* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Review - Worth County Schools
N-body problem wikipedia , lookup
Quantum vacuum thruster wikipedia , lookup
Symmetry in quantum mechanics wikipedia , lookup
Modified Newtonian dynamics wikipedia , lookup
Elementary particle wikipedia , lookup
Relativistic quantum mechanics wikipedia , lookup
Photon polarization wikipedia , lookup
Centripetal force wikipedia , lookup
Specific impulse wikipedia , lookup
Equations of motion wikipedia , lookup
Laplace–Runge–Lenz vector wikipedia , lookup
Accretion disk wikipedia , lookup
Matter wave wikipedia , lookup
Angular momentum wikipedia , lookup
Classical mechanics wikipedia , lookup
Theoretical and experimental justification for the Schrödinger equation wikipedia , lookup
Angular momentum operator wikipedia , lookup
Atomic theory wikipedia , lookup
Mass in special relativity wikipedia , lookup
Classical central-force problem wikipedia , lookup
Electromagnetic mass wikipedia , lookup
Work (physics) wikipedia , lookup
Rigid body dynamics wikipedia , lookup
Center of mass wikipedia , lookup
Relativistic angular momentum wikipedia , lookup
Momentum • A measure of how hard it is to stop a moving object. • Related to both mass and velocity. • Possessed by all moving objects. Calculating Momentum • For one particle p = mv • For a system of multiple particles P = pi = mivi • Momentum is a vector! Which has the most momentum? Impulse (J) The product of an external force and time, which results in a change in momentum •J = F t •J = P •Units: N s or kg m/s Impulse (J) F(N) 3000 2000 area under curve 1000 0 0 1 2 3 4 t (ms) Law of Conservation of Momentum pb = pa If the resultant external force on a system is zero, then the vector sum of the momenta of the objects will remain constant. Collisions • Collisions are governed by Newton's laws. • Newton’s Third Law tells us that the force exerted by body A on body B in a collision is equal and opposite to the force exerted on body B by body A. Collisions During a collision, external forces are ignored. The time frame of the collision is very short. The forces are impulsive forces (high force, short duration). Collision Types • Elastic (hard, no deformation) – P is conserved, K is conserved • Inelastic (soft; deformation) – P is conserved, K is NOT conserved • Perfectly Inelastic (stick together) – P is conserved, K is NOT conserved Golf and Momentum Consider the elastic collision between the club head and the golf ball in the sport of golf. Golf and Momentum Forces are on the clubhead and ball are equal and opposite. Golf and Momentum The acceleration of the ball is greater because its mass is smaller. Pool and Momentum Consider the elastic collision between a moving ball and a ball that is at rest in the sport of billiards. Pool and Momentum The balls experience forces which are equal in magnitude and opposite in direction. Pool and Momentum Since the balls have equal masses, they experience equal accelerations. Explosion • When an object separates suddenly, this is the reverse of a perfectly inelastic collision. • Mathematically, it is handled just like an ordinary inelastic collision. • Momentum is conserved, kinetic energy is not. • Examples: – Cannons, Guns, Explosions, Radioactive decay. Perfectly Inelastic Collision #1 An 80 kg roller skating grandma collides inelastically with a 40 kg kid as shown. What is their velocity after the collision? Perfectly Inelastic Collisions #2 A train of mass 4m moving 5 km/hr couples with a flatcar of mass m at rest. What is the velocity of the cars after they couple? Perfectly Inelastic Collisions #3 A fish moving at 2 m/s swallows a stationary fish which is 1/3 its mass. What is the velocity of the big fish and after dinner? Recoil Problem #1 A gun recoils when it is fired. The recoil is the result of action-reaction force pairs. As the gases from the gunpowder explosion expand, the gun pushes the bullet forwards and the bullet pushes the gun backwards. Sample Problem Suppose three equally strong, equally massive astronauts decide to play a game as follows: The first astronaut throws the second astronaut towards the third astronaut and the game begins. Describe the motion of the astronauts as the game proceeds. Assume each toss results from the same-sized "push." How long will the game last? Announcements 5/22/2017 • Tomorrow -- Graded Quiz • Lunch Bunch Wednesday this week! • Lunch Bunch HW due Wednesday. • Exam Thursday on Momentum. • Energy Exam corrections M,Tue,Thu • Makeup lab on Friday. Center of Mass • Physicist like to deal with particles because it is relatively easy to deal with an object that has position and mass, but no real size. • But what do you do if you have a real object with a non-zero size? Or if you have a collection of particles? • You turn the object into a particle by pretending all the mass resides at the center of mass. Calculate momentum of the balls before and after the collision. 2 m/s 3 m/s 2 kg 0 m/s 8 kg Before 2 kg 50o 8 kg V? After Center of Mass The point at which all of the mass of an object or system may be considered to be concentrated. Center of Mass for solid objects Pick the geometric center of the object x x x Center of Mass for collection of points xcm = mixi / M ycm= miyi / M zcm= mizi / M Center of Mass Problem (SOS 8.10) A system consists of the following masses in the x,y plane: 4 kg at (0, 5m), 7 kg at (3m, 8m), and 5 kg at (-3 m, -6m). Find the position of its center of mass.