Today Finish Power Momentum Impulse Conservation of Momentum

• Today: Finish Power, Momentum, Impulse, Conservation of Momentum Introduction to Collisions Recitation Quiz #5 Tomorrow HW #5 due Thursday, 11: 59 p. m. Out of town on Thursday (but will be in email contact) Lecture will be given by Dr. Tim Gorringe (other lecturer for PHY 211) 1

Review: Power Note that we can write : Average power is a constant force times the average speed. Note on units : 1 Watt = 1 Joule/second = 1 kg-m 2/s 3 2

Example: 5. 53 The electric motor of a model train accelerates the train from rest to 0. 620 m/s in 0. 021 s. The total mass of the train is 0. 875 kg. Find the average power delivered to the train during its acceleration. 3

Momentum ? If both are moving at 1 mph, it is much more difficult to stop the train than the mosquito ! 4

Definition of Momentum The linear momentum p of an object with mass m moving with velocity v is : [ SI Unit: kg·m/s ] 1 Momentum is a vector quantity (same direction as velocity) 2 Magnitude of the momentum is proportional to both the mass and velocity. 3 Magnitude of the momentum is related to the object’s KE : 5

Conceptual Question Two masses, m 1 and m 2, where m 1 < m 2, have equal kinetic energy. How do the magnitudes of their momenta compare ? (a) Not enough information is given. (b) p 1 < p 2 (c) p 1 = p 2 (d) p 1 > p 2 6

Force and Momentum Intuitively … • • A net force causes an acceleration An acceleration means the velocity changes If the velocity changes, the momentum changes … So a net force causes the momentum to change. Newton’s Second Law “re-stated” : change in momentum time interval This step assumes the mass does not change. 7

Impulse The impulse I delivered to an object by a constant force F acting over a time interval Δt is given by [ SI Unit: kg·m/s ] • A vector quantity with same direction as force F Impulse-Momentum Theorem : • The impulse of the force acting on an object equals the change in the object’s momentum. • Generally, the force is not constant, so we replace F with the average force, Fav. 8

Example: Problem 6. 9 A 0. 280 -kg volleyball approaches a player horizontally with a speed of 15. 0 m/s. The player strikes the ball, causing it to move with a speed of 22. 0 m/s in the opposite direction. (a) What impulse is delivered to the volleyball by the player ? (b) If the player’s fist is in contact with the volleyball for 0. 060 s, find the magnitude of the average force exerted by the player. 9

What is the Physics of Seat Belts ? http: //www. youtube. com/watch? v=tj. Iud 8 z. YRb. I&NR=1 (Crash Test Dummies commercial from 1988. Some/most of you were probably not even born in 1988! I was in 6 th grade…) A seat belt (or an air bag) increases the time interval Δt over which you come to a complete stop. Let’s analyze this in terms of force, impulse, momentum … 10

What is the Physics of Seat Belts ? Consider a “typical” car collision involving a 75 -kg person : • Initial velocity of 27 m/s (60 mph) • No seat belt, come to rest in ~0. 010 s (dashboard, windshield) Assume one-dimensional motion. Use the concept of impulse to find the average force : And this force is applied at one point ! 11

What is the Physics of Seat Belts ? Consider a “typical” car collision involving a 75 -kg person : • Initial velocity of 27 m/s (60 mph) • With seat belt, come to rest in ~0. 15 s (~15 times longer) Assume one-dimensional motion. Use the concept of impulse to find the average force : And this force is applied over a much larger area 12

Collisions Between Objects Q: What happens to the total momentum of this “system” during the collisions ? Here, “system” refers to the entire collection of billiards balls (i. e. , all considered together). 13

Collisions Between Objects Consider a collision between two balls : “Before” m 1 “After” m 2 m 1 m 2 They exert EQUAL BUT OPPOSITE forces on each other when they collide. (just Newton’s Third Law in action !!) : “force exerted by 2 on 1” : “force exerted by 1 on 2” 14

Collisions Between Objects By the Impulse-Momentum Theorem But we have 15

Collisions Between Objects What does this mean ? • The vector sum of the momenta before and after the collision are identical (i. e. , it is conserved). • This means it applies to both the x- and y-components : 16

Collisions Between Objects Note: We derived this result assuming the only forces acting on the balls were the action/reaction forces resulting from their contact during the collision. There were no external forces. In general, the Law of Conservation of Momentum : When no net external forces act on a system, the total vector momentum of the system remains constant. Example: For the billiards balls (ignoring friction) : • There are external forces acting on each billiards ball (gravity, and the normal force), but they cancel, so there is no net external force. Total vector momentum will be conserved. 17

Conceptual Question / Example A 70. 0 -kg man and a 55. 0 -kg woman, both on ice skates, stand facing each other. If the woman pushes the man backwards, what happens to the woman? Ignore friction, and assume they move in one-dimension only. If the man moves backwards at 1. 50 m/s, at what speed does the woman move? 18

Problem 6. 24 A 730 -N man stands in the middle of a frozen pond of radius 5. 0 m. He cannot get to the other side, because of a lack of friction between his shoes on the ice. So, he throws his 1. 2 -kg physics textbook horizontally toward the North shore at 5. 0 m/s. How long does it take him to reach the South shore? 19

Introduction to Collisions If there are no net external forces, the total momentum is conserved in any type of collision. The kinetic energy is NOT, however, always conserved. Some of the initial KE may be converted to sound energy, heat, or the work that deforms the involved objects (e. g. , car crash). Inelastic collisions Elastic collisions Momentum IS conserved Kinetic energy IS NOT conserved Kinetic energy IS conserved If the two objects stick together: “perfectly inelastic” Examples: Billiards balls, atomic/subatomic particles 20

Next Class • 6. 3 – 6. 4 : Collisions • We will NOT cover 6. 5 (Rocket Propulsion) 21