Impulse and Momentum. AP Physics B

Transcription

1 Imulse and Momentum P Physics B

2 Imulse Momentum Consider Newton s nd Law and the definition of acceleration Units of Imulse: Ns Units of Momentum: Kg x m/s Momentum is defined as Inertia in Motion

3 Imulse Momentum heorem Ft m IMPULSE CHNGE IN MOMENUM his theorem reeals some interesting relationshis such as the INVERSE relationshi between FORCE and IME F m t

4 Imulse Momentum Relationshis

5 Imulse Momentum Relationshis f m V Constant Since IME is directly related to the VELOCIY when the force and mass are constant, the LONGER the cannonball is in the barrel the greater the elocity. lso, you could say that the force acts oer a larger dislacement, thus there is more WORK. he work done on the cannonball turns into kinetic energy.

6 How about a collision? Consider objects seeding toward each other. When they collide... Due to Newton s 3 rd Law the FORCE they exert on each other are EQUL and OPPOSIE. he IMES of imact are also equal. F ( Ft) J F J t ( Ft) t herefore, the IMPULSES of the objects colliding are also EQUL

7 J How about a collision? If the Imulses are equal then the MOMENUMS are also equal! m m J ( m o ) o m ( o ) o before after o mo m m

8 Momentum is consered! he Law of Conseration of Momentum: In the absence of an external force (graity, friction), the total momentum before the collision is equal to the total momentum after the collision. o( truck ) o( car) o( total) truck car total m o (400)() 800kg * m / s 3300kg * m / s 500*3 500kg * m / s 400* kg * m / s 3300kg * m / s (500)(5) 500kg * m / s

9 yes of Collisions situation where the objects DO NO SICK is one tye of collision Notice that in ECH case, you hae WO objects BEFORE and FER the collision.

10 no stick tye collision Σ before Σ after (000)(0) 0 (000)( o -0 m/s o ) (3000)(0)

11 yes of Collisions nother tye of collision is one where the objects SICK together. Notice you hae WO objects before the collision and ONE object after the collision.

12 stick tye of collision Σ before Σ after (000)(0) o 5 m/s o m (4000) 4000

13 he exlosion tye his tye is often referred to as backwards inelastic. Notice you hae ONE object ( we treat this as a SYSEM) before the exlosion and WO objects after the exlosion.

14 Backwards Inelastic - Exlosions Suose we hae a 4-kg rifle loaded with a 0.00 kg bullet. When the rifle is fired the bullet exits the barrel with a elocity of 300 m/s. How fast does the gun RECOIL backwards? Σ before Σ after (4.00)(0) 0 (0.00)(300) m/s (4)( )

15 Collision Summary Sometimes objects stick together or blow aart. In this case, momentum is LWYS consered. 0 m 0 total before o( total) 0 0 m total after total When objects collide and DON stick When objects collide and stick together When object breaks into objects Elastic Collision Kinetic Energy is Consered Inelastic Collision Kinetic Energy is NO Consered

16 Elastic Collision KE KE KE car truck car ( Before) ( fter) ( fter) m 0.5(000)(0) 0.5(3000)(0) 50,000J 0.5(000)( 0) 50,000J 00,000J Since KINEIC ENERGY is consered during the collision we call this an ELSIC COLLISION.

17 Inelastic Collision KE KE car ( Before) truck / car ( fter) m 0.5(4000)(5) 0.5(000)(0) 50,000J 00,000J Since KINEIC ENERGY was NO consered during the collision we call this an INELSIC COLLISION.

18 Examle How many objects do I hae before the collision? How many objects do I hae after the collision? Granny (m80 kg) whizzes around the rink with a elocity of 6 m/s. She suddenly collides with mbrose (m40 kg) who is at rest directly in her ath. Rather than knock him oer, she icks him u and continues in motion without "braking." Determine the elocity of Granny and mbrose. o b (80)(6) 4 m/s o a m (40)(0) 0

19 Collisions in Dimensions cosθ B sinθ B cosθ B sinθ he figure to the left shows a collision between two ucks on an air hockey table. Puck has a mass of 0.05-kg and is moing along the x-axis with a elocity of 5.5 m/s. It makes a collision with uck B, which has a mass of kg and is initially at rest. he collision is NO head on. fter the collision, the two ucks fly aart with angles shown in the drawing. Calculate the seeds of the ucks after the collision.

20 Collisions in dimensions sinθ ox m ox m B x oxb m x m ( 0.05)(5.5) 0 (.05)( cos 65) (.050)( B cos37) B xb B cosθ B B cosθ oy 0 my m B sinθ 0 (0.05)( B B y B yb sin 65) (0.050)( 0.07 B sin 37)

21 Collisions in dimensions B B m / s (0.050)( ) B 0.757(.84).5m / s