Contents. Objectives IAI motion w/o force motion with force F=ma third law work and energy circular motion Final Exam mechanics questions Recap IAI

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1 Physics 121 for Majors Section 1 IAI Review 4 Review for IAI and Final Exam Exam Details In the Testing Center Friday - Wednesday Wed. is a late day with a $5 fee Hours: 8 am 9 pm Friday 10 am 3 pm Saturday 8 am 6 pm Monday 8 am 9 pm, Tue. & Wed. Allow 1 hour + A calculator is not needed There are 30 multiple choice Last Class Solving force problems with stationary objects using 0 0 motion with no force 1

2 x,v,a Which of the following are not possible motions for an object that experiences no forces at all? A. remaining at rest B. moving in a straight line at constant speed C. slowing down to a stop D. orbiting a massive planet Discuss x, v, and a for an object with no forces. Empty Space A space ship drifts in empty space. Describe its motion. You are in a spaceship in empty space. Describe an experiment you can do to see if you re accelerating. You are in a spaceship in empty space and you are not accelerating. You see another spaceship drifting past you at constant speed. Which spaceship is at rest? x,v,a Which of the following are not possible motions for an object that experiences no net force? A. remaining at rest B. moving in a straight line at constant speed C. slowing down to a stop D. orbiting a massive planet Discuss x, v, and a for an object with no forces. Hockey Puck 1 A hockey puck slides frictionlessly across an ