Systems of Particles

Rigid Bodies Rigid Bodies - A collection of particles that do not move relative to each other. What forces are present with the 4 blocks given below? m1m1 m2m2 m3m3 m4m4

Center of Mass Total external force dictates the motion of the center of mass of the collection of objects.

Earth & Moon Where is the center of mass between the earth and the moon? r em

Balancing an ‘E’ Where is the center of mass for the metal plate illustrated below? (0 cm, 0 cm) (5 cm, 3 cm)

Momentum Momentum - Newton called it “Quantity of motion.” Ex. Find the momentum of a 40 kg ball traveling with velocity

Momentum Total momentum for a system of particles Newton’s law for multiple particles becomes If there is no net external force then

Exploding Shells A cannon shell is fired at 100 m/s with an angle of 60° w.r.t. horizontal. At the top of the trajectory, it explodes into two pieces of equal mass. The one piece has no velocity immediately after the explosion. What is the velocity of the second piece and where do the pieces land?

Kinetic Energy For multiple particles Velocity w.r.t. to center of mass Then,

Exploding Shell A 10 kg shell is traveling with a velocity of. It explodes into two pieces, one which is 3 kg traveling at. What is the velocity of the 2nd piece and the energy released in the explosion?

Impulse From Newton’s 2nd Law Impulse - Change in momentum If constant force or average force

Bouncing Ball A 0.15 kg ball strikes the floor with a velocity of. Its velocity after striking the floor is. What is the average force the floor exerts on the ball, if the ball is in contact with the floor for 0.25s?

Conservation Laws Conservation of Momentum –Valid when collision takes place fast enough. –External forces can’t change momentum significantly. Conservation of Energy –Elastic Collision - Kinetic energy is conserved. –Inelastic Collision - Kinetic energy is not conserved. (Totally inelastic - Objects stick)

Identify Collisions Classify the following collisions –Two billiard balls collide. –Two cars collide and lock bumpers. –A bat strikes a baseball. –A ball of clay is thrown at a wall and sticks. –Two nitrogen molecules in the air collide. –A receiver leaps and catches a football. –Two hydrogen atoms in the air collide.

Flying Tackle An 85 kg running back is traveling downfield at 9 m/s. A 120 kg tackle hits him 30° from head on at a speed of 7 m/s. Assuming both are not in contact with the ground during the tackle and they move as one after the tackle, what is their velocity after the tackle?

Elastic Collisions In 1-D can get 2 equations for 2 unknowns Ex. Rutherford studied the composition of matter by scattering alpha particles off of thin sheets of gold. If an alpha particle hits a stationary gold atom head on with a velocity of 200 m/s, what are the final velocities of both particles?

Elastic Collisions (2-D) 2-D can get 3 equations for 3 unknowns Ex. The cue ball hits a stationary pool ball with a velocity of 1.0 m/s. If the stationary ball travels away from the collision at an angle of 30°, what are the velocities of the two balls after the collision? 30° 1.0 m/s