1 / 47

Physics 114A - Mechanics Review for Exam 3 (Walker: Chapters 9-11) March 6, 2014

Physics 114A - Mechanics Review for Exam 3 (Walker: Chapters 9-11) March 6, 2014. John G. Cramer Professor Emeritus, Department of Physics B451 PAB jcramer@uw.edu. Announcements. The new seat assignments for Exam 3 have been posted on Catalyst.

twila
Download Presentation

Physics 114A - Mechanics Review for Exam 3 (Walker: Chapters 9-11) March 6, 2014

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Physics 114A - MechanicsReview for Exam 3(Walker: Chapters 9-11)March 6, 2014 John G. Cramer Professor Emeritus, Department of Physics B451 PAB jcramer@uw.edu

  2. Announcements • The new seat assignments for Exam 3 have been posted on Catalyst. • Homework Assignment #8 is due at 11:59 PM on Thursday, March 6 (tonight!). Homework Assignment #9 is due at 11:59 PM on Sunday, March 16. • I will have office hours in the Study Center immediately after class oday. Physics 114A - Review 03

  3. About Exam 3 • On Friday, March 7 (tomorrow) we will have Exam 3, which covers Walker, Chapters 9, 10 and 11, and my lectures 20-28. • Exam 3 will have assigned seating. Seat assignments have been posted on Catalyst. I will also bring a seating list to the exam. • Exam 3 is closed-book, but you may bring with you one page of notes on a 8½x11” sheet of paper (both sides). Also bring youe UW Photo ID, which will be checked when the exam starts. • Bring a Scantron sheet , a straight-edge, and a scientific calculator with good batteries. • Exam 3 will have a multiple-choice section (75 pts) based on questions taken from homework, lecture example problems, and “two-dot” end-of-chapter problems in Walker. • Exam 3 will have a free-response section (25 pts) based on “Conceptual Questions” and “Conceptual Exercises” from the end-of-chapter questions in Walker requiring written answers. Physics 114A - Review 03

  4. Lecture Schedule (Part 3) We are here. Physics 114A - Review 03

  5. You are looking down the axis ofrotation (x) of a balanced gyroscopethat is turning rapidly in a counter-clockwise direction. You hang aweight on the end of the axlenearest you and observe thatthe gyroscope begins to precess(i.e., its axis of rotation moves). In what direction does it precess? (A) Up (B) Down (C) Right (D) Left Clicker Question 1 Physics 114A - Review 03

  6. Chapter 9 Linear Momentum and Collisions Physics 114A - Review 03

  7. Units of Chapter 9 • Linear Momentum • Momentum and Newton’s Second Law • Impulse • Conservation of Linear Momentum • Inelastic Collisions • Elastic Collisions Physics 114A - Review 03

  8. Units of Chapter 9 • Center of Mass • Systems with Changing Mass: Rocket Propulsion Physics 114A - Review 03

  9. Linear momentum: • Momentum is a vector • Newton’s second law: F = ma = Dp/Dt • Impulse: • Impulse is a vector • The impulse is equal to the change in momentum • If the time is short, the force can be quite large Summary of Chapter 9 Physics 114A - Review 03

  10. 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 114A - Review 03

  11. Example: Hitting a Baseball (2) Use the impulse approximation: Neglect all other forces on ball during the brief duration of the collision. Physics 114A - Review 03

  12. Summary of Chapter 9 • Momentum is conserved if the net external force is zero. • Internal forces within a system always sum to zero. • In collision, assume external forces can be ignored. • Elastic/(Inelastic) collision: kinetic energy is/(is not) conserved. • Completely inelastic collision: the objects stick together afterward. Physics 114A - Review 03

  13. 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 114A - Review 03

  14. Summary of Chapter 9 • A one-dimensional collision takes place along a line. • In two dimensions, conservation of momentum is applied separately in each dimension. • Elastic collision: kinetic energy is conserved. • Center of mass: Physics 114A - Review 03

  15. Example: Ballistic Pendulum A projectile of mass mis fired with an initialspeed v0 at the bob of apendulum. The bob hasmass M and is suspendedby a rod of negligible mass.After the collision the projectile and bob stick together and swing at speed vf through an arc reaching height h. Find the height h. Physics 114A - Review 03

