Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Relativistic quantum mechanics wikipedia , lookup
Fictitious force wikipedia , lookup
Lorentz force wikipedia , lookup
Negative mass wikipedia , lookup
Weightlessness wikipedia , lookup
Woodward effect wikipedia , lookup
Matter wave wikipedia , lookup
Momentum 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=Ft 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 pi = pf 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 by body B on 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, KE is conserved • Inelastic (soft; deformation) – p is conserved, KE is NOT conserved • Perfectly Inelastic (stick together) – p is conserved, KE is NOT conserved Inelastic Collisions • Only momentum is conserved. • Kinetic Energy is not conserved. • Some deformation of the object(s) will occur. • Perfectly inelastic collision is when the objects actually “stick” together. • Examples are: automobile crashes, catching a ball, recoil of a gun. 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 1.14-kg skateboard is coasting along the pavement at a speed of 3.53 m/s, when a 1.1-kg cat drops from a tree vertically down on the skateboard. What is the speed of the skateboard-cat combination? Explosions and Recoil • 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. Recoil Problem #1 A gun recoils when it is fired. The recoil is the result of action-reaction force pairs. Calculate the Recoil velocity Mass of Gun = 2.1 kg Mass of Man= 75 kg Mass of Bullet = 0.001 Kg Muzzle Velocity = 450 m/s Elastic Collisions • Momentum and Kinetic Energy are conserved. • No deformation of objects occurs. • Examples are: billiard balls (pool), particle collisions, marbles. i f KE i KE f Elastic Collision #1 • A 7-g marble has a head-on collision with a 3-g marble, initially at rest on a playing surface. The speed of the 7-g marble is reduced from 1.08 m/s to 0.75 m/s in the collision. What is the speed of 3-g marble after the collision? Elastic Collision #2 • A 4-gram object moving to the right with a speed of 3.9 cm/s makes an elastic headon collision with a 6-gram object moving in the opposite direction with a speed of 6.6 cm/s. Find the velocities after the collision.