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# Physics - Chapter 6 - Momentum and Collisions

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Bellaire High School
Chapter 6 - Momentum and Collisions

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### Physics - Chapter 6 - Momentum and Collisions

1. 1. Lesson 6-1 Momentum and Impulse
2. 2. Linear Momentum  Think of a batter hitting a baseball  When the batter swings and makes contact, the ball changes velocity very quickly  We could use kinematics to study the motion of the ball  We could use Newton’s Laws to explain why the ball changes direction  We are now concerned with the force and duration of the collision
3. 3. Momentum  Momentum describes an object’s motion  To describe force and duration of a collision, we must first start with a new concept  Momentum  This word is used in everyday conversation, and means about the same thing in physics
4. 4. Momentum  We might say a semi-truck has a large amount of momentum  Compared to the semi-truck, a person would have a small amount of momentum  Linear momentum directly relates an object’s velocity to the object’s mass  Momentum (P)  P=mv
5. 5. Momentum  Momentum is a vector quantity, with the vector matching the direction of the velocity  The SI unit is kg∙m/s
6. 6. Bowling  If you bowl with a light ball, you have to throw the ball pretty fast to make the pins react  A heavier ball will allow a good pin reaction with a lower velocity  Because of the added mass  Example 209  Practice 209
7. 7. Change in Momentum  Recall: change in velocity takes an acceleration and time  If there is an acceleration, there exists a net force  Since P depends on velocity, ΔP requires  Force  Time
8. 8. Change in Momentum  Say there is a ball rolling on the ground  You must use a large force to stop a fast rolling ball  You could use a smaller force to stop a slower rolling ball  Imagine catching a basketball  A faster pass stings the hands a bit  A softer pass causes almost no feeling
9. 9. Newton’s Second Law  Imagine a toy fire truck and a real fire truck sitting at the top of a hill  If they both begin to roll down the hill, which will have the greater velocity?  Recall: all objects fall due to gravity at the same rate  But which would require the greater force to stop  Examples like this show us that P is closely related to force
10. 10. Newton’s Second Law  When Newton first wrote his second law (F=ma), he wrote it as F p = D D t F p = D D t F mv t mv t = = = ma
11. 11. Impulse – Momentum Theorem FDt = Dp F t p mv mv f i D = D = -  This states a net external force, F, applied for a certain time interval, Δt, will cause a change in the object’s momentum equal to the product of the force and time interval  In simpler terms, a large constant force will cause a rapid change in P  A small constant force would take a much longer time to cause a change in P
12. 12. Impulse – Momentum Theorem  The Impulse – Momentum theorem explains why “follow through” is so important in many sports such as baseball, basketball, and boxing  When a baseball player hits a baseball and “follows through” the ball is in contact much longer and the force is applied over a greater period of time  If the player does some sort of check swing, the force is applied over a smaller period of time
13. 13.  Sample 211  Practice 211  Sample 212  Practice 213
14. 14. Impulse – Momentum Theorem  Change in momentum over a longer time requires less force  Engineers use the impulse – momentum theorem to design safety equipment  Safety gear aims to reduce the force exerted on the body during a collision
15. 15. Impulse – Momentum Theorem  Think of jumping on a trampoline  Do you think you could jump that high and land on the ground and not get hurt?  The impact with the ground is sudden and occurs over a short period of time  The impact with the trampoline is the same, but occurs over a longer period of time  Longer time interval = less force
16. 16. Lesson 6-2 Conservation of Momentum
17. 17. Billiards  In a game of pool:  The object ball is stationary  The cue ball is moving  During the collision, the object ball gains momentum and the cue ball loses the same amount of momentum  The momentum of each ball changes during the collision but total momentum remains constant
18. 18. Conservation of Momentum  Since the momentum of the two billiard balls remains constant after the collision we say momentum is conserved P P P P Ai Bi Af Bf + = + m1v1i m2v2i m1v1 f m2v2 f + = +
19. 19. Conservation of Momentum  As we just discussed, momentum is conserved during collisions  Momentum is also conserved when objects push away from each other
