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Momentum and Energy PHYS 1090 Unit 3 Question If a car collides with a bug, which experiences the greatest force? A. B. C. D. The car. The bug. It’s a tie. Insufficient information to answer. Force Meters 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. FA→B = −FB→A Bug + Windshield Small car: 1250 kg Large insect: 0.00025 kg From the same force, the bug accelerates a lot more! Forces are the same—the accelerations are different. Interaction Forces All forces are interaction forces! – gravity – wind – jumping – everything! • This means: whenever something accelerates, something else accelerates in the opposite direction! Whoa! Pulleys Pulleys • 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 Levers Levers • To balance a load, the force closest to the fulcrum must be larger Levers • To balance a load, the force closest to the fulcrum must be larger • The load farthest from the fulcrum moves the most Inclined Planes Inclined Planes • The steeper the plane, the greater the force required • The steeper the plane, the shorter the distance pulled to reach the same height Simple Machines • All are a trade-off between force and distance (or force and speed) • The greater force moves the least distance F1Dd1 = F2Dd2 Work Formula work = F·Dd F = force applied Dd = distance traveled Simple Machines F1Dd1 = F2Dd2 Work input = Work output • Forces are different • Distances are different • Work is the same. Work and Energy • Doing work on something changes its energy. • Energy: “the ability to do work” Conservation of Energy • Energy can be transferred between objects or transformed into different forms, but the total amount of energy can never change. Rail Cart Collisions Rail Cart Collisions • 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 Air Hockey Collisions Air Hockey Collisions • Accelerations are in opposite directions • More massive disk accelerates the least 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. Momentum Formula p = mv momentum is a vector. Momentum Changes and Newton’s Third Law • At any instant: Dp = D(mv) = mDv = maDt = m(F/m)Dt = FDt • For interacting objects, FA = −FB, so: DpA = FADt DpB = FBDt = −FADt DpA = − DpB Conservation of Momentum • Momentum can be transferred between objects, but the total momentum can never change. Dp1 + Dp2 = 0 Rollerballs and Drag Meters Rollerballs and Drag Meters • 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. Some Forms of Energy • Potential Energy • Kinetic energy Work Against Gravity Force = –w = mg distance = h work = mgh Source: Griffith, The Physics of Everyday Phenomena Get It Back? Gravity exerts force mg as object drops distance h. work = mgh Source: Griffith, The Physics of Everyday Phenomena Potential Energy The energy of relative position of two objects gravity springs electric charges chemical bonds 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 A Moving Object Can Do Work Source: Griffith, The Physics of Everyday Phenomena Kinetic Energy the work that a moving object does in stopping – or – the work to bring a motionless object to speed KE = 1 2 mv2 Rollerball Energy Conversions Potential energy work Kinetic energy work The more work you put in, the more work you get out!