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Momentum and Collisions

Momentum and Collisions. Chapter 6. 6.1 Momentum. Momentum: the quantity of motion an object has p=mv p is momentum (kgm/s) m is mass (kg) v is velocity (m/s) Momentum is a vector (direction is with the motion). p x =mv x and p y =mv y. 6.1 Momentum Continued.

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Momentum and Collisions

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  1. Momentum and Collisions Chapter 6

  2. 6.1 Momentum • Momentum: the quantity of motion an object has • p=mv • p is momentum (kgm/s) • m is mass (kg) • v is velocity (m/s) • Momentum is a vector (direction is with the motion). • px=mvx and py=mvy

  3. 6.1 Momentum Continued • Momentum is dependent on mass and velocity: • Double the mass, double the momentum • Triple the velocity, triple the momentum p=mv

  4. Practice • A 2250 kg truck moving at 25 m/s to the east. What is the momentum? • What speed must a 1250 kg car have to have the same momentum?

  5. 6.1 Impulse • Changing momentum of an object requires a force to be applied over a certain time period. F=ma=m() Ft=m()t Ft=mv

  6. 6.1 Impulse Continued • Ft=mv • I=Ft • I is impulse (kgm/s) and is a vector quantity in the direction of F • F is a force being applied (N or kgm/s2) • t is time the force was applied (s) • mv=p • Change in momentum • I=p(Impulse is the change in momentum due to Fapp)

  7. 6.1 Impulse-Momentum Theorem • Impulse-momentum theorem: the impulse of the force acting on an object equals the change in momentum of that object Ft=p=mvf-mvi

  8. Practice • A 0.0035 kg bug travels at 1.1 m/s west and collides with a 1550 kg car traveling at 7.5 m/s. Which has the greater initial momentum? Which has the greater change in momentum? Which has the greater impulse acting on it? • Truck two has twice the mass as truck one. Both are traveling at the same speed and have the same stopping force. Which requires a greater distance to stop? How much more?

  9. Practice (pg. 163) A 0.050 kg golf ball is struck with a club and remains in contact for 9.1 x 10-4 s. The ball leaves the club at a velocity of 44 m/s. • Find the magnitude of the impulse. • Estimate the force of the club.

  10. Practice (pg. 164) In a crash test, a 1500 kg car collides with a wall and rebounds. The initial velocity was 15.0 m/s to the left and the final velocity was 2.60 m/s to the right. If the collision lasts for 0.150 s, what is the impulse delivered to the car due to the collision? What is the size and direction of the force exerted on the car?

  11. 6.1 Relationships between variables • Ft=mv • Force and time are inversely proportional • Mass and force are directly proportional • Mass and velocity change are inversely proportional • How would this apply in the real world?

  12. 6.1 Real-World Applications • To minimize the effect of a force on an object, the time of collision must be increased. • Airbags extend the time required to stop momentum. • Dashboards are padded to extend time. • Crumple zones in cars. • Boxers relax their necks so their head can move backwards. • Climber’s rope are stretchy in case of a fall.

  13. Homework • Water balloon activity • Homework: • Pg 181-182 • Problems #1, 4, 5, 10

  14. 6.2 Conservation of momentum • In a collision, objects experience forces that are equal in magnitude but opposite in direction (Newton’s Third Law). F1=-F2 • Although the force may be the same, the accelerations of the two objects are NOT, unless they have equal mass. (m1a1=-m2a2) • A club with a golf ball hit with the same force, but the ball has a greater acceleration because it has a smaller mass. • Two billiard balls strike with the same force, and they bounce off each other with the same acceleration because they have the same mass. • A male figure skater is holding a female skater as they glide across the ice. The male throws the woman forward. He slows down (backwards F and a), while she speeds up in the forward direction.

  15. What do you think? Two skaters have equal mass and are at rest. They are pushing away from each other as shown. • Compare the forces on the two girls. • Compare their velocities after the push. • How would your answers change if the girl on the right had a greater mass than her friend? • How would your answers change if the girl on the right was moving toward her friend before they started pushing apart?

  16. 6.2 Conservation of momentum Continued • When a collision occurs in an ISOLATED system, total momentum (magnitude and direction) does not change. • Isolated: no net external forces (assume friction is negligible) F1=-F2 t1=t2 F1t1=-F2t2

  17. 6.2 Conservation of momentum Continued • The momentum lost by one object (slows down) is gained by the other (speeds up). • To solve these problems, you can: • Use vector diagrams • Use momentum tables

  18. Practice (pg. 168) An archer stands at rest on frictionless ice and fires a 0.500 kg arrow horizontally at 50.0 m/s. The combined mass of the archer and the bow is 60.0 kg. With what velocity does the archer move across the ice after firing the arrow?

  19. 6.3 Types of Collisions • Elastic: both momentum and kinetic energy are conserved • Inelastic: momentum is conserved, but kinetic energy is not (converted to heat or sound and results in a deformity of an object) • Perfectly inelastic: when two objects collide and stick together • We will focus on perfectly inelastic and elastic collisions in 1D. • Most collisions fall between elastic and perfectly inelastic.

