From last timeMassForce, weight, and massIs ‘pounds’ really weight?Momentum conservationNewton’s third lawNewton’s lawsExample: More than one forceColliding balls againBalancing forcesHow can the table exert a force?Force of table on block3rd law: Law of force pairsIdentifying forcesKeep the forces straight!How can a car move?RocketsPowerPoint PresentationAnother explanationGravitational forceEqual accelerationsA fortunate coincidencePhysics 107, Fall 2006 1From 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•Started exploring the meaning of these concepts using Newton’s LawsPhysics 107, Fall 2006 2Mass•Define mass to be ‘the amount of inertia of an object’.•Can also say mass characterizes the amount of matter in an object.•Symbol for mass usually m•Unit of mass is the kilogram (kg).• Said before that• Find experimentally that € a ∝ F € Acceleration=ForceMass€ a =FmPhysics 107, Fall 2006 3Force, weight, and mass•1 Newton = force required to accelerate a 1.kg mass at 1 m/s2. € F = ma ⇒ F = (kg) ×(m/s2)= kg − m /s2≡ NewtonBut then what is weight?—Weight is a force, measured in Newton’s—It is the net force of gravity on a body.—F=mg, g=F/mPhysics 107, Fall 2006 4Is ‘pounds’ really weight?•In the English system (feet, pounds, seconds), pounds are a measure of force.•So it is correct to say my weight is 170 pounds.•Then what is my mass?€ m =Fg=170lbs32 ft /s2= 5.3slugs!!Physics 107, Fall 2006 5Momentum conservation•We said before that an impressed force changes the momentum of an object.•We also said that momentum is conserved.•This means the momentum of the object applying the force must have decreased.•According to Newton, there must be some force acting on that object to cause the momentum change.Physics 107, Fall 2006 6Newton’s third law•This is the basis for Newton’s third law:To every action there is always opposed an equal reaction. This is momentum conservation in the language of forces.Physics 107, Fall 2006 7Newton’s laws1st law: Law of inertiaEvery object continues in its state of rest, or uniform motion in a straight line, unless acted upon by a force.2nd law: F=ma, or a=F/m The 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.Physics 107, Fall 2006 8Example: 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/s2Physics 107, Fall 2006 9Colliding balls againBefore collision:After collision:1122During collision1 2Force on ball 2 accelerates itForce on ball 1 decelerates it to zero velocityPhysics 107, Fall 2006 10Balancing forcesForce of gravity acts downward on the block. But since the block is not accelerating. The net (total) force must be zero.Another force is present, which balances the gravitational force.It is exerted by the table, on the block.Force of gravity on blockForce of table on blockPhysics 107, Fall 2006 11How can the table exert a force?•The interaction between the table and the block is a microscopic one.QuickTime™ and aSorenson Video decompressorare needed to see this picture.Physics 107, Fall 2006 12Force of table on block•The table can compress, bend, and flex by distorting the atomic positions.•The atomic bond is like a spring and it exerts a force on the block.•All forces arise at the atomic (or smaller) scale.Physics 107, Fall 2006 133rd 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!Physics 107, Fall 2006 14Identifying forces•If horse exerts force on cart, and cart exerts equal and opposite force on horse, how can the horse and cart move?Physics 107, Fall 2006 15Keep the forces straight!•For motion of cart, need to identify the net force on the cart.•Net horizontal force is force from horse, combined with frictional force of wheels.Physics 107, Fall 2006 16How can a car move?Gravitational forceon carForce exertedby road on carVertical forcesHorizontal forcesDrive Force by road on tiresRolling resistance by road on tiresWheels push push backward against the road,Road pushes forward on the tirePhysics 107, Fall 2006 17Rockets•I apply a force to a ball for a short time t to get it to move. •During that time, the ball exerts an equal and opposite force on me!The forces cause the ball and I to move in opposite directionsPhysics 107, Fall 2006 18The forces resulted in accelerations during the short time t € 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 velocityPhysics 107, Fall 2006 19Another 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)Physics 107, Fall 2006 20Gravitational forceGravitational force on apple by earthGravitational force on Earth by appleThese forces are equal and opposite, But mearth=6x1024 kg mapple=1 kg€ mEarthaEarth= mappleaapple⇒aEarthaapple=mapplemEarthPhysics 107, Fall 2006 21Equal accelerations•If more massive bodies accelerate more slowly with the same force…… why do all bodies fall the same, independent of mass?•Gravitational force on a body depends on its mass:•Therefore acceleration is independent of mass: € Fgravity= mg€ a =Fgra vitym=mgm= gPhysics 107, Fall 2006 22A fortunate coincidence•A force exactly proportional to mass, so that everything cancels nicely.•But a bit unusual.•Einstein threw out the gravitational
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