define: momentum impulse impulse momentum theorem

Transcription

1 define: momentum impulse impulse momentum theorem an 800. kg car traveling at 30. m/s applies it brakes for 4.0 seconds to bring it rest. What is the size of the force? This time the same car slows to 10. m/s. What is the impulse applied? 1

2 F(N) A 55.0 kg person traveling at 10.0 m/s experiences an impulse shown at the right. What is the resulting velocity after the impulse? t(ms) F(N) A 55.0 kg person traveling at 10.0 m/s experiences an impulse shown at the right. What is the t(ms) resulting velocity after Ft = m v the impulse? Ft = p 2 p 2 Ft = mv 2 mv 1 v 2 = Ft + mv 1 m 2 v 2 = 1500N(.06 s) + 55 kg(10. m/s)/55kg v 2 = 11.6 m/s 2

3 F(N) A 55.0 kg person traveling at 10.0 m/s experiences an impulse shown at the right. What is the resulting velocity after the impulse? t(ms) F(N) A 55.0 kg person traveling at 10.0 m/s experiences an impulse shown at the right. What is the resulting velocity after the impulse? t(ms) 3000 Ft = m v Ft = p 2 p 2 Ft = mv 2 mv 1 v 2 = Ft + mv 1 m 2 v 2 = 1500N(.06 s) + 55 kg(10. m/s) 55kg = 1/2(3000N x.06 s) +(55 kg x 10 m/s) v 2 = 8.36 m/s 55 kg 3

4 F(N) A 45.0 kg person traveling at 14.0 m/s experiences an impulse shown at the right. What is the resulting velocity after the impulse? t(ms) F(N) A 45.0 kg person traveling at 14.0 m/s experiences an impulse shown at the right. What is the resulting velocity after the impulse? Ft = m v Ft = p 2 p 2 Ft = mv 2 mv 1 v 2 = Ft + mv 1 m t(ms) v 2 = 3000N(.04 s) + 1/2(2000 N x.02 s)+ 45 kg(14.0 m/s) 45kg v 2 = 11.8 m/s 4

5 F(N) A 45.0 kg person traveling at 14.0 m/s experiences an impulse shown at the right. What is the resulting velocity after the impulse? t(ms) Ft = m v Ft = p 2 p 2 Ft = mv 2 mv 1 v 2 = Ft + mv 1 m 2 v 2 = 1500N(.04 s) + 45 kg(14. m/s) 45kg v 2 = 12.7 m/s F(N) A 55.0 kg person traveling at 10.0 m/s experiences an impulse shown at the right. What is the resulting velocity after the impulse? t(ms) 3000 Ft = m v Ft = p 2 p 2 Ft = mv 2 mv 1 v 2 = Ft + mv 1 m 2 v 2 = 1500N(.06 s) + 55 kg(10. m/s) 55kg v 2 = 8.36 m/s 5

6 Momentum Inertia of a moving object How much it wants to keep moving "Quantity of motion" Property (tendency) of moving matter Completes our understanding of Newton's 1 st Law Momentum p = mv p = kg x m/s 6

7 speeding bullet: a 15.0 g bullet travels at 500. m/s v b = 500. m/s m b = 15.0 g p = mv p =.0150 kg x 500. m/s p = 7.5 kg x m/s a walking Noah A 75.0 kg Noah walks at 1.5 m/s p = mv p = kg x 1.5 m/s p = 110 kg x m/s 7

8 speeding car: a kg car travels at 65 mph v c = 65 km/hr. m c = kg 18 m/s p = mv p = kg x 18 m/s p = 18,000 kg x m/s 2nd Law ΣF = ma a = Δv/t ΣF = mδv/t Ft = mv Ft = mv N s = kg m/s kg m/s 2 (s) = kg m/s impulse momentum kg m/s = kg m/s 8

9 Impulse Momentum Theorm Impulse = momentum Ft = mv impulse momentum impulse causes a change in momentum bullet from slide #3 The gun pushes the bullet with 3750 N of force. What time did the gun act on Ft = mv the bullet? speeding bullet v b = 500. m/s t = mv/f m b = 15.0 g d g = 1.0 m t =.0150 kg(500. m/s) 3750 N t = s 9

10 Impulse Momentum Theorem Ft = Δp Ft = p 2 p 1 m b = g Baseball thrown and hit v b1 = 76.0 mph? m/s v b2 = mph Ft =? F =?? m/s A 138 g baseball is thrown at 76 mph and then hit at 130 mph in the opposite direction. Ft = Δmv 10

