Momentum Conceptual Physical Science Newton’s 2nd Law

2/6/2019MomentumConceptualPhysicalScienceMomentum Important property closely related toNewton’s 2nd law6th Edition Includes effects of both motion (velocity)and inertia (mass)Chapter 3:MOMENTUM ANDENERGYSections 3.1-3.6 only121

2/6/2019Momentum (p) ::: ExamplesMomentumMomentum—is inertia in motiondefined as the product of mass andvelocity:momentum mv The units for momentum are kilogrammeter per second (kg·m/s).Mass 60 kgVelocity 2mph 0.9m/sWhat is the momentum?Mass 0.5 kgVelocity -90mph -40m/sMass 1000 kgVelocity 50mph 22m/s342

2/6/2019MomentumCHECK YOUR NEIGHBORConservation of MomentumWhen the speed of an object is doubled, its momentumA.B.C.D.mava msvsremains unchanged in accord with the conservation ofmomentum.doubles.quadruples.decreases. The total momentum of a group of interacting objectsremains the same in the absence of external forces. Applications: Collisions, analyzing action/reactioninteractions563

2/6/2019Conservation of MomentumConservation of MomentumLaw of conservation of momentum:In every case, the momentum of a system cannotchange unless it is acted on by external forces.In the absence of an external force, themomentum of a system remains unchanged.A system will have the same momentum bothbefore and after any interaction occurs. When themomentum does not change, we say it is conserved.Equation form:(total momentum)before (total momentum)afterConservationof Momentum mAvA mBvB7AB84

2/6/2019Conservation of Momentum: ExampleAt restQuestion 18A student with mass 50 kg is standing in a canoe(with mass of 30 kg) in still water. The studentthen jumps out of the canoe to the right with aspeed of 1.5 m/s. The initial velocity of the canoeisMass 100 KgMass 50 KgPerson kicks the boxVelocityof 4 m/sA. 1.5 m/s to the left.B. 2.5 m/s to the left.C. 0. The canoe does not move.D. 2.5 m/s to the right.E. 1.5 m/s to the right.?How fast is the box moving?9105

2/6/2019Conservation of MomentumConservation of MomentumElastic collisionCollisionsis defined as a collision whereupon objectscollide without permanent deformation or thegeneration of heat. (The elastic balls bounce!)When objects collide in the absence ofexternal forces,net momentum before collision net momentum aftercollisionExamples:Elastic collisionsInelastic collisions11126

2/6/2019Change in Momentum ImpulseConservation of MomentumMomentum in terms of stopping a moving object, impulse.Inelastic collisionMomentum, p mvis defined as a collision whereupon collidingobjects become tangled or coupledtogether, generating heat. (Inelasticcollisions are often sticky.)Wherem mass (kg) and v velocity (m/s)Δp Δmv mfvf -mivi Force Time13147

2/6/2019Change in Momentum ImpulseImpact ForceΔp ΔmvChangein Momentum ImpulseChange in Momentum ImpulseChangein MomentumImpulse Δp FtImpulse Δp FtImpact timeFFΔp Δmvvi 10m/svf 0Δmv (1kg x 0m/s) – (1kg x 10m/s) -10Kgm/sF(N)F15t(sec)ΔpF(N)(Kg m/s)1011010011001010100Impulse -10Kgm/st(sec)Δp-101-10-110-10168

2/6/2019Impulse Changes MomentumImpulseWhen a car is out of control, it is better to hit ahaystack than a concrete wall. Common sense, butwith a physics reason:Same impulse occurseither way, but extensionof hitting time reduceshitting force. A force acting on an object for some time (t) An impulse produces a change in momentum Applications: airbags, padding for elbows andknees, protective plastic barrels on highways17189

