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Physics 114A - Mechanics Lecture 20 (Walker: Ch. 9.1-3) Momentum & Impulse February 18, 2014

Physics 114A - Mechanics Lecture 20 (Walker: Ch. 9.1-3) Momentum & Impulse February 18, 2014. John G. Cramer Professor Emeritus, Department of Physics B451 PAB jcramer@uw.edu. Announcements. HW#6 is due at 11:59 PM on Thursday, February 20.

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Physics 114A - Mechanics Lecture 20 (Walker: Ch. 9.1-3) Momentum & Impulse February 18, 2014

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  1. Physics 114A - MechanicsLecture 20 (Walker: Ch. 9.1-3)Momentum & ImpulseFebruary 18, 2014 John G. Cramer Professor Emeritus, Department of Physics B451 PAB jcramer@uw.edu

  2. Announcements • HW#6 is due at 11:59 PM on Thursday, February 20. • The Exam 2 solutions are available from the Physics 114A Course Schedule by clicking on “Exam 2”. I plan to return Exam 2 on Thursday. Scores for the two parts of Exam 2 will be posted on WebAssign as they become available. • My office hours are 12:30-1:20 PM on Tuesdays and 2:30-3:20 PM on Thursdays, both in the “114” area of the Physics Study Center on the Mezzanine floor of PAB A (this building) Physics 114 - Lecture 20

  3. Lecture Schedule (Part 3) We are here. Physics 114 - Lecture 20

  4. Linear Momentum Momentum is a vector; its direction is the same as the direction of the velocity. Physics 114 - Lecture 20

  5. Change in Momentum Which object has the largest change in momentum? Change in momentum:Dp = pafter - pbefore Teddy Bear: Dp = 0-(-mv) = mv Bouncing Ball: Dp = mv-(-mv) = 2mv Physics 114 - Lecture 20

  6. Momentum &Newton’s Second Law Newton’s second law, as we wrote it before, is: is only valid for objects that have constant mass. Here is a more general form in terms of momentum, which is also useful when the mass is changing: Physics 114 - Lecture 20

  7. Impulse Impulse is a vector, in the same direction as the average force. Physics 114 - Lecture 20

  8. Impulse We can rewrite as So we see that The impulse I is equal to the change in momentum Dp(and has the same units). Physics 114 - Lecture 20

  9. y x Clicker Question 1 A 10 kg cart collides with a wall and changes its direction. What is its change in x-momentum Dpx? • -30 kg m/s • -10 kg m/s • 10 kg m/s • 20 kg m/s • 30 kg m/s Physics 114 - Lecture 20

  10. Momentum and Impulse Microscopic view of a “bounce”. Profile of the force during a collision. Physics 114 - Lecture 20

  11. Impulse and Average Force Same area. Physics 114 - Lecture 20

  12. Problem Solving Strategy Picture: To estimate the average force Fav, we first estimate the impulse I of the force. Assuming other forces are negligible, the impulse of the force is the net impulse, which is equal to the change in momentum, i.e., the mass times the change in velocity. An estimate of the velocity change Dvcan be made from estimates of the collision time Dt and displacement Dr. Solve:1. Calculate (or estimate) the impulse I and the time Dt. This estimate assumes that during the collision, the collision force is very large compared to all other forces on the object. This procedure works only if the displacement during collision can be determined.2. Draw a sketch showing before and after positions of the object. Add coordinate axes and label velocities and displacement.3. Calculate the momentum change during the collision. (I=Dp=mDv)4. Use Fav=I/Dt to calculate the average force. Check: Average force is a vector, and should be in the same direction as Dv. Physics 114 - Lecture 20

  13. Impulse Therefore, the same change in momentum may be produced by a large force acting for a short time, or by a smaller force acting for a longer time. Physics 114 - Lecture 20

  14. Example: Hitting a Baseball (1) A 150 g baseball is thrown at a speed of 20 m/s. It is hit straight back to the pitcher at a speed of 40 m/s. The interaction force is as shown here. What is the maximum force Fmax that the bat exerts on the ball? What is the average force Fav that the bat exerts on the ball? Physics 114 - Lecture 20

  15. Example: Hitting a Baseball (2) Use the impulse approximation: Neglect all other forces on ball during the brief duration of the collision. Physics 114 - Lecture 20

  16. Example: A Bouncing Ball A 100 g rubber ball is dropped from a height of 2.0 m onto a hard floor. The floor exertsa force on the ballas shown above. How high does the ball bounce? Physics 114 - Lecture 20

  17. Example: A Karate Collision With an expert karate blow, you shatter a concrete block. Consider that you hand has a mass of 0.70 kg, is initially moving downward at 5.0 m/s, and stops 6.0 mm beyond the point of contact. (a) What impulse does the block exert on your hand? (b) What is the approximate collision time and average force that the block exerts on your hand? Physics 114 - Lecture 20

  18. Example: A Crumpled Car A car equipped with a 80 kg crash dummy drives into a massive concrete wall at 25 m/s (about 56 mi/h). (a) Estimate the displacement of the dummy during the crash. (b) Estimate the average force that the seat belt exerts on the dummy. If the front 25% of a 4.0 m long car crumples, the displacement of the car and dummy during the crash is about 1.0 m. Physics 114 - Lecture 20

  19. Conservationof Linear Momentum Momentum: Conservationof Momentum Physics 114 - Lecture 20

  20. Problem Solving Strategy Picture: Determe that the net external force SFext (or SFext x) on the system is negligible for some time interval. (If the net force is NOT determined to be negligible, do not proceed.) Solve:1. Draw a sketch showing the system before and after the time interval. Include coordinate axes and label the initial and final velocity vectors.2. Equate the initial momentum to the final momentum and express this as a vector equation (or one or more scalar equations involving x, y, and z components.)3. Substitute the given information into the equation(s) and solve for the quantity or quantities of interest. Check: Make sure you include any minus signs that accompany velocity components, because momentum can have either sign. Physics 114 - Lecture 20

  21. Example: A Space Repair During repair of the Hubble Space Telescope, an astronaut replaces a damaged solar panel during a spacewalk. Pushing the detached panel away into space, he is propelled in the opposite direction. The astronaut’s mass is 60 kg, and the panel’s mass is 80 kg. Both astronaut andpanelare initially at rest relative to the telescope, until the astronaut gives the panel a shove, giving it a velocity of 0.30 m/s relative to the telescope. Assuming his tether is slack, what is his velocity relative to the telescope? Physics 114 - Lecture 20

  22. Example:A Runaway Railroad Car A runaway 14,000 kg railroad car is rolling horizontally ay 4.00 m/s toward a switchyard. As it passes a grain elevator, 2,000 kg of grain suddenly drops into the car. Assume that the grain drops vertically and that rolling friction and air drag are negligible. How long does it take for the car to travel the 500 m distance from the grain elevator to the switchyard? Physics 114 - Lecture 20

  23. End of Lecture 20 • Before Thursday, read Walker Chapter 9.4-5. • Homework Assignments #6 should be submitted using the WebAssign system by 11:59 PM on Thursday, February 20. Physics 114 - Lecture 20

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