ch7 - Linear Momentum Chapter Outline GENERAL PHYSICS PHY...

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Unformatted text preview: Linear Momentum Chapter Outline GENERAL PHYSICS PHY 302K Momentum Chapter 7: Linear Momentum Impulse Conservation of Momentum Maxim Tsoi Collisions: Elastic and Inelastic Physics Department, The University of Texas at Austin http://www.ph.utexas.edu/~tsoi/302K.htm 302K - Ch.7 302K - Ch.7 Linear Momentum Linear Momentum Concept of momentum Newton’s 2nd law • The linear momentum of a particle or an object that can be modeled as a particle of mass m moving with a velocity v is defined to be the product of the mass and velocity: • The time rate of change of the linear momentum of a particle is equal to the net force acting on the particle: pm v v mv p F m am t t t vector quantity SI unit of momentum is kg m/s • in components: • in components: px m v x py m v y F pz m v z x 302K - Ch.7 p x t F y p y t F z p z t 302K - Ch.7 Linear Momentum Impulse and Momentum Conservation of momentum • Two particles interact with each other: Impulse-momentum theorem F12 F21 F12 F21 0 m1a1 m2 a2 0 v v m1v1 m2 v 2 m1 1 m2 2 0 0 t t t t m1v1 m2 v 2 p1 p2 0 0 t t p1 p2 const • The momentum of a particle changes if a net force (F) acts on the particle: p F t p Ft • Impulse of the force F acting on a particle over time interval: I Ft • The impulse of the force F acting on a particle equals the change in the momentum of the particle I p mv f mv i • Whenever two or more particles in an isolated system interact, the total momentum of the system remains constant 302K - Ch.7 Example 7.1 302K - Ch.7 1 Collisions in 1D Collisions in 1D Elastic vs inelastic collisions Perfectly inelastic collisions • COLLISION event during which two • PERFECTLY INELASTIC COLLISION particles come close to each other and the colliding objects stick together after interact by means of forces the collision • TOTAL MOMENTUM IS CONSERVED! • TOTAL MOMENTUM IS CONSERVED! m1v1i m2v 2 i ( m1 m2 ) v f • ELASTIC COLLISION the total kinetic energy of the system is the same before m v m2 v 2 i v f 1 1i m1 m 2 and after the collision • INELASTIC COLLISION the total kinetic energy of the system is not the same before and after the collision 302K - Ch.7 302K - Ch.7 Collisions in 1D Collisions in 2D Elastic collisions Glancing collision • Two component equations for conservation of momentum: • ELASTIC COLLISION the total kinetic m1v1ix m2 v 2 ix m1v1 fx m2v 2 fx m1v1iy m2 v 2 iy m1v1 fy m2v 2 fy energy of the system is the same before and after the collision 2 2 2 2 m1v1i m2 v 2 i m1v1 f m2 v 2 f 2 2 2 2 • TOTAL MOMENTUM IS CONSERVED! m1v1i m2v 2 i m1v1 f m2v 2 f m m2 2m 2 v1 f 1 m m v1i m m v 2 i 2 2 1 1 2m1 m 2 m1 v2 f m m v1i m m v 2 i 2 2 1 1 302K - Ch.7 m1v1i m1v1 f cos m2 v 2 f cos 0 m1v1 f sin m2v 2 f sin 302K - Ch.7 For elastic collision: 2 2 m1v12i m1v1 f m2 v 2 f 2 2 2 Example 7.5-6 SUMMARY Linear Momentum • Linear momentum: pm v • The law of conservation of linear momentum: • Impulse delivered to a particle by force (impulse-momentum theorem): • Inelastic and elastic collisions p1 p2 const p Ft kinetic energy is not conserved kinetic energy is conserved 302K - Ch.7 2 ...
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