Momentum & its Conservation Unit 4

What is momentum? “Mass in motion”- objects at rest have no momentum A vector quantity in units of kg ∙ m/s Symbolized by a lower case “p” ∆p = mass x change in velocity Objects with large p have either a large mass or a high velocity Objects with small p have either a small mass or a small velocity

It takes an impulse to change momentum…. A force acting over a given time will change an object’s momentum An unbalanced force always accelerates an object…speeding it up or slowing it down

Impulse-Momentum Theorem From Newton’s 2nd law: F = m a Substituting v/t for a we get F = m Δv/t or F t = m Δv The product F x t is called the impulse (J) which results in a change in momentum (Δp) The impulse (J) causes and is equal to the change in momentum (Δp).

Impulse-momentum Theorem FΔt = mΔv In a collision, an object experiences a force for a specific amount of time which results in a change in momentum (speeding up or slowing down). Momentum is conserved…any change in p by one object is balanced by the change in p in the other object.

Self-Check

Elastic Collisions A collision in which the total momentum of the two objects is conserved, while the individual momenta of each object changes. Δp are always equal, but in opposite directions from Newton’s 3rd law. Moving R (or east) is noted as positive Moving L (or west) is noted as negative

Elastic Collisions Force and time are inversely proportional A force applied over a greater time will minimize the effect of the force A force applied over a shorter time will maximize the effect of the force

Elastic Collisions Examples: padded dashboards, “riding the punch,” nylon ropes in rock climbing, follow-through in bat & racket sports

Elastic Collisions Momentum and Kinetic Energy Are Conserved in an Elastic Collision

Elastic Collisions

Self-Check While driving down the road, a firefly strikes the windshield of a bus and makes a quite obvious mess in front of the face of the driver. This is a clear case of Newton's third law of motion. The firefly hit the bus and the bus hits the firefly. Which of the two forces is greater: the force on the firefly or the force on the bus?

Self-Check For years, space travel was believed to be impossible because there was nothing that rockets could push off of in space in order to provide the propulsion necessary to accelerate. This inability of a rocket to provide propulsion in space is because... a. space is void of air so the rockets have nothing to push off of. b. gravity is absent in space. c. space is void of air and so there is no air resistance in space. d.... nonsense! Rockets do accelerate in space and have been able to do so for a long time.

Self-Check Many people are familiar with the fact that a rifle recoils when fired. This recoil is the result of action-reaction force pairs. A gunpowder explosion creates hot gases that expand outward allowing the rifle to push forward on the bullet. Consistent with Newton's third law of motion, the bullet pushes backwards upon the rifle. The acceleration of the recoiling rifle is... a. greater than the acceleration of the bullet. b. smaller than the acceleration of the bullet. c. the same size as the acceleration of the bullet.

Elastic Collisions p f - p i = 0 since momentum is conserved and objects bounce apart with no loss of energy. p a + p b = p’ a + p’ b m a v a + m b v b = m’ a v’ a + m’ b v’ b The momenta of the two objects before the collision must be equal to the momenta of the two objects after the collision. The object with the smaller mass experiences the greatest change in velocity.

Practice Problem In a physics lab, kg cart (Cart A) moving rightward with a speed of 92.8 cm/s collides with a 1.50-kg cart (Cart B) moving leftward with a speed of 21.6 cm/s. The two carts stick together and move as a single object after the collision. Determine the post-collision speed of the two carts.

Practice Problem A 25.0-gram bullet enters a 2.35-kg watermelon and embeds itself in the melon. The melon is immediately set into motion with a speed of 3.82 m/s. The bullet remains lodged inside the melon. What was the entry speed of the bullet? (CAUTION: Be careful of the units on mass.)

Inelastic Collisions When objects collide, some mechanical energy is transformed into heat energy and is dissipated. Common inelastic collisions occur when objects stick together or are deformed (cars colliding or bullet hitting a target) or when they start out stuck together and then separate (firing of the bullet from a gun).

Inelastic collisions The masses of each object remains the same, but they share a common velocity either before or after the event. There is no rebounding effect. m a v a + m b v b = (m a + m b ) v f (m a + m b ) v i = m a v a + m b v b When the two objects are stuck together, they have the same velocity.

Practice Problem During a goal-line stand, a 75-kg fullback moving eastward with a speed of 8 m/s collides head-on with a 100-kg lineman moving westward with a speed of 4 m/s. The two players collide and stick together, moving at the same velocity after the collision. Determine the post-collision velocity of the two players.

Practice Problem A 3000-kg truck moving rightward with a speed of 5 km/hr collides head-on with a 1000-kg car moving leftward with a speed of 10 km/hr. The two vehicles stick togetherand move with the same velocity after the collision. Determine the post- collision velocity of the car and truck.