic

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Kinetic Energy ( KE ) – the energy an object possesses due to its motion. Which picture has more Kinetic Energy? KE = ½ mv 2 Units – Joules (J)

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Gravitational Potential Energy ( PE g ) – the energy possessed by an object due to its position. ΔPE g = mgΔh Units – Joules (J) Which mass has more Potential Energy?

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Sketch the following relationships.

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Other Forms of Energy

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Internal Energy ( Q ) – total energy possessed by the particles that make up an object.

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Transformation – a conversion from one form of energy to another. Transferal – the passing of energy between masses. Energy Transformation & Transferal

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Energy can neither be created nor destroyed. It can only be transformed or transferred from one form to another within a closed system. The total mechanical energy within a closed system will always remain the same. Energy Conservation Principle in Ideal Mechanical Systems

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E t = PE + KE + Q E i = E f * Not on Reference Table

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Using a Pie Chart to Understand Conservation of Energy Size of Circle represents total energy remains the same size in a closed system

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Using a Pie Chart to Understand Conservation of Energy Size of Slices represents specific types of mechanical energy red = Kinetic blue = Gravitational Potential green = Thermal orange = Elastic Potential

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100. m 75 m 50. m 25 m 0 m

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A 10. – kilogram block starts from rest at point A and slides along a frictionless track. (Neglect air resistance)

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Do NOT affect the total mechanical energy of a system. F grav F spring Internal Forces

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Increase or decrease the total mechanical energy of a system. F app F fric F air F tens F norm External Forces

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When work is done upon an object by an external force, the total mechanical energy (KE + PE) of that object is changed. W = ΔE T = E f - E i Work Energy Theorum * Already on page 128

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If the work is "positive work", then the object will gain energy. If the work is "negative work", then the object will lose energy. The gain or loss in energy can be in the form of potential energy, kinetic energy, or both. Work Energy Theorum

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Pendulums While at Pisa, Galileo was also inspired to study pendulums. Galileo was sitting in the pews of a cathedral, gazing upwards, when he noticed that one of the great lamps was swinging back and forth. He noticed that the swing of the lamp was incredibly regular. This motivated him to study pendulums.

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Common Uses for Pendulums

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Why use the word “Simple”? Disregard the effects of air resistance. Assume that the mass of the bob is concentrated at one point. Assume that mass of string is negligible.

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1. Length of the pendulum 2. Acceleration due to gravity 3. Unit – seconds (s) * Not on Reference Table Factors affecting the period of a pendulum

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Pendulum Graphs

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States of a Spring

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Spring Force Spring Force (F spring ) – a force that always pushes or pulls the mass back toward its original equilibrium position. Considered a restoring force Units – Newtons (N)

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In 1678, Robert Hooke discovered the following relationship: Spring constant ( k ) - resistivity of spring Units – N/m F spring = k x Hooke’s Law

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x FsFs

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Elastic Potential Energy (PE s ) – the energy stored in a spring when it is compressed or stretched. Units – Joules (J) Elastic Potential Energy

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A spring is set up in a lab and is stretched various amounts. The Potential Energy in the spring is then measured. Below is the data obtained from the experiment. Elastic Potential Energy

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What is the relationship between the potential energy stored in a spring and the amount it is stretched? Quadratic PE spring = ½ kx 2

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Potential Energy ~March 1, 2006.

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