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Bellaire High School

Advanced Physics

Chapter 6 - Momentum and Collisions

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- 1. Lesson 6-1 Momentum and Impulse
- 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. 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. 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. Momentum Momentum is a vector quantity, with the vector matching the direction of the velocity The SI unit is kg∙m/s
- 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. 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. 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. 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. 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. 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. 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. Sample 211 Practice 211 Sample 212 Practice 213
- 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. 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. Lesson 6-2 Conservation of Momentum
- 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. 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. Conservation of Momentum As we just discussed, momentum is conserved during collisions Momentum is also conserved when objects push away from each other
- 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. 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. Sample 218 Practice 219
- 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. 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. 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. Lesson 6-3 Elastic and Inelastic Collisions
- 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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

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