{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

P161Sp08Chapter_09

# P161Sp08Chapter_09 - Chapter 9 Impulse Momentum Linear...

This preview shows pages 1–13. Sign up to view the full content.

Chapter 9 Impulse & Momentum

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Linear Momentum n 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: n p = m v n The terms momentum and linear momentum will be used interchangeably in the text
Linear Momentum, cont n Linear momentum is a vector quantity n Its direction is the same as the direction of v n The dimensions of momentum are ML/T n The SI units of momentum are kg m / s n Momentum can be expressed in component form: n p x = m v x p y = m v y p z = m v z

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Newton and Momentum n Newton called the product m v the quantity of motion of the particle n Newton’s Second Law with constant mass (i.e. dm/dt = 0) can be used to relate the momentum of a particle to the resultant force acting on it This is a generalization of Newton’s 2nd Law.
Newton’s Second Law n The time rate of change of the linear momentum of a particle is equal to the net force acting on the particle n This is the form in which Newton presented the Second Law n It is a more general form than the one we used previously n This form also allows for mass changes n Applications to systems of particles are particularly powerful

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Conservation of Linear Momentum n Whenever two or more particles in an isolated system , i.e no outside forces are present , interact the total momentum of the system remains constant n The momentum of the system is conserved, not necessarily the momentum of an individual particle n This also tells us that the total momentum of an isolated system equals its initial momentum
Conservation of Momentum, 2 n Conservation of momentum can be expressed mathematically in various ways n p total = p 1 + p 2 = constant n p 1i + p 2i = p 1f + p 2f n In component form, the total momenta in each direction are independently conserved n p ix = p fx p iy = p fy p iz = p fz n Conservation of momentum can be applied to systems with any number of particles

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Conservation of Momentum, Archer Example n The archer is standing on a frictionless surface (ice) n Approaches: n Newton’s Second Law no, we have no information about F or a n Energy approach – no, no information about work or energy n Momentum – yes
Archer Example, 2 n Let the system be the archer with bow (particle 1) and the arrow (particle 2) n There are no external forces in the x -direction, so it is isolated in terms of momentum in the x -direction n Total momentum before releasing the arrow is 0 n The total momentum after releasing the arrow is p 1f + p 2f = 0

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Archer Example, final n The archer will move in the opposite direction of the arrow after the release n Agrees with Newton’s Third Law n Because the archer is much more massive than the arrow, his acceleration and velocity will be much smaller than those of the arrow
Conservation of Momentum, Kaon Example n The kaon decays into a positive p and a negative p particle n Total momentum before decay is zero n Therefore, the total momentum after the decay must equal zero n p + + p - = 0 or p + = -p -

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Momentum Conservation Demos n Gas powered Tricycle n Water Rocket n Ballistic Cannon
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}