20. 20. Conservation of Momentum  Imagine you stand on the ground and jump up  It seems as if momentum is not conserved because you leave the ground with a velocity  Recall, the Earth does move away when you jump (a very small distance), so total momentum is conserved in reality  You exert a downward force on the Earth and the Earth exerts an upward force on you  Total momentum is ZERO
21. 21. Conservation of Momentum  The reason total momentum is zero when two objects push apart is based on sign  The objects have the same amount of momentum  But in opposite directions  So when the two momentums are summed, the result is zero
22. 22.  Sample 218  Practice 219
23. 23. Relation to Newton’s Third Law  Consider two bumper cars of mand m1 2  FDt = Dp describes the change in momentum is one of the cars  and F t m v 1 1 1i D = F t m v 2 2 2i D =  F1 is the force that m1 exerts on m2  F2 is the force that m2 exerts on m1
24. 24. Relation to Newton’s Third Law  Since the only forces are from the two bumper cars, Newton’s third law tells us the forces must be equal and opposite  Additionally, the impulse (time of collision) is equal and opposite for both cars  This means EVERY interaction between the two cars is equal and opposite and can be expressed by: m1v1i m1v1 f m2v2i m2v2 f - = -d - i
25. 25. Relation to Newton’s Third Law  The equation says ‘if the momentum of one object decreases during a collision, the momentum of another object will increase by the same amount’  At all times during a collision the forces are equal and opposite  The magnitudes and directions are constantly changing  The value we use for force is equal to average force
26. 26. Lesson 6-3 Elastic and Inelastic Collisions
27. 27. Everyday Collisions  You see collisions everyday  In some collisions, the objects stick together and travel as one mass  In another type of collision, the objects hit and bounce apart  In either case, total momentum is conserved  KE is usually not conserved because some energy is lost to heat and sound energies
28. 28. Perfectly Inelastic Collisions  When two objects collide and move together as one mass, the collision is called perfectly inelastic  A good example of this type of collision is a meteor hitting the Earth  Perfectly inelastic collisions are easy to analyze in terms of momentum because the two objects essentially become one after the collision
29. 29. Perfectly Inelastic Collisions  The final mass is equal to the combined mass of the two objects  The two objects travel together with one final velocity after the collision  Studied with the following equation: m1v1i m2v2i m1 m2 v f + = ( + )
30. 30. Perfectly Inelastic Collisions  KE does not remain constant in an inelastic collision  KE is lost due to sound, internal energy, and heat of fusion
31. 31. Elastic vs Inelastic  The phenomena of fusion helps us to understand the difference between elastic and inelastic collisions  When we think of something that is elastic (a rubber band, a bungee cord, a spring) we think of something that returns to its original shape  During an elastic collision, the objects maintain their original shapes
32. 32. Elastic vs Inelastic  Objects in inelastic collisions do not maintain their original shapes as they form a new mass after the collision  We can calculate the loss of KE with the conservation of KE formula  KEnet = KEf – Kei  Sample 225  Practice 226
33. 33. Elastic Collisions  When a soccer player kicks a soccer ball, the ball and the player’s foot remain separate  Since there are no shape changes or deformities, the is no change in KE  As with any collision, total momentum is conserved
34. 34. In the Real World  It should be mentioned that there is no such thing as a perfectly inelastic or perfectly elastic collision in the real world  Objects do not hit into each other and fuse together and move as one object  Objects do not bounce off of each other without loss of KE  KE lost to heat, sound, deformation
35. 35. In the Real World  So that means that most collisions fall into a third category called inelastic collisions (note: not perfectly inelastic)  This is where objects collide, make noise, give off heat, do not stick together, and travel in another direction with separate velocities  These are impossible to study to complete exactness  To study these types of collisions, we simplify things
36. 36. Elastic Collisions  KE is conserved in elastic collisions  There are instances that are very, very close to perfectly elastic collisions  Bowling ball into bowling pins  Golf club hitting a golf ball  In these instances, we assume total KE and total momentum remain constant throughout the collision
37. 37. Elastic Collisions  We can study elastic collisions with the following formulas: m1v1i m2v2i m1v1 f m2v2 f + = + 1 2 m v m v m v m v 2 i i f f + = +  Sample 228  Practice 229 1 2 1 2 1 2 1 1 2 2 2 2 1 1 2 2 2