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Chapter 9

Chapter 9. Momentum and Its Conservation. What’s the relationship between force and velocity?. What happens when the baseball is struck by the bat? _______________tells us that the forces on the bat and ball are equal.

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Chapter 9

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  1. Chapter 9 Momentum and Its Conservation

  2. What’s the relationship between force and velocity? • What happens when the baseball is struck by the bat? • _______________tells us that the forces on the bat and ball are equal. • _______________tells us that both bat and ball will experience an acceleration proportional to their masses. • But what is the relationship between the velocities of the ball and the bat and the forces they experience?

  3. “The Big Mo”: Momentum • The ________________ of an object of mass m moving with a velocity is defined as the __________ of the ______ and the __________. • SI Units are kg m/s (Dimensions = ML/T) • Vector quantity, the direction of the momentum is the same as the velocity’s.

  4. More About Mo • Momentum components: • px = m vx and py = m vy • Applies to two-dimensional motion. • Again the direction of momentum and velocity are the same. • Momentum is related to ________________. • We can derive an equation that relates KE and momentum. • More on kinetic energy in chapter 10.

  5. Changing the big mo • How does an object change its acceleration? • How would an object change its momentum? • In order to change the momentum of an object, a _______________ must be applied.

  6. Impulse • The _________of change of momentum of an object is equal to the __________acting on it. • Just like with acceleration, when the __________is zero, no change occurs to momentum. • Gives an alternative statement of Newton’s second law.

  7. Impulse • When a single, constant force acts on the object, there is an ____________ delivered to the object. • is defined as the impulse. • ____________________, the direction is the same as the direction of the __________. • The impulse is also described using the letter J. • Impulse is useful for describing ______________ that do not last a long time. (More on this later.)

  8. Impulse-Momentum Theorem • The theorem states that the ___________ acting on the object is equal to the ___________________ of the object. • This theorem holds for _________ and ____________ forces. • If the force is not constant, use the average forceapplied.

  9. Sample Problem Rico strikes a 0.058 kg golf ball with a force of 272 N and gives it a velocity of 62.0 m/s. How long was Rico’s club in contact with the ball?

  10. Average Force in Impulse • The ______________can be thought of as the constant force that would give the same impulse to the object in the time interval as the actual time-varying force gives in the interval.

  11. Average Force and collisions

  12. Impulse and collisions • Impulse is most useful in describing _________ of _______________. • The impulse-momentum theorem allows us to study the effects that the ________________of a collision has on the _________ felt by the ____________. • For example, why is it important for boxers to wear boxing gloves?

  13. Changing Impulse and Collisions • _____________ the contact time increases the ___________ but reduces the _________ during the collision. • Increasing force increases the impulse as well.

  14. Impulse Applied to Auto Collisions • The most important factor is the ___________or the time it takes the person to come to a rest. • Increasing the collision time is the key factor. • This will reduce the chance of dying in a car crash.

  15. Ways to increase the time • Crumple zones • Air • bags • Seat • belts

  16. Typical Collision Values • For a 75 kg person traveling at 27 m/s and coming to stop in 0.010 s. • F = -2.0 x 105 N • a = 280 g • Almost certainly fatal: • F = 90 kN fractures bone. • a = 150 g for 4 ms causes spinal cord damage (causes the nerves to enter the base of the brain)

  17. Collisions • ______________ is conserved in any _________. • ______________is not always conserved. • Some KE is converted to other forms of energy (i.e. internal energy, sound energy, etc.) or is used to do the work needed to deform an object. • Two broad categories of collisions: • Elastic collisions • Inelastic collisions: Perfectly inelastic and inelastic • Elastic and perfectly inelastic collisions represent ideal cases of collisions. • Most real world cases fit somewhere between these two extremes.

  18. Conservation of Momentum • Momentum in an isolated system in which a collision occurs is conserved. • A collision may be the result of _______________ between two objects. • “Contact” may also arise from the ______________ interactions of the electrons in the surface atoms of the bodies. • An isolated system will have no external forces acting on the objects.

  19. Conservation of Momentum • The principle of conservation of momentum states when no external forces act on a system consisting of two objects that collide with each other, the total momentum of the system remains constant in time. • Specifically, the total momentum before the collision will equal the total momentum after the collision. F

  20. Forces in a Collision • The force with which object 1 acts on object 2 is equal and opposite to the force with which object 2 acts on object 1. • Impulses are also equal and opposite.

  21. Conservation of Momentum formula • Mathematically: • Momentum is conserved for the system of objects. • The system includes _____________________ interacting with each other. • Assumes only internal forces are acting during the collision. • Can be generalized to any number of objects.

  22. Sample Problem A 1875 kg car going 23 m/s rear-ends a 1025 kg compact car going 17 m/s on ice in the same direction. The two cars stick together. How fast do the two cars move together immediately after the collision?

  23. Recoil and Propulsion in Space • Xe atoms are expelled from the ion engine. • vatoms = 30km/h; Fatoms = 0.092 N • Advantage: runs for a very long time

  24. Glancing Collisions • For a general collision of two objects in three-dimensional space, the conservation of momentum principle implies that the total momentum of the system in each direction is conserved. • Use subscripts for identifying the object, initial and final velocities, and components. • We will examine collisions in two-dimensions.

  25. Glancing Collisions • The “after” velocities have x and y components. • Momentum is conserved in the x direction and in the y direction. • Apply conservation of momentum separately to each direction.

  26. Sample problem A 1,500 kg car traveling east with a speed of 25.0 m/s collides at an intersection with a 2,500 kg van traveling north at a speed of 20.0 m/s as shown in the figure. Find the direction and magnitude of the velocity of the wreckage after the collision, assuming that the vehicles undergo a perfectly inelastic collision and assuming that friction between the vehicles and the road can be neglected.

  27. THE END Chapter 9 Momentum and Its Conservation

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