11. HW5 due Feb 25.2. Midterm 1 is being graded. 3. Hope to post grades and solutions by Monday4. If you forgot to bring ID during exam, you must see Prof. Chan with your ID or your exam will not be graded.AnnouncementsMomentum()finetmv vtt−∆==∆∆pFrralternative statement of Newton’s second lawThe time rate of change of momentum of an object is equal to the net force acting on itpImpulse When a single, constant force acts on the object for time ∆t, there is an impulse delivered to the object:tFI ∆=rrIr()finetmv vtt−∆==∆∆pFrrpr∆=)(ifvvmrr−=Ft= area under F-t curveAverage Force in Impulse The average force can be thought of as the constant force that would give the same impulse to the object in the time interval as the actual time-varying force gives in the intervaltFpIav∆=∆=rrrConservation of Momentum Momentum in an isolated system in which a collision occurs is conserved A collision may be the result of physical contact between two objects “Contact” may also arise from the electrostatic interactions of the electrons in the surface atoms of the bodies An isolated system will have not external forces the total momentum before the collision will equal the total momentum after the collisionConservation of Momentum, cont. Mathematically: Momentum is conserved for the system of objects Assumes only internal forces are acting during the collision Can be generalized to any number of objects2Notes About A System Remember conservation of momentum applies to the system You must define the isolated systemSo its not the velocity which is conserved but the momentum mv.Types of Collisions Momentum is conserved in any collision Inelastic collisions Kinetic energy is not conserved Some of the kinetic energy is converted into other types of energy such as heat, sound, work to permanently deform an object Perfectly inelastic collisions occur when the objects stick together Not all of the KE is necessarily lostTypes of Collisions Elastic collision both momentum and kinetic energy are conserved Actual collisions Most collisions fall between elastic and perfectly inelastic collisions73. A tennis ball of mass 57.0 g is held just above a basketball of mass 590 g. With their centers vertically aligned, both balls are released from rest at the same time, to fall through a distance of 1.20 m, as shown in Figure P6.69. (a) Find the magnitude of the downward velocity with which the basketball reaches the ground. (b) Assume that an elastic collision with the ground instantaneously reverses the velocity of the basketball while the tennis ball is still moving down. Next, the two balls meet in an elastic collision. (b) To what height does the tennis ball