2/6/2019Impulse Changes MomentumCHECK YOUR NEIGHBORWhen a dish falls, will the change in momentum be less if itlands on a carpet than if it lands on a hard floor? (Careful!)A.B.C.D.No, both are the same.Yes, less if it lands on the carpet.No, less if it lands on a hard floor.No, more if it lands on a hard floor.Explanation:Explanation:The momentum becomes zero in both cases, so both change by theThe momentum becomes zero in both cases, so both change bysame amount. Although the momentum change and impulse are thethe same amount. Although the momentum change and impulsesame, the force is less when the time of momentum change isare the same, the force is less when the time of momentumextended. Be careful to distinguish between force, impulse, andchange is extended. Be careful to distinguish between force,momentum.impulse, and momentum.192010

2/6/2019Impulse Changes MomentumCHECK YOUR NEIGHBORWorkWhen a dish falls, will the change in momentum be less if itlands on a carpet than if it lands on a hard floor? (Careful!)A.B.C.D.Work defined as the product of forceexerted on an object and the distancethe object moves (in the samedirection as the force) is done only when the force succeedsin moving the body it acts upon equation: work force distanceNo, both are the same.Yes, less if it lands on the carpet.No, less if it lands on a hard floor.No, more if it lands on a hard floor.Explanation:The momentum becomes zero in both cases, so both change bythe same amount. Although the momentum change and impulseare the same, the force is less when the time of momentumchange is extended. Be careful to distinguish between force,impulse, and momentum.212211

2/6/2019WorkWorkTwo things enter wherework is done:Force (N) application of force movement of something bythat forceDistance (d) metersWork done on the barbell isthe average force multipliedby the distance throughwhich the barbell is lifted.W F d(N m)(N m Joule)wF dWork232412

2/6/2019WorkCHECK YOUR NEIGHBORWork- Practice problemsForceIf you push against a stationary brick wall for severalminutes, you do no workWork ?distanceA.B.C.D. A large box is pushed a distance of 2 mwith a force of 20 N. The work done onthe box ison the wall.at all.Both of the above.None of the above.Explanation::ExplanationYou maymay dodo workwork onon youryourYoumuscles, butbut notnot onon thethemuscles,wall.wall.252613

2/6/2019Work- Practice problemsWork PracticeForce ? When you pick up your backpack,you do 58J of work to lift it up1.3m to put it on your back.What is the force on thebackpack? It takes 80 J to push a large crate 4 macross a floor. The force exerted onthe crate is272814

2/6/2019WorkCHECK YOUR NEIGHBORYou do work when pushing a cart. If you push the carttwice as far with the same constant force, then thework you do isA.B.C.D.29EnergyEnergy– defined as that which produces changes in matter- Or the property on a system that enables it to doworkless than twice as much.twice as much.more than twice as much.zero.- Both work and energy are measured injoules.3015

2/6/2019EnergyTwo types:Potential energyKinetic EnergyPotential EnergyPotential Energyis defined as stored energy due toposition, shape, or state. In its storedstate, energy has the potential fordoing work.Both work and energy are measured injoules.31Examples:Stretched rubber band3216

2/6/2019Potential EnergyGravitational Potential EnergyThe amount of gravitational potential energypossessed by an elevated object is equal to thework done against gravity in raising it.Example: potential energy of 10-N ball is thesame in all 3 cases because work done in elevatingit is the sameWork done equals force required to move itupward the vertical distance moved (W Fd).The upward force is the weight, mg, of theobject. So the work done in lifting it throughheight h is the product mgh.This is also known as the gravitational PotentialEnergy of that object, PE333417

2/6/2019Gravitational Potential EnergyGravitational Potential EnergyEquation for gravitational potential energy:PE weight heightor PE mghEquation for gravitational potential energy:PE weight heightorPE mghGravitational potential energy example:hA 10-kg box is held 3 m above the ground. Itspotential energy relative to the ground isGravitational potential energy examples:Water in an elevated reservoirh 3m353618

2/6/2019WorkCHECK YOUR NEIGHBORWorkCHECK YOUR ANSWERWork is done in lifting a barbell. How much work is donein lifting a twice-as-heavy barbell the same distance?Work is done in lifting a barbell. How much work is donein lifting a twice-as-heavy barbell the same distance?A.B.C.D.A.B.C.D.Twice as much.Half as much.The same.Depends on the speed of the lift.Twice as much.Half as much.The same.Depends on the speed of the lift.Explanation:This is in accord with work force distance. Twice the forcefor the same distance means twice the work done on thebarbell.373819