11 m b = g Baseball thrown and hit v b1 = 76.0 mph A 138 g baseball is thrown at 76 mph and then hit at 130 mph in the opposite direction m/s v b2 = mph 58.0 m/s Ft =? Thrown: pitcher applies an impulse to the ball Ft = Δmv Ft = mv b2 mv b1 Ft = m(v b2 v b1 ) Ft =.138 kg(34.0 m/s 0) Ft = 4.69 kg m/s m b2 = m b1 m b = g Baseball thrown and hit v b1 = 76.0 mph 34.0 m/s v b2 = mph 58.0 m/s Ft =? ball hit Ft = Δmv Ft = mv b2 mv b1 Ft = m(v b2 v b1 ) A 138 g baseball is thrown at 76 mph and then hit at 130 mph in the opposite direction. m b2 = m b1 11

12 m b = g Baseball thrown and hit v b1 = 76.0 mph 34.0 m/s v b2 = mph 58.0 m/s Ft =? A 400 g baseball is thrown at 76 mph and then hit at 130 mph in the opposite direction. ball hit: bat applies in impulse on the ball and changes the balls momentum Ft = Δmv Ft = mv b2 mv b1 Ft = m(v b2 v b1 ) Ft =.138 kg[( 58 m/s) (34 m/s)] Ft = 12.7 kg m/s contact time = 0.7 ms... F =? m b = g v b1 = 76.0 mph 34.0 m/s v b2 = mph 58.0 m/s Ft =? Baseball thrown and hit Ft = Δmv Ft = mv b2 mv b1 Ft = m(v b2 v b1 ) Ft =.138 kg[( 58 m/s) (34 m/s)] Ft = 12.7 kg m/s contact time = s... F =? F = Δmv/t = 12.7 kg m/s/.0007 s F = 18,100 N force on ball Ft = Δmv 18,100N(.0007 s) =.138 kg[( 58 m/s) (34 m/s)] 12.7 kg m/s = 12.7 kg m/s A 138 g baseball is thrown at 76 mph and then hit at 130 mph in the opposite direction. 12

13 m b = g Baseball thrown and hit m bat =.96 kg v 1bat = 49 m/s v b1 = 76.0 mph 34.0 m/s v b2 = mph 58.0 m/s Ft =? Ft = Δmv Ft = mv 2bat mv 1bat Ft + mv 1bat = mv 2bat Ft + mv 1bat = v 2bat m bat A 138 g baseball is thrown at 76 mph and then hit at 130 mph in the opposite direction. Δv on bat Δp ball = Δp bat Ft ball = -Ft bat 12.7 Ns +.96 kg( 49 m/s) = v 2bat.96 kg v 2bat = 36 m/s Your book (2.6 kg)falls off the table ( 1.0 m high) and hits the floor ( 4.4 m/s) and does not bounce. What impulse does the floor apply? oh no! 13

14 oh no! Your book (2.6 kg)falls off the table and hits the floor ( 4.4 m/s) and does not bounce. What impulse does the floor apply? Ft = Δmv Ft = mv b2 mv b1 Ft = m(v b2 v b1 ) Ft = kg[(0 m/s) ( 4.4 m/s)] Ft = 11.4 kg m/s contact time = 0.060s... F =? F = Δmv/t = 11.4 kg m/s/.060 s F = 190 N Conservation of Momentum Momentum before a collision equals momentum after a collision! p = p' "Law of interaction" "Law of collisions" 3rd Law If "A" acts then "B", forces then, "B" acts on "A" impulse If "A" acts then "B", then, "B" acts on "A" 14

15 A 1kg B 2 kg A 1kg B 2 kg A 1kg B 2 kg 1 m/s 1 m/s p A1 = 1 kg m/s p B1 = 2 kg m/s F BA = F AB and, F BA (t)= F AB (t).6 m/s.2 m/s p 1 = p A1 + p B1 p 1 = 1 kg m/s + ( 2 kg m/s) p 1 = 1 kg m/s p A2 =.6 kg m/s p B2 =.4 kg m/s p 2 = p A2 + p B2 p 2 = mv A2 + mv B2 p 2 = 1 kg m/s(.6 m/s) + 2 kg(.2m/s) p 2 =.6 kg m/s + (.4 kg m/s) p 2 = 1 kg m/s p 1 = p 2 C8 race car mph 15

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