1Phy107, Spring 2006 1Fri. Jan. 26From Last Time…• Defined mass m and inertia:– Mass is amount of inertia of a body– Measured in kg• Defined momentum p:– p=mv, momentum is said to be conserved• Defined force F:– Something that changes a body’s velocity– Can transfer momentum from one body to another• Related force, mass, and acceleration:– F=ma, or a=F/m– Subject to the same force,more massive objects accelerate more slowly.• Weight:– Force of gravity on a body = mg– Measured in newtons (N). 1 N = 1 kg-m/s2Phy107, Spring 2006 2Fri. Jan. 26Newton’s laws1st law: Law of inertiaEvery object continues in its state of rest, or uniform motion in a straightline, unless acted upon by a force.2nd law: F=ma, or a=F/mThe acceleration of a body along a direction is– proportional to the total force along that direction, and– inversely the mass of the body3rd law: Action and reactionFor every action there is an equal an opposite reaction.Phy107, Spring 2006 3Fri. Jan. 26Q: Force and Diff MassesA force F acting on an object results in some acceleration a1.The same force on a different object results in twice the acceleration.How does the second mass compare to the first?A. m2=2m1 B. m2= m1 C. C. m2= m1/2F a1m1F a2 = 2a1m2F=ma is the same for both objects.If theOr in words…twice the acceleration means half the massPhy107, Spring 2006 4Fri. Jan. 26Example: More than one forceMF1M=10 kg, F1=200 NFind aa = Fnet/M = 200N/10kg = 20 m/s2M=10 kg F1=200 N F2 = 100 NFind aMF1F2a = Fnet/M = (200N-100N)/10kg = 10 m/s2Phy107, Spring 2006 5Fri. Jan. 26Colliding balls againBefore collision:After collision:1122During collision1 2Force on ball 2accelerates itForce on ball 1decelerates it tozero velocityPhy107, Spring 2006 6Fri. Jan. 26QuestionA person weighing 600 N wants to hover using a jetpack. What should the thrust be?A. 0B. 600 NC. 9.8 m/s/s2Phy107, Spring 2006 7Fri. Jan. 26Question, part 2• The thrust of the jet pack is increased to 800 N.What is the acceleration of the person?A. gB. (4/3)gC. g/3Net force = 800N-600N = 200NWhat is the mass? mg=600N (weight), so m=600N/ga=Fnet/m = 200N/(600N/g)=g/3Phy107, Spring 2006 8Fri. Jan. 26Balancing forcesForce of gravity actsdownward on the block.But since the block is notaccelerating. The net(total) force must be zero.Another force is present,which balances thegravitational force.It is exerted by the table, onthe block.Force ofgravity onblockForce of tableon blockPhy107, Spring 2006 9Fri. Jan. 26How can the table exert a force?• The interaction between the table and the block is amicroscopic one.Phy107, Spring 2006 10Fri. Jan. 26Force of table on block• The table cancompress, bend, andflex by distorting theatomic positions.• The atomic bond islike a spring - itexerts a force on theblock.• All forces arise at theatomic (or smaller)scale.Phy107, Spring 2006 11Fri. Jan. 263rd law: Law of force pairs• Every force is an interaction between two objects• Each of the bodies exerts a force on the other.• The forces are equal and opposite– An action-reaction pair.Force on theblock by youForce by theblock on youand the earth!Phy107, Spring 2006 12Fri. Jan. 26Question, part 1Suppose you are an astronaut in outer space giving a brief push to ablock whose mass is bigger than your own.Compare, while you are pushing,the magnitude of the force you exert on the block, FBlock,to the magnitude of the force exerted by the block on you, FAstronaut,A. FAstronaut = FBlockB. FAstronaut > FBlockC. FAstronaut < FBlockThird law! Equal and opposite reaction force3Phy107, Spring 2006 13Fri. Jan. 26Question, part 2Compare, while you are pushing,the magnitudes of the acceleration you experience, aAstronaut,to the magnitude of the acceleration of the block, aBlockA. aAstronaut = aBlockB. aAstronaut > aBlockC. aAstronaut < aBlocka=F/mWith the same F, the smaller mass has the greater a Phy107, Spring 2006 14Fri. Jan. 26Identifying forces• If horse exerts force on cart, and cart exerts equaland opposite force on horse, how can the cart move?Phy107, Spring 2006 15Fri. Jan. 26Keep the forces straight!• For motion of cart, need to identify the net force onthe cart.• Net horizontal force is force from horse, combinedwith frictional force of wheels.Phy107, Spring 2006 16Fri. Jan. 26How can a car move?Gravitational forceon carForce exertedby road on carVertical forcesHorizontal forcesDrive Forceby road ontiresRollingresistanceby roadon tiresWheels push push backward against the road,Road pushes forward on the tirePhy107, Spring 2006 17Fri. Jan. 26Rockets• I apply a force to a ball for a short time Δtto get it to move.• During that time,the ball exerts an equal and opposite force on me!The forces cause the ball and I tomove in opposite directionsPhy107, Spring 2006 18Fri. Jan. 26The forces resulted in accelerationsduring the short time Δt ! acceleration = Forcemy massMe ! acceleration = Forceball massBallMy acceleration is smaller since my mass is much larger.The acceleration changes my velocity. ! acceleration = change in velocitychange in timeacceleration( )" change in time( )= change in velocityWhy did the ball and I move? ! Forcemass" change in time( )= change in velocity4Phy107, Spring 2006 19Fri. Jan. 26Another explanation• Before the throw,both the ball and I have zero momentum.• So the total momentum is zero. ! my velocity( ) = — ball velocity( )"ball massmy massThe total momentum is conserved,so after the throw the momenta must cancel (my momentum) + (ball momentum) = 0(my mass) x (my velocity) = — (ball mass) x (ball velocity)Phy107, Spring 2006 20Fri. Jan. 26Gravitational forceGravitationalforce on appleby earthGravitationalforce on Earthby appleThese forces areequal and opposite,But mearth=6x1024 kg mapple=1 kg! mEarthaEarth= mappleaapple"aEarthaapple=mapplemEarthPhy107, Spring 2006 21Fri. Jan. 26Equal accelerations• If more massive bodies accelerate more slowly with thesame force…… why do all bodies fall the same, independent of mass?• Gravitational force on a body depends on its mass:! Fgravity= mg• Therefore acceleration is independent of mass: ! a =Fgravitym=mgm= gPhy107, Spring 2006 22Fri. Jan. 26A fortunate coincidence• A force exactly proportionalto mass, so that everythingcancels nicely.• But a bit unusual.• Einstein threw out thegravitational forceentirely, attributing theobserved acceleration to adistortion of space-time.Phy107, Spring 2006 23Fri. Jan. 26Curved
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