2/6/2019Potential EnergyCHECK YOUR NEIGHBORDoes a car hoisted for repairs in a service station haveincreased potential energy relative to the floor?A.B.C.D.Yes.No.Sometimes.Not enough information.Kinetic EnergyYesExplanation:And if the car were twice as heavy, its increase in potentialenergy would be twice as much.394020

2/6/2019Kinetic Energy -Practice problemKinetic EnergyKinetic Energyis defined as the energy of a moving objectEquation for kinetic energy:Kinetic energy 1/2 mass speed2orKE 1/2 mv2What is the kinetic energy a2000 kg car traveling at 100m/s?KE 1/2 mv2small changes in speed large changes in KE414221

2/6/2019The Work-Energy TheoremCHECK YOUR NEIGHBORWork-Energy TheoremConsider a problem that asks for the distance a fastmoving crate slides across a factory floor in coming to astop. The most useful equation for solving this problemisWhen work is done on an object to change its KE,the amount of work done is equal to the change in KE.Equation for work-energy theorem:Net work change in KEA.B.C. If there is no change in object’s energy, then nowork is done on the object. Applies to potential energy:For a barbell held stationary, no further work isdone no further change in energy. Applies to decreasing energy:The more kinetic energy something has the morework is required to slow it or stop it43D.F ma.Ft mv.KE 1/2mv2.Fd 1/2mv2.4422

2/6/2019Work and EnergyThe Work-Energy TheoremCHECK YOUR ANSWERConsider a problem that asks for the distance a fastmoving crate slides across a factory floor in coming to astop. The most useful equation for solving this problemisA.B.C.D.F ma.Ft mv.KE 1/2mv2.Fd 1/2mv2.Work-energy theorem— the work done on an object equals thechange in kinetic energy of the object: Work ΔKEForce 50N5 kgv 10 m/s4186 joules 1 food caloried 5mExplanation:W F d (50N)(5m) 250JThe work-energy theorem is the physicist’s favorite startingpointfor solving many motion-related problems.Food calories Work KE45ΔKE ½ mass v2 1/2x 5 x 100250J4623

2/6/2019Kinetic EnergyCHECK YOUR NEIGHBORMust a car with momentum have kinetic energy?A.B.C.D.Yes, due to motion alone.Yes, when motion is nonaccelerated.Yes, because speed is a scalar and velocity is a celeration, speed being a scalar, and velocity being a vectorAcceleration,speed beinga scalar,velocitybeing a vectorquantity, are irrelevant.Anymovingandobjecthas bothquantity,areirrelevant.Any moving object has bothmomentumandkinetic energy.momentum and kinetic energy.47Kinetic Energy and MomentumComparison of Kinetic Energy and Momentum Both depend on mass and velocity—Momentum depends on mass and velocity.KE depends on mass and the square of itsvelocity (or speed). Momentum is a vector quantity (direction).Kinetic energy is a scalar quantity (nodirection).4924

2/6/2019Conservation of EnergyConservation of EnergyExample: energy transforms without net lossor net gain in the operation of a pile driverConservation defined in everyday language as “ to save” physics as to “remain unchanged”Law of conservation of energy In the absence of external work input or output,the energy of a system remains unchanged. Energy cannot be created or destroyed.505125

2/6/2019Conservation of EnergyConservation of EnergyEnergy cannot be created nor destroyedA 1-kg ball dropped from a height of 2 m rebounds only 1.5 m afterhitting the ground. The amount of energy converted to heat isaboutPE (weight) x highA) 0.5 J.B) 1.0 J.C) 1.5 J.D) 2.0 J.E) more than 2.0 J.PE mass x g x highKE ½ mass x v2Thermal energyWork PE KE Thermal Energy525326

2/6/2019PowerPower measure of how fast work is done equation:PowerPower work donetime interval units in joule per second or watt(One watt 1 joule of work per second)545527