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Transcript
Impulse and Momentum AP Physics 1 Momentum Momentum The product of a particle’s mass and velocity is called the momentum of the particle: Momentum is a vector, with units of kg m/s. A particle’s momentum vector can be decomposed into x- and y-components. Slide 9-21 QuickCheck 9.1 The cart’s change of momentum px is A. B. C. D. E. –20 kg m/s. –10 kg m/s. 0 kg m/s. 10 kg m/s. 30 kg m/s. Slide 9-22 QuickCheck 9.1 The cart’s change of momentum px is A. B. C. D. E. –20 kg m/s. –10 kg m/s. 0 kg m/s. 10 kg m/s. 30 kg m/s. px = 10 kg m/s (20 kg m/s) = 30 kg m/s Negative initial momentum because motion is to the left and vx < 0. Slide 9-23 Impulse Impulse = Momentum Consider Newton’s 2nd Law and the definition of acceleration Units of Impulse: Ns Units of Momentum: Kg x m/s Momentum is defined as “Inertia in Motion” Impulse is the Area Since J=Ft, Impulse is the AREA of a Force vs. Time graph. Impulse During a Collision A large force exerted for a small interval of time is called an impulsive force. The figure shows a particle with initial velocity . The particle experiences an impulsive force of short duration t. The particle leaves with final velocity . Slide 9-26 Conservation of Momentum Collisions A collision is a shortduration interaction between two objects. The collision between a tennis ball and a racket is quick, but it is not instantaneous. Notice that the right side of the ball is flattened. It takes time to compress the ball, and more time for the ball to re-expand as it leaves the racket. Slide 9-24 Atomic Model of a Collision Slide 9-25 How about a collision? Consider 2 objects speeding toward each other. When they collide...... Due to Newton’s 3rd Law the FORCE they exert on each other are EQUAL and OPPOSITE. The TIMES of impact are also equal. F1 F2 t1 t 2 ( Ft )1 ( Ft ) 2 J1 J 2 Therefore, the IMPULSES of the 2 objects colliding are also EQUAL How about a collision? If the Impulses are equal then the MOMENTUMS are also equal! J1 J 2 p1 p2 m1v1 m2 v2 m1 (v1 vo1 ) m2 (v2 vo 2 ) m1v1 m1vo1 m2 v2 m2 vo 2 p before p after m1vo1 m2 vo 2 m1v1 m2 v2 QuickCheck 9.8 A mosquito and a truck have a head-on collision. Splat! Which has a larger change of momentum? A. The mosquito. B. The truck. C. They have the same change of momentum. D. Can’t say without knowing their initial velocities. Slide 9-60 QuickCheck 9.8 A mosquito and a truck have a head-on collision. Splat! Which has a larger change of momentum? A. The mosquito. B. The truck. C. They have the same change of momentum. D. Can’t say without knowing their initial velocities. Momentum is conserved, so pmosquito + ptruck = 0. Equal magnitude (but opposite sign) changes in momentum. Slide 9-61 Momentum is conserved! The Law of Conservation of Momentum: “In the absence of an external force (gravity, friction), the total momentum before the collision is equal to the total momentum after the collision.” po (truck) mvo (500)(5) 2500kg * m / s po ( car ) (400)( 2) 800kg * m / s po (total) 3300kg * m / s ptruck 500 * 3 1500kg * m / s pcar 400 * 4.5 1800kg * m / s ptotal 3300kg * m / s Several Types of collisions Sometimes objects stick together or blow apart. In this case, momentum is ALWAYS conserved. p before p after m1v01 m2 v02 m1v1 m2 v2 When 2 objects collide and DON’T stick m1v01 m2 v02 mtotalvtotal When 2 objects collide and stick together mtotalvo (total) m1v1 m2 v2 When 1 object breaks into 2 objects Elastic Collision = Kinetic Energy is Conserved Inelastic Collision = Kinetic Energy is NOT Conserved Collisions and Explosion Example A bird perched on an 8.00 cm tall swing has a mass of 52.0 g, and the base of the swing has a mass of 153 g. Assume that the swing and bird are originally at rest and that the bird takes off horizontally at 2.00 m/s. If the base can swing freely (without friction) around the pivot, how high will the base of the swing rise above its original level? How many objects due to have BEFORE the action? 1 How many objects do you have AFTER the action? 2 EB E A K o ( swing ) U swing pB p A mT vo T m1v1 m2 v2 (0.205)(0) (0.153)v1( swing) (0.052)( 2) vswing -0.680 m/s 1 mvo2 mgh 2 vo2 (0.68) 2 h 0.024 m 2g 19.6 Example How many objects do I have before the collision? 2 How many objects do I have after the collision? 1 Granny (m=80 kg) whizzes around the rink with a velocity of 6 m/s. She suddenly collides with Ambrose (m=40 kg) who is at rest directly in her path. Rather than knock him over, she picks him up and continues in motion without "braking." Determine the velocity of Granny and Ambrose. pb pa m1vo1 m2vo 2 mT vT (80)(6) (40)(0) 120vT vT 4 m/s Momentum in Two Dimensions The total momentum is a vector sum of the momenta of the individual particles. Momentum is conserved only if each component of is conserved: Slide 9-86 Collisions in 2 Dimensions The figure to the left shows a collision between two pucks on an air hockey table. Puck A has a mass of 0.025-kg and is vA vAsinq moving along the x-axis with a velocity of +5.5 m/s. It makes a collision with puck B, which vAcosq has a mass of 0.050-kg and is initially at rest. The collision is vBcosq vBsinq NOT head on. After the vB collision, the two pucks fly apart with angles shown in the drawing. Calculate the speeds of the pucks after the collision. Collisions in 2 dimensions p ox px m AvoxA mB voxB m AvxA mB vxB (0.025)(5.5) 0 (.025)(v A cos 65) (.050)(vB cos 37) vA vAsinq vAcosq vBcosq vB 0.1375 0.0106vA 0.040vB p oy py 0 m Av yA mB v yB vBsinq 0 (0.025)(v A sin 65) (0.050)( vB sin 37) 0.0300vB 0.0227v A vB 0.757v A Collisions in 2 dimensions 0.1375 0.0106vA 0.040vB vB 0.757vA 0.1375 0.0106v A (0.050)(0.757v A ) 0.1375 0.0106v A 0.03785v A 0.1375 0.04845v A v A 2.84m / s vB 0.757(2.84) 2.15m / s