  20. Name Each • Two bowling balls collide head on. • A snowball hits someone in the head. • A football player wraps arms around another and brings them down. • Marbles striking each other. • A car is rear ended. • A ball is kicked.

  21. Momentum Lab Use data gathered from each situation to answer the following (support your answers with detailed observations and identify the situation used): • How can you tell which car was moving faster? • How does the addition of mass to one cart affect the location of the collision point? How does it affect what happens to the carts after the collision? • If one cart has more momentum than the other, what happens when the carts collide? • If two carts having the same momentum are traveling in opposite directions, what is the total momentum of the two cart system?

  22. 6.3 Perfectly Inelastic Collisions • Momentum is conserved but NOT kinetic energy (BE CAREFUL WITH THE SIGNS FOR VELOCITY) m1v1i+m2v2i=(m1+m2)vf

  23. Practice • Gerard is a quarterback and John is a defensive lineman. Gerard’s mass is 75.0 kg, and he is at rest. Tyler has a mass of 112 kg, and is moving at 8.25 m/s when he tackles Gerard by holding on while they fly through the air. With what speed will the two players move together after the collision?

  24. Practice (pg. 170) An 1800 kg SUV is traveling east at 15.0 m/s while a 900 kg compact car is traveling west at 15.0 m/s. The cars collide head-on, while becoming entangled. • What is the speed of the entangled cars after the collision? • What is the change in velocity for each car? • What is the change in the kinetic energy of the system?

  25. Practice (pg. 171) The ballistic pendulum is a device used to measure speed of a fast-moving projectile, such as a bullet. The bullet is fired into a large block of wood suspended by light wires (1.00 kg). The bullet (5.00 g) is stopped by the block, and the entire system swings to a height (5.00 cm). It is possible to find the initial speed of the bullet by measuring the height and the two masses.

  26. 6.3 Elastic Collisions • Momentum and kinetic energy are BOTH conserved. pi=pf m1v1i+m2v2i=m1vif +m2v2f KEi=KEf m1v1i2+m2v2i2=m1vif 2+ m2v2f2

  27. Practice • A 62.0 kg astronaut on a spacewalk tosses a 0.145 kg baseball at 26.0 m/s out into space. • What is the initial momentum for the astronaut and the baseball? • What is the final momentum of the astronaut? • What speed does the astronaut recoil? • How would this change for a baseball player pitching a baseball?

  28. Practice (pg. 174) A block of mass 1.60 kg moves to the right with a velocity of 4.00 m/s and collides with a massless spring attached to a second block of mass 2.10 kg moving left with a velocity of 2.50 m/s. The spring has a spring constant of 600. N/m. • What is the velocity of block 2 when block 1 is moving to the right with a velocity of 3.00 m/s? • What is the compression of the spring?

  29. Homework • BRING YOUR TEXTBOOK

  30. 6.4 Glancing Collisions In 3D, total momentum of the system is conserved in EACH direction. pix=pfx andpiy=pfy

  31. Practice (pg. 176) A 1500 kg car is traveling east at 25.0 m/s. At an intersection, the car collides with a 2500 kg van traveling north at 20.0 m/s. Find the magnitude and direction of the velocity of the wreckage after the collision (assume they undergo a perfectly inelastic collision).

  32. Practice Shown below, the cue ball hits a stationary ball at an angle of 45°, such that it goes into the corner pocket with a speed of 2.0 m/s. Both balls have a mass of 0.50 kg, and the cue ball is traveling at 4.0 m/s before the collision. Recalling that this collision is elastic, calculate the angle with which the cue is deflected by the collision.

  33. Homework • Pg. 183-184 • #20, 25, 27, 41a

  34. 6.5 Rocket Propulsion Reaction forces (Newton’s 3rd Law) propel a rocket. A chamber of combustible gases expand and press against the chamber, and then is released from a hole. The reaction force pushes the rocket upward.

  35. 6.5 Rocket propulsion continued • Initially, the momentum of the rocket has both the mass of the rocket (M) and the mass of the fuel (m). • Then, as the fuel is ignited, the rocket’s speed increases (v+v). The fuel is ejected with exhaust speed ve (v-ve). • (M+m)v=M(v+v)+m(v-ve)

  36. 6.5 Rocket Thrust • (M+m)v=M(v+v)+m(v-ve) can be simplified to Mv=vem • Since m=-M, then Mv=-veM • With calculus, vf-vi=veln() • Thrust=Ma=M

  37. Practice (pg. 179) • A rocket has a total mass of 1.00x105 kg and a burnout mass of 1.00x104 kg. The rocket blasts off from Earth and exhausts all of its fuel in 4.00 min, with an exhaust velocity of 4.50x103 m/s. • If gravity is neglected, what is the speed of the rocket at burnout? • What thrust does the engine develop? • What is the initial acceleration of the rocket if gravity is not neglected? • Estimate the speed of burnout if gravity is not neglected.

  38. Homework

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