Fri. Feb. 25th1 PHSX213 class Class stuff –Questions ? Conservation of Linear Momentum Collision terminology Collisions

Fri. Feb. 25th2 In an inelastic collision, A. impulse is conserved. B. momentum is conserved. C. force is conserved. D. energy is conserved. E. elasticity is conserved. Reading Quiz

Fri. Feb. 25th3 Linear momentum p = m v –( =  m v, with  ≡ (1-  2 )  1/2 and  ≡ v/c. For non- relativistic velocities,  ≈0,  = 1 ) –is defined as the linear momentum of a particle –a vector quantity –SI units kg m/s The definitive version of Newton II is : –  F = d p /dt, and applying these definitions to a system of particles of constant mass, M, one sees that –  F = d P /dt = M a CM, where P =  p i = M v CM

Fri. Feb. 25th4 Linear Momentum P is very useful because in systems with no net external force, P, is constant. Ie it doesn’t change, it is a conserved quantity. P i = P f

Fri. Feb. 25th5 Check-Point 1 Suppose you are on a cart, initially at rest on a track with very little friction. You throw balls at a partition that is rigidly mounted on the cart. If the balls bounce straight back as shown, is the cart put in motion? A. Yes, it moves to the right. B. Yes, it moves to the left. C. No, it remains in place.

Fri. Feb. 25th6 Collisions and Impulse What happens during a collision ? Force(s) act on the object changing the object’s momentum ie. dp = F(t) dt. If we integrate over the time of the collision, we find that  p = p f –p i = ∫ F(t) dt ≡ J where J is defined as the impulse.

Fri. Feb. 25th7 A.The clay ball exerts a larger impulse because it sticks. B.The rubber ball exerts a larger impulse because it bounces. C.They exert equal impulses because they have equal momenta. D.Neither exerts an impulse on the wall because the wall doesn’t move. A 10 g rubber ball and a 10 g clay ball are thrown at a wall with equal speeds. The rubber ball bounces, the clay ball sticks. Which ball exerts a larger impulse on the wall? Check-Point 2

Fri. Feb. 25th8 DVD Demos 5.09 Egg in Sheet

Fri. Feb. 25th9 Demo Define types of collision: –Elastic : Kinetic Energy conserved –Inelastic : Kinetic Energy not conserved –Completely Inelastic : Colliding objects stick together (think of two balls of putty) –Explosive : Kinetic Energy increases due to some source of stored energy (eg. potential energy)

Fri. Feb. 25th10 Two-ball Bounce

Fri. Feb. 25th11 Check-Point 3 A compact car and a large truck collide head on and stick together. Which undergoes the larger momentum change? A. car B. truck C. The momentum change is the same for both vehicles. D. Can’t tell without knowing the final velocity of combined mass.

Fri. Feb. 25th12 Inelastic and Elastic 1-D Collisions Write down principles and derive relationships for both.

Fri. Feb. 25th13 Ballistic Pendulum Bullet of mass m, traveling at velocity, v, is fired at wooden block with mass, M. The bullet becomes embedded in the wood. If the bullet-block system rises to a height of 10 cm. What is the velocity of the bullet ?

Fri. Feb. 25th14 Ballistic Pendulum Demo

Fri. Feb. 25th15 Problem 9.56 Block A (mass 1.6 kg) slides into block B (mass 2.4 kg) along a frictionless surface. Initially, v A =+5.5 m/s and v B = +2.5 m/s. After the collision, v B =+4.9 m/s. What is the speed and direction of A ? Is the collision elastic ?

Fri. Feb. 25th16 Next time More on collisions More details re: project