  16. Summary of Chapter 9 • Center of mass: Physics 114A - Review 03

  17. Summary of Chapter 9 • Motion of center of mass: • Rocket propulsion: Physics 114A - Review 03

  18. Chapter 10 Rotational Kinematics & Energy Physics 114A - Review 03

  19. Units of Chapter 10 • Angular Position, Velocity, & Acceleration • Rotational Kinematics • Connections Between Linear & Rotational Quantities • Rolling Motion • Rotational Kinetic Energy & the Moment of Inertia • Conservation of Energy Physics 114A - Review 03

  20. Summary of Chapter 10 • Describing rotational motion requires analogs to position, velocity, and acceleration • Average and instantaneous angular velocity: • Average and instantaneous angular acceleration: Physics 114A - Review 03

  21. Summary of Chapter 10 • Period: • Counterclockwise rotations are positive, clockwise negative • Linear and angular quantities: Physics 114A - Review 03

  22. Summary of Chapter 10 • Linear and angular equations of motion: Tangential speed: Centripetal acceleration: Tangential acceleration: Physics 114A - Review 03

  23. Summary of Chapter 10 • Rolling motion: • Kinetic energy of rotation: • Moment of inertia: • Kinetic energy of an object rolling without slipping: • When solving problems involving conservation of energy, both the rotational and linear kinetic energy must be taken into account. Physics 114A - Review 03

  24. Moments of Inertia Physics 114A - Review 03

  25. Example: Thrown for a Curve To throw a curve ball, a pitchergives the ball an initial angularspeed of 36.0 rad/s. When thecatcher gloves the ball 0.595 sater, its angular speed hasdecreased (due to air resistance)to 34.2 rad/s. (a) What is the ball’s angular acceleration, assuming it to be constant? (b) How many revolutions does the ball make before being caught? Physics 114A - Review 03

  26. Example: Time to Rest A pulley rotating in the counterclockwise direction is attached to a mass suspended from a string. The mass causes the pulley’s angular velocity to decrease with a constant angular acceleration a = -2.10 rad/s2. (a) If the pulley’s initial angular velocity is w0 = 5.40 rad/s, how long does it take for the pulley to come to rest? (b) Through what angle does the pulley turn during this time? Physics 114A - Review 03

  27. Example: The Microhematocrit In a microhematocrit centrifuge, small samples of blood are placed in heparinized capillary tubes (heparin is an anticoagulant). The tubes are rotated at 11,500 rpm, with the bottom of the tubes 9.07 cm from the axis of rotation. (a) Find the linear speed at the bottom of the tubes. (b) Find the centripetal acceleration at the bottom of the tubes. Physics 114A - Review 03

  28. Example: A Dumbbell Use the definition of momentof inertia to calculate that of adumbbell-shaped object withtwo point masses m separatedby a distance of 2r and rotatingabout a perpendicular axis throughtheir center of symmetry. Physics 114A - Review 03

  29. Example: Like a Rolling Disk A 1.20 kg disk with a radius 0f 10.0 cm rolls without slipping. The linear speed of the disk is v = 1.41 m/s. (a) Find the translational kinetic energy. (b) Find the rotational kinetic energy. (c) Find the total kinetic energy. Physics 114A - Review 03

  30. Example: Compare Heights A ball is released from rest on a no-slip surface, as shown. After reaching the lowest point, it begins to rise again on a frictionless surface. When the ball reaches its maximum height on the frictionless surface, it is higher, lower, or the same height as its release point? The ball is not spinning when released, but will be spinning when it reaches maximum height on the other side, so less of its energy will be in the form of gravitational potential energy. Therefore, it will reach a lower height. Physics 114A - Review 03

  31. Example: A Bowling Ball A bowling ball that has an 11 cm radius and a 7.2 kg mass is rolling without slipping at 2.0 m/s on a horizontal ball return. It continues to roll without slipping up a hill to a height h before momentarily coming to rest and then rolling back down the hill. Model the bowling ball as a uniform sphere and calculate h. Physics 114A - Review 03

  32. Chapter 11 Rotational Dynamics and Static Equilibrium Physics 114A - Review 03

  33. Units of Chapter 11 • Torque • Torque and Angular Acceleration • Zero Torque and Static Equilibrium • Center of Mass and Balance • Dynamic Applications of Torque • Angular Momentum Physics 114A - Review 03

  34. Units of Chapter 11 • Conservation of Angular Momentum • Rotational Work and Power • The Vector Nature of Rotational Motion Physics 114A - Review 03

