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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: Impulsemomentum 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 7.56 SUMMARY
Linear Momentum
• Linear momentum: pm v • The law of conservation of linear momentum:
• Impulse delivered to a particle by force
(impulsemomentum 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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