Impulse and Momentum Chapter problems Serway –5,6,10,13,16,17,18,27,29,33,43,44,52,54,59,60 –cw.prenhall.com/~bookbind/pubbooks/giancoli

Linear momentum & impulse Linear momentum is defined as the product of mass and velocity –p=mv, p x =mv x, p y = mv y –units of momentum are kgm/s From Newtons 2nd law F= ma F=mdv/dt F= dp/dt The rate of momentum change with respect to time is equal to the resultant force on an object The product of Force and time is known as IMPULSE J= Fdt units of impulse are Ns

Linear momentum & impulse Examples of impulses being applied on everyday objects

Impulse Momentum Theorem Fdt=mdv You apply an impulse on an object and you get an equal change in momentum Area under a Force vs time graph

Impulse Graph

Linear Momentum and Impulse Example problems 1,2,3 Chapter questions 5,6,10,13,16

Conservation of momentum 2 particle system For gravitational or electrostatic force m1 m2 F 12 F 21 F 12 is force of 1 on 2 F 21 is force of 2 on 1 F 12 =dp 1 /dt F 21 = dp 2 /dt

Conservation of momentum 2 particle system From Newton’s 3rd Law F 12 = - F 21 or F 12 + F 21 = 0 m1 m2 F 12 F 21 F 12 is force of 1 on 2 F 21 is force of 2 on 1 F 12 + F 21 =dp 1 /dt + dp 2 /dt = 0 d(p 1 + p 2 )/dt= 0 Since this derivative is equal to 0

Conservation of momentum 2 particle system d(p 1 + p 2 )/dt= 0 then integration yields p 1 + p 2 = a CONSTANT m1 m2 F 12 F 21 F 12 is force of 1 on 2 F 21 is force of 2 on 1 Since this derivative is equal to 0 Thus the total momentum of the system of 2 particles is a constant.

Conservation of linear momentum m1 m2 F 12 F 21 Simply stated: when two particles collide,their total momentum remains constant. p i = p f p 1i + p 2i = p 1f + p 2f (m 1 v 1 ) i + (m 2 v 2 ) i = (m 1 v 1 ) f + (m 2 v 2 ) f Provided the particles are isolated from external forces, the total momentum of the particles will remain constant regards of the interaction between them

Conservation of linear momentum Serway problems & 18

Collisions

Event when two particles come together for a short time producing impulsive forces on each other., No external forces acting. Or for the enthusiast: External forces are very small compared to the impulsive forces Types of collisions 1) Elastic- Momentum and Kinetic energy conserved 2) Inelastic- Momentum conserved, some KE lost 3) Perfectly(completely) Inelastic- Objects stick together

Collisions in 1 d Perfectly Elastic 1) Cons. of mom. 2) KE lost in collision 3) KE changes to PE

Elastic Collision Calculation 2 objects

Collisions - Examples Computer Simulations example 2, problems 5,24,29 Serway Problems 27,29,33,37

Collisions in 2 dimensions m a v ax m b vel=0 p=0 Before collision After Collision m a v af m b v bf m a v afx m b v bxf x momentum before collision equals x momentum after the collision 11 22

Collisions in 2 dimensions m a v ax= m a v afx + m b v bxf or m a v ax= m a v af cos  1 + m b v bf cos  2

Collisions in 2 dimensions m a v ax m b vel=0 p=0 Before collision After Collision m a v af m b v bf m a v ayf M b v byf y momentum before collision equals y momentum after the collision Velocity y axis =0 p y =o 22 11

Collisions in 2 dimensions 0= m a v afy - m b v bfy or 0= m a v af sin  1 -m b v bf sin  2

Collisions in 2 dimensions 0= m a v af sin  1 -m b v bf sin  2 m a v ax= m a v af cos  1 + m b v bf cos  2 Problems ex ,44