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Momentum and Energy PHYS 1090 Unit 3

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Question If a car collides with a bug, which experiences the greatest force? A.The car. B.The bug. C.It’s a tie. D.Insufficient information to answer.

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Force Meters

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Newton’s Third Law Whenever one object exerts a force on a second object, the second object exerts an equal and opposite force on the first, along the same line of interaction. To every action there is always an opposed equal reaction. If object A exerts force F on object B, object B exerts force –F on object A. F A→B = −F B→A

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Bug + Windshield Small car: 1250 kg From the same force, the bug accelerates a lot more! Large insect: kg Forces are the same—the accelerations are different.

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Interaction Forces All forces are interaction forces! –gravity –wind –jumping –everything! This means: whenever something accelerates, something else accelerates in the opposite direction! Whoa!

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Pulleys

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Change the direction but not magnitude of the tension in the cable Lift force is tension times number of segments lifting Lift height is pull divided by number of segments

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Levers

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To balance a load, the force closest to the fulcrum must be larger

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Levers To balance a load, the force closest to the fulcrum must be larger The load farthest from the fulcrum moves the most

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Inclined Planes

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The steeper the plane, the greater the force required The steeper the plane, the shorter the distance pulled to reach the same height

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Simple Machines All are a trade-off between force and distance (or force and speed) The greater force moves the least distance F 1 d 1 = F 2 d 2

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Work Formula work = F· d F = force applied d = distance traveled

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Simple Machines F 1 d 1 = F 2 d 2 Work input = Work output Forces are different Distances are different Work is the same.

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Work and Energy Doing work on something changes its energy. Energy: “the ability to do work”

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Conservation of Energy Energy can be transferred between objects or transformed into different forms, but the total amount of energy can never change.

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Rail Cart Collisions

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Accelerations are in opposite directions More massive cart accelerates the least Equal-mass carts have equal accelerations (in opposite directions) Total Mass·Velocity the same before and after collisions

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Air Hockey Collisions

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Accelerations are in opposite directions More massive disk accelerates the least

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Momentum “Inertia in motion” Massive objects are hard to get going. Massive objects are hard to stop. It is hard to give an object a high speed. It is hard to stop a high-speed object.

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Momentum Formula momentum is a vector. p = mv

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Momentum Changes and Newton’s Third Law At any instant: p = (mv)= m v= ma t= m(F/m) t= F t For interacting objects, F A = −F B, so: p A = F A t p B = F B t = −F A t p A = − p B

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Conservation of Momentum Momentum can be transferred between objects, but the total momentum can never change. p 1 + p 2 = 0

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Rollerballs and Drag Meters

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The lighter the meter, the farther it drags. The heavier the ball, the farther it drags a meter. The higher the ramp, the farther a ball drags a meter. The higher the ramp, the faster a ball rolls at the bottom. The mass of the ball has no influence on how fast it rolls at the bottom.

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Some Forms of Energy Potential Energy Kinetic energy

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Work Against Gravity Force = –w = mg distance = h work = mgh Source: Griffith, The Physics of Everyday Phenomena

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Get It Back? Gravity exerts force mg as object drops distance h. work = mgh Source: Griffith, The Physics of Everyday Phenomena

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Potential Energy The energy of relative position of two objects gravity springs electric charges chemical bonds

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Potential Energy Gravitational potential energy = the work done by gravity in lowering an object – or – the work to raise an object to a height Gravitational PE = mgh

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A Moving Object Can Do Work Source: Griffith, The Physics of Everyday Phenomena

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Kinetic Energy the work that a moving object does in stopping – or – the work to bring a motionless object to speed KE = 1 2 mv 2

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Rollerball Energy Conversions work Potential energy Kinetic energy work The more work you put in, the more work you get out!

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