Chapters 5 & 6 More Third Law Vectors at Angles Momentum Conservation of Momentum

Transcription

1 Lecture 6 Chapters 5 & 6 More Third Law Vectors at Angles Momentum Conservation of Momentum Help sessions Announcements M in TH116 (A. Kelly) M in TH116 (D. Lim) T in TH118 (Z. Hadley) W in TH118 (J.M. Lockhart) Course web page 1

2 IMPORTANT!!! Action force & reaction force NEVER cancel, because they act on different objects! Repeat this to yourself over and over again Check Yourself Miss A pushes the car (action); car pushes back on her (reaction). Do these forces cancel? Force on Miss A is to the left; how can she move forward (to the right)? What if floor had zero friction? Miss A Action Reaction Reaction Action Action- Reaction Pairs 2

3 Check Yourself Miss B also pushes the car; can she move the car by herself? In terms of Newton s laws, why is this not possible? What other force does Miss B exert on the car besides her hands? Action- Reaction Pairs Miss B Action Reaction Reaction Action Adding Forces When two forces or more forces act in different directions, finding the net force is more complicated. Have to consider the angle for each force. 3

4 Vector Addition Forces are vectors, with magnitude & direction. How two vectors add together depends on the two magnitudes and the two directions. Force B (10 N) Net Force A + B (25 Newtons) Object Force A (20 Newtons) Parallelogram rule Magnitude & Angle of Vector Sum Vector magnitude and angle of the sum of two perpendicular vectors can be calculated using trigonometry and Pythagorean theorem: A = A + A θ = 2 2 x y 1 tan Ay / A x 4

5 Magnitude & Angle Example Cartesian Coordinates Polar Coordinates r = r + r = (1.36 m) + (0.634 m) = 2.25 m = 1.50 m θ x y [ ] 1 1 = tan (0.634 m) / (1.36 m) = tan (0.466) = 25.0 Demo: Straighten the Line Pull on the line to make it horizontal. HORIZONTAL Pull Pull As the angle gets smaller, must pull much harder. 15 pound Bowling Ball 5

6 Demo: Straighten the Line (II) 5 N 5 N 15 N As the angle gets smaller, must pull much harder. 15 N 10 Newton Weight 10 Newton Weight Parallelogram Rule Net force is the same in both cases but pulling forces different. Net Force PULL! pull pull PULL! Weight 6

7 Check Yourself Nellie Newton hangs motionless by one hand from a clothesline which is on the verge of breaking. Which side of the line is more likely to break? Two upward forces must add together to balance Nellie s weight. 1. Left side 2. Right side 3. 50/50 chance of either side breaking Lab: Force Table Practice addition of forces as vectors in the Physics 102 lab using force tables. Hang weights and adjust angles until forces balance. 7

8 Force, Momentum, Energy With Newton s Laws, we can understand motion just using forces. Can also eat food just using knives or chopsticks. Easier to understand motion by introducing concepts of momentum and energy. Think of them as the fork and spoon of mechanics. Momentum Inertia of Motion Momentum of an object is: (Momentum) = (Mass) X (Velocity) Vector quantity; direction is direction of velocity SI Unit: kg m/s Examples of objects with large momenta: supertanker (large mass); bullet (large velocity). 8

9 Momentum Example A 0.25 kg baseball is moving North at 10 m/s. What is its momentum? Momentum = mv = (0.25 kg)(10 m/s North) = 2.5 kg m/s North Check Yourself A 2 ton car, going 60 m.p.h. hits 5 ton truck, going 20 m.p.h.. Which vehicle, car or truck, has greater momentum? What would the car s speed have to be for the momenta to match? Aren t you forgetting something? How does that matter? 9

10 Momentum and Force To stop an object with a large momentum requires either: Large force (stopping the object quickly). Small force applied for a long time. Notice that changing object s momentum depends on force and time interval. Impulse Define impulse acting on an object as (Impulse) = (Force on object) X (Time interval for force ) Objects have momentum. Impulse acts on an object. 10

11 Impulse & Momentum Impulse is related to momentum by, or (Change in momentum) = (Impulse) (Mass) X (Change in velocity) = (Force) X (Time interval) This relation comes from Newton s 2 nd law. Check Yourself Throw egg at sheet or wall with same speed. Which case has: Greater change of velocity? Greater change of momentum? Largest impulse on the egg? LONG TIME small force Largest time of impact? Largest force on the egg? short time LARGE FORCE 11

12 Demo: Vampire Stake Safest when slow moving stake is placed on a soft, fleshy spot on the chest. (force) x (TIME) (FORCE) x (time) X X Ouch! Not safe if stake strikes hard skull Check Yourself A 2 ton car going 60 m.p.h. hits 5 ton truck going 20 m.p.h.. Force of impact is greatest on which vehicle, car or truck? Impulse is greatest on which vehicle, car or truck? Change of momentum greatest? Change of velocity greatest? Driver injury greatest? 12

13 Automobile Safety Maximizing the time of impact on the driver minimizes the force of impact. This principle used in design of: Seatbelts Air Bags Crumple Zones Conservation of Momentum The principle of conservation of momentum states: When there is no net external force on a system of objects, the total momentum of the system does not change. We say that the momentum of such a system is conserved since it does not change. 13

14 Conservation of Momentum in Collisions When two objects collide, impulse is equal and opposite for the two objects if there is no net external force. Before collision IMPULSE IMPULSE Impact After collision Each object has equal and opposite change in momentum. The momentum of the system of 2 objects is conserved. Conservation of Momentum The change of momentum of the two objects in a collision is equal and opposite -- the momentum gained by one object is the amount lost by the other. Momentum Object A Before Collision + Momentum Object B Before Collision Momentum = Object A + After Collision Momentum Object B After Collision A B A B Actual amount of momentum exchanged depends on the details of the collision, such as whether or not collision is elastic, but total momentum is always conserved if there is no net external force. 14

15 Demo: Elastic Collisions Objects of equal mass exchange momentum in elastic collisions. Demo: Newton s Balls Steel balls collide elastically, exchanging momentum on collision. 15

16 Demo: Don t Scratch To sink a billiard ball that is very close to the pocket without having the cue ball go in as well ( scratching ), strike the cue ball hard so it makes a crisp, elastic collision. As with Newton s balls, cue ball will stop after giving all its momentum to the other ball in the collision. Demo: Blaster Balls When masses unequal, momentum change can be large. Ping pong ball Speed of ping-pong ball is 3x larger (Slingshot effect) Golf ball 16

17 Demo: Inelastic Collisions Objects stick together after colliding. A B A B A B Check Yourself Large (4 kg) fish swims at 3 m/s towards a small (2 kg) fish (at rest) and swallows it for lunch. Total momentum before lunch? Total momentum after lunch? Velocity of the large fish (with small fish inside)? 17

18 Recoil Momentum conservation also explains recoil (MASS) x (velocity) (mass) x (VELOCITY) Recoil effect is like an inelastic collision in reverse. Key Points of Lecture 6 Third Law Details Combining Two Perpendicular Vectors Momentum (Mass Velocity) Impulse (Force time_applied) Impulse = momentum change Conservation of momentum Collisions Before next lecture, read Hewitt through Chap.6 Homework Assignment #3 is due before 11:00 PM on Thursday, Sept