* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Momentum
Velocity-addition formula wikipedia , lookup
Brownian motion wikipedia , lookup
Specific impulse wikipedia , lookup
Uncertainty principle wikipedia , lookup
Hunting oscillation wikipedia , lookup
Internal energy wikipedia , lookup
Lagrangian mechanics wikipedia , lookup
Eigenstate thermalization hypothesis wikipedia , lookup
Renormalization group wikipedia , lookup
Analytical mechanics wikipedia , lookup
Tensor operator wikipedia , lookup
Symmetry in quantum mechanics wikipedia , lookup
Classical mechanics wikipedia , lookup
Old quantum theory wikipedia , lookup
Hamiltonian mechanics wikipedia , lookup
Monte Carlo methods for electron transport wikipedia , lookup
Quantum vacuum thruster wikipedia , lookup
Matter wave wikipedia , lookup
Accretion disk wikipedia , lookup
Classical central-force problem wikipedia , lookup
Traffic collision wikipedia , lookup
Angular momentum wikipedia , lookup
Kinetic energy wikipedia , lookup
Relativistic quantum mechanics wikipedia , lookup
Routhian mechanics wikipedia , lookup
Laplace–Runge–Lenz vector wikipedia , lookup
Equations of motion wikipedia , lookup
Angular momentum operator wikipedia , lookup
Photon polarization wikipedia , lookup
Newton's laws of motion wikipedia , lookup
Theoretical and experimental justification for the Schrödinger equation wikipedia , lookup
Relativistic mechanics wikipedia , lookup
Momentum What do you think? • Imagine an automobile collision in which an older model car from the 1960s collides with a car at rest while traveling at 15 mph. Now imagine the same collision with a 2013 model car. In both cases, the car and passengers are stopped abruptly. – List the features in the newer car that are designed to protect the passenger and the features designed to minimize damage to the car. – How are these features similar? What do you think? • What are some common uses of the term momentum? – In your group, write a sentence using the term momentum. • Do any of the examples provided reference the velocity of an object? • Do any of the examples reference the mass of an object? Momentum p = m·v momentum = mass x velocity • Momentum (p) is proportional to both mass and velocity. • A vector quantity • SI Units: kg • m/s Momentum and Newton’s 2nd Law • Prove that the two equations shown below are equivalent. F = ma and F = p/t • Newton actually wrote his 2nd Law as F = p/t. – Force depends on how rapidly the momentum changes. Notes About A System • Remember conservation of momentum applies to the system • You must define the isolated system Types of Collisions • Momentum is conserved in any collision • Inelastic collisions – Kinetic energy is not conserved • Some of the kinetic energy is converted into other types of energy such as heat, sound, work to permanently deform an object – Perfectly inelastic collisions occur when the objects stick together • Not all of the KE is necessarily lost More Types of Collisions • Elastic collision – both momentum and kinetic energy are conserved • Actual collisions – Most collisions fall between elastic and perfectly inelastic collisions More About Perfectly Inelastic Collisions • When two objects stick together after the collision, they have undergone a perfectly inelastic collision • Conservation of momentum becomes m 1 v 1i m 2 v 2 i ( m 1 m 2 ) v f Some General Notes About Collisions Momentum is a vector quantity Direction is important Be sure to have the correct signs More About Elastic Collisions Both momentum and kinetic energy are conserved Typically have two unknowns m1v 1i m 2 v 2i m1v 1f m 2 v 2 f 1 1 1 1 2 2 2 2 m1v 1i m 2 v 2i m1v 1f m 2 v 2 f 2 2 2 2 Solve the equations simultaneously Elastic Collisions, cont. A simpler equation can be used in place of the KE equation v 1i v 2 i ( v 1f v 2 f ) This equation will be used to solve problems dealing with perfectly elastic head-on collisions Summary of Types of Collisions In an elastic collision, both momentum and kinetic energy are conserved In an inelastic collision, momentum is conserved but kinetic energy is not In a perfectly inelastic collision, momentum is conserved, kinetic energy is not, and the two objects stick together after the collision, so their final velocities are the same Problem Solving for One Dimensional Collisions Coordinates: Set up a coordinate axis and define the velocities with respect to this axis It is convenient to make your axis coincide with one of the initial velocities Diagram: In your sketch, draw all the velocity vectors and label the velocities and the masses Problem Solving for One Dimensional Collisions, 2 Conservation of Momentum: Write a general expression for the total momentum of the system before and after the collision Equate the two total momentum expressions Fill in the known values Problem Solving for One Dimensional Collisions, 3 Conservation of Energy: If the collision is elastic, write a second equation for conservation of KE, or the alternative equation This only applies to perfectly elastic collisions Solve: the resulting equations simultaneously Sketches for Collision Problems Draw “before” and “after” sketches Label each object include the direction of velocity keep track of subscripts Sketches for Perfectly Inelastic Collisions The objects stick together Include all the velocity directions The “after” collision combines the masses