Lecture PowerPoints Chapter 7 Physics: Principles . - Marlington Local

Lecture PowerPointsChapter 7Physics: Principles withApplications, 6th editionGiancoli 2005 Pearson Prentice HallThis work is protected by United States copyright laws and is provided solely forthe use of instructors in teaching their courses and assessing student learning.Dissemination or sale of any part of this work (including on the World Wide Web)will destroy the integrity of the work and is not permitted. The work and materialsfrom it should never be made available to students except by instructors usingthe accompanying text in their classes. All recipients of this work are expected toabide by these restrictions and to honor the intended pedagogical purposes andthe needs of other instructors who rely on these materials.

Chapter 7Linear Momentum

Units of Chapter 7 Momentum and Its Relation to Force Conservation of Momentum Collisions and Impulse Conservation of Energy and Momentum inCollisions Elastic Collisions in One Dimension

Units of Chapter 7 Inelastic Collisions Collisions in Two or Three Dimensions Center of Mass (CM) CM for the Human Body Center of Mass and Translational Motion

7-1 Momentum and Its Relation to ForceMomentum is a vector symbolized by thesymbol p, and is defined as(7-1)The rate of change of momentum is equal to thenet force:(7-2)This can be shown using Newton’s second law.

7-2 Conservation of MomentumDuring a collision, measurements show that thetotal momentum does not change:(7-3)

7-2 Conservation of MomentumMore formally, the law of conservation ofmomentum states:The total momentum of an isolated system ofobjects remains constant.

7-2 Conservation of MomentumMomentum conservation works for a rocket aslong as we consider the rocket and its fuel tobe one system, and account for the mass lossof the rocket.

7-3 Collisions and ImpulseDuring a collision, objectsare deformed due to thelarge forces involved.Sincewrite, we can(7-5)The definition of impulse:

7-3 Collisions and ImpulseSince the time of the collision is very short, weneed not worry about the exact time dependenceof the force, and can use the average force.

7-3 Collisions and ImpulseThe impulse tells us that we can get the samechange in momentum with a large force acting for ashort time, or a small force acting for a longer time.This is why you should bendyour knees when you land;why airbags work; and whylanding on a pillow hurts lessthan landing on concrete.

7-4 Conservation of Energy and Momentumin CollisionsMomentum is conservedin all collisions.Collisions in whichkinetic energy isconserved as well arecalled elastic collisions,and those in which it isnot are called inelastic.

7-5 Elastic Collisions in One DimensionHere we have two objectscolliding elastically. Weknow the masses and theinitial speeds.Since both momentumand kinetic energy areconserved, we can writetwo equations. Thisallows us to solve for thetwo unknown finalspeeds.

7-6 Inelastic CollisionsWith inelastic collisions, some ofthe initial kinetic energy is lost tothermal or potential energy. Itmay also be gained duringexplosions, as there is theaddition of chemical or nuclearenergy.A completely inelastic collision isone where the objects sticktogether afterwards, so there isonly one final velocity.

7-7 Collisions in Two or Three DimensionsConservation of energy and momentum can alsobe used to analyze collisions in two or threedimensions, but unless the situation is verysimple, the math quickly becomes unwieldy.Here, a moving objectcollides with an objectinitially at rest. Knowingthe masses and initialvelocities is not enough;we need to know theangles as well in order tofind the final velocities.

7-7 Collisions in Two or Three DimensionsProblem solving:1. Choose the system. If it is complex,subsystems may be chosen where one ormore conservation laws apply.2. Is there an external force? If so, is thecollision time short enough that you canignore it?3. Draw diagrams of the initial and finalsituations, with momentum vectors labeled.4. Choose a coordinate system.

7-7 Collisions in Two or Three Dimensions5. Apply momentum conservation; there will beone equation for each dimension.6. If the collision is elastic, apply conservationof kinetic energy as well.7. Solve.8. Check units and magnitudes of result.

7-8 Center of MassIn (a), the diver’s motion is pure translation; in (b)it is translation plus rotation.There is one point that moves in the same path aparticle wouldtake if subjectedto the same forceas the diver. Thispoint is called thecenter of mass(CM).

7-8 Center of MassThe general motion of an object can beconsidered as the sum of the translationalmotion of the CM, plus rotational, vibrational, orother forms of motion about the CM.

7-8 Center of MassFor two particles, the center of mass lies closerto the one with the most mass:where M is the total mass.

7-8 Center of MassThe center of gravity is the point where thegravitational force can be considered to act. It isthe same as the center of mass as long as thegravitational force does not vary among differentparts of the object.

7-8 Center of MassThe center of gravity can be found experimentallyby suspending an object from different points.The CM need not be within the actual object – adoughnut’s CM is in the center of the hole.

7-9 CM for the Human BodyThe x’s in the small diagram mark the CM ofthe listed body segments.

7-9 CM for the Human BodyThe location of the center ofmass of the leg (circled) willdepend on the position ofthe leg.

7-9 CM for the Human BodyHigh jumpers havedeveloped a techniquewhere their CM actuallypasses under the bar asthey go over it. This allowsthem to clear higher bars.

7-10 Center of Mass and Translational MotionThe total momentum of a system of particles isequal to the product of the total mass and thevelocity of the center of mass.The sum of all the forces acting on a system isequal to the total mass of the system multipliedby the acceleration of the center of mass:(7-11)

7-10 Center of Mass and Translational MotionThis is particularly useful in the analysis ofseparations and explosions; the center ofmass (which may not correspond to theposition of any particle) continues to moveaccording to the net force.

Summary of Chapter 7 Momentum of an object: Newton’s second law: Total momentum of an isolated system of objects isconserved. During a collision, the colliding objects can beconsidered to be an isolated system even if externalforces exist, as long as they are not too large. Momentum will therefore be conserved duringcollisions.

Summary of Chapter 7, cont. In an elastic collision, total kinetic energy isalso conserved. In an inelastic collision, some kinetic energyis lost. In a completely inelastic collision, the twoobjects stick together after the collision. The center of mass of a system is the point atwhich external forces can be considered toact.

7-3 Collisions and Impulse. The impulse tells us that we can get the same change in momentum with a large force acting for a short time, or a small force acting for a longer time. This is why you should bend your knees when you land; why airbags work; and why landing on a pillow hurts less than landing on concrete.