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Chapter 9: Linear Momentum and Collisions Reading assignment: Chapter 10.1-10.5 Homework #16 : Problems: (due Monday, Oct. 10, 2005): Q1, Q14, 9, 14, 21, 28 • Momentum p mv • Momentum is conserved – even in collisions with energy loss due to friction/deformation. • Impulse Black board example 9.3 You (100kg) and your skinny friend (50.0 kg) stand face-to-face on a frictionless, frozen pond. You push off each other. You move backwards with a speed of 5.00 m/s. (a) What is the total momentum of the you-and-your-friend system? (b) What is your momentum after you pushed off? (c) What is your friends speed after you pushed off? Impulse (change in _________________) A change in _________ is called “impulse”: J p p f pi During a collision, a force F acts on an object, thus causing a change in momentum of the object: For a constant (average) force: tf p J ______ dt ti p J Favg ___ Think of hitting a soccer ball: A force F acting over a time t causes a change p in the momentum (velocity) of the ball. Black board example 10.1 A soccer player hits a ball (mass m = 440 g) coming at him with a velocity of 20 m/s. After it was hit, the ball travels in the opposite direction with a velocity of 30 m/s. (a) What impulse acts on the ball while it is in contact with the foot? (b) The impact time is 0.1s. What is the acting on the ball? Elastic and inelastic collisions in one dimension ________________ is conserved in any collision, elastic and inelastic. ___________________ is only conserved in elastic collisions. Perfectly inelastic collision: After colliding, particles __________________. There is a loss of kinetic energy (deformation). Inelastic collisions: Particles _________________ with some loss of kinetic energy. Perfectly elastic collision: Particles __________________ without loss of kinetic energy. Perfectly _____________ collision of two particles (Particles stick together) pi p f m1v1i m2v2i (________)v f Notice that p and v are vectors and, thus have a direction (+/-) K i Eloss K f 1 1 1 2 2 2 m1v1i m2v2i Eloss (_______)v f 2 2 2 There is a loss in kinetic energy, Eloss Perfectly _________ collision of two particles (Particles bounce off each other without loss of energy. Momentum is ____________: m1v1i m2 v2i m1v1 f m2v2 f Energy is _____________: 1 1 1 1 2 2 2 2 m1v1i m2 v2i m1v1 f m2 v2 f 2 2 2 2 For elastic collisions in : Suppose we know the initial masses and velocities. Then: m1 m2 ____ v1i v2i v1 f m1 m2 m1 m2 (10.38) ____ m2 m1 v1i v2i m1 m2 m1 m2 (10.39) v2 f (10.30) (10.31) Black board example 9.2 Two carts collide elastically on a frictionless track. The first cart (m1 = 1kg) has a velocity in the positive x-direction of 2 m/s; the other cart (m = 0.5 kg) has velocity in the negative x-direction of 5 m/s. (a) Find the speed of both carts after the collision. (b) What is the speed if the collision is inelastic? (c) How much energy is lost in the inelastic collision? Black board example 9.5 Ballistic Pendulum: In a ballistic pendulum a bullet (0.005 kg) is fired into a block (1.0 kg) that is suspended from a light string. The block (with the bullet stuck in it) is lifted up by 0.05 m. (a) What is the speed of the combined bullet/pendulum right after the collision? (b) Find the initial speed of the bullet? (c) Find the loss in mechanical energy due to the collision _______________ collisions (Two particles) Conservation of momentum: m1v1i m2 v2i m1v1 f m2v2 f Split into components: m1v1ix m2v2ix m1v1 fx m2v2 fx m1v1iy m2v2iy m1v1 fy m2v2 fy If the collision is ____________, we can also use conservation of energy. Black board example 9.3 Accident investigation. Two automobiles of equal mass approach an intersection. One vehicle is traveling towards the east with 29 mi/h 13.0 m/s (13.0 m/s) and the other is traveling north with unknown speed. The vehicles collide in the intersection and stick together, leaving skid marks at an angle of 55º north of east. The second driver claims he was driving below the speed limit of 35 mi/h (15.6 m/s). ??? m/s Is he telling the truth? What is the speed of the “combined vehicles” right after the collision? How long are the skid marks (mk = 0.5)