Ch 7, Momentum and Collisions Definition of impulse Definition of momentum Impulse-Momentum Theorem

Transcription

1 Today Ch 7, Momentum and Collisions Definition of impulse Definition of momentum Impulse-Momentum Theorem System of particles Conservation of Momentum 1 Data : Fatality of a driver in head-on collision (With a passenger) < (Without a passenger) 2 1

2 Definition of Impulse Impulse: I F t F : force, Δt: time A vector quantity SI Unit: N s 3 Definition of (Linear) Momentum (Linear) Momentum (m: mass, v: velocity) A vector quantity SI Unit: kg m/s 4 2

3 Impulse-Momentum Theorem Let s rewrite Newton s Second Law v f vi mv f mvi p Fnet ma m t t t I p p net f i Fnet t p Net impulse is equal to the change in momentum p p I f i net Momentum changes by the amount of impulse 5 Impulse by a constant force I F t F (Area in F vs. t graph) = (Impulse by F) 0 t t 6 3

4 Impulse by a varying force Impulse is an area under F(t) graph! F p i p f F t I p net, average net t 7 iclicker Quiz A paratrooper whose chute fails to open lands in snow; he is hurt slightly. Had he landed on bare ground, the stopping time would have been 10 times shorter and the collision lethal. Does the presence of the snow (a) increase, (b) decrease, or (c) leave unchanged the values of (1) the paratrooper's change in momentum, (2) the impulse stopping the paratrooper, and (3) the force stopping the paratrooper? 8 4

5 Example 2 A kg baseball, thrown with a speed of 40 m/s, is hit straight back at the pitcher with a speed of 50 m/s. (a)what is the impulse delievered by the bat to the baseball? (b) Find the magnitude of the average force exerted by the bat on the ball if the two are in contact for 2.0x10-3 s. 9 iclicker Quiz A ball with original momentum +4.0 kg m/s hits a wall and bounces straight back without losing any kinetic energy. The change in momentum of the ball is : a. 0. b. 4.0 kg m/s. c. 8.0 kg m/s. d. 8.0 kg m/s. 10 5

6 Example A 3.0-kg steel ball strikes a massive wall at 10.0 m/s at an angle of 60 deg with the plane of the wall. It rebounces off the wall with the same speed and angle. If the ball is in contact with the wall for s, what is the average force exerted by the wall on the ball? 60 deg 60 deg 12 6

7 Net momentum conservation for collision Right Before collision v1i m1 F on m1 from m2 During collision for t v1f Right After collision F v2i m2 F on m2 from m1 v2f F From Newton s 3 rd law, on m1 from m2 on m2 from m1 Multiplying Using I-M Theorem, t on both sides, Ifor m1 Ifor m2 p p I 1 f 1i for m1 p p I p p p I p I p p +x direction 2 f 2i for m2 1 f 2 f 1i for m1 2i for m2 1i 2i 13 System of objects We consider system of multiple objects, which we can choose any way convenient for us. For example, The system: m1, m2 and m3; however m4 and m5 are external objects! m1 m2 m3 m4 m5 14 7

8 Internal vs. External Forces Internal forces: Forces between objects within the system External forces: Forces from outside the system m1 m3 m2 m5 m4 15 Net Momentum of System of Particles (or, Objects) P p p... m v m v... net The system: m1, m2 and m3; however m4 and m5 are external objects! v 1 m1 v 5 v 2 m2 m5 m3 v 3 v 4 m4 16 8

9 Net external force, Net external impulse Net external force : F F F net, ext ext,1 ext,2... sum of all external forces acting on the system m1 m3 system m2 Net external impulse: m4 m5 I F t net, ext net, ext 17 Impulse-Momentum Theorem for System of Particles I P P net, ext net, f net, i Net external impulse is equal to net momentum change. Proof: use Newton s 3rd law (see textbook) Note: Internal forces do not matter for net momentum change. 18 9

10 Conservation of momentum If I net, ext 0, for example, F net, ext 0 or t is small P P net, f net, i If the net external impulse is zero, for example, if the net external force is zero, the net momentum of a system is conserved. 19 Example Before collision 1 m/s 4 m/s 3 kg particle 1 kg particle +x direction During collision 1 m/s??? m/s After collision Two objects on a frictionless horizontal surface collide as shown above. We choose two objects as a system. Find the velocity of the 1 kg object

11 Example Before collision 1 m/s 4 m/s glue 3 kg particle 1 kg particle +x direction During collision After collision??? m/s Two objects on a frictionless horizontal surface collide and they move together after collision. Find the velocity after collision