  35. Summary of Chapter 11 • A force applied so as to cause an angular acceleration is said to exert a torque. • Torque due to a tangential force: • Torque in general: • Newton’s second law for rotation: • In order for an object to be in static equilibrium, the total force and the total torque acting on the object must be zero. • An object balances when it is supported at its center of mass. Physics 114A - Review 03

  36. Summary of Chapter 11 • In systems with both rotational and linear motion, Newton’s second law must be applied separately to each. • Angular momentum: • For tangential motion, • In general, • Newton’s second law: • In systems with no external torque, angular momentum is conserved. Physics 114A - Review 03

  37. Summary of Chapter 11 • Work done by a torque: • Power: • Rotational quantities are vectors that point along the axis of rotation, with the direction given by the right-hand rule. Physics 114A - Review 03

  38. Example:A Uniform Rod Pivoted at an End A uniform thing rod of length L and mass M is pivoted at one end. It is held horizontal and released. Neglect friction and air drag. (a) Find the angular acceleration a of the rod immediately after its release.(b) Find the magnitude of the force FA exerted by the rod on the pivot at that instant. Physics 114A - Review 03

  39. Example: The Pulley Matters A cart with M = 0.31 kgon a horizontal air trackis attached to a stringthat passes over adisk-shaped pulley ofmass m = 0.08 kg and aradius r= 1.2 cm. The string is pulled downward with a force T1 = 1.1N. (a) Find the tension T2 in the string between the pulley and the cart. (b) Find the acceleration a of the cart. Physics 114A - Review 03

  40. Example: Rod and Wire A rigid vertical rod of length L and negligible mass is connected to the floor by a bolt through its lower end. The rod also has a 45° wire connecting its top end to the floor. If a horizontal force F is applied to the center of the rod, find the tension in the wire. Find the horizontal and vertical components of the force exerted by the bold on the rod. Physics 114A - Review 03

  41. Example: Spinning the Wheel You are sitting on a stool on a frictionless turntable holding a bicycle wheel. Initially, neither the wheel nor the turntable is spinning. You hold the axel vertical with one hand and spin the wheel counterclockwise with the other hand. You observe that the stool and turntable begin to rotate clockwise. Then you stop the wheel with your free hand. What happens to the turntable rotation? Physics 114A - Review 03

  42. Example: A Rotating Disk Disk 1 is rotating freely and has angularvelocity wi and moment of inertia I1about its symmetry axis, as shown.It drops onto disk 2 of moment ofinertia I2, initially at rest. Becauseof kinetic friction, the two diskseventually attain a common angularvelocity wf. (a) What is wf? (b) What is the ratio of final to initial kinetic energy? Physics 114A - Review 03

  43. Example: Wrapping the Post A puck on a frictionless plane is given an initial speed v0. The puck is attached to a massless string that wraps around a vertical post. Is angular momentum conserved? Physics 114A - Review 03

  44. Example: Pulling Through a Hole A particle of mass m moves with speed v0 in a circleof radius r0 on a frictionless tabletop. The particle is attached to a massless string that passes through a holein the table as shown. The string is pulled slowlydownward until the particle is a distance rf from the hole and continues to rotate in a circle of that radius. (a) Find the final velocity vf.(b) Find the tension T in the string when the particle moves in a circle of radius r in terms of the angular momentum L.(c) Are energy and/or angular momentum conserved when the string is pulled? Angular momentum is conserved, but energy is not. Physics 114A - Review 03

  45. Example: Angular Momentum About the Origin Find the angular momentum about the origin for the following situations: (a) A car of mass 1200 kg moves in a counterclockwise circle in the xy plane of radius 20 m with a speed of 15 m/s;(b) The same car moves with along the liney = y0 = 20 m parallel to the x axis;(c) A uniform disk in the xy plane of radius 20 m and mass 1200 kg rotates at 0.75 rad/s along its axis, which is the z axis. Physics 114A - Review 03

  46. Gyroscopic Motion The magnitude of the torque about the pivot is = mgd. The direction of this torque at the instant shown is out of the page (using the right hand rule). The change in angular momentum at the instant shown must also be out of the page! d L  mg Physics 114A - Review 03

  47. Before next Monday, read Walker Chapter 12.1-3 • HW #8 should be submitted to WebAssign by 11:59 PM on Thursday, March 6 (Tonight!). HW#9 should be submitted by 11:59 PM on Sunday, March 16. End of Review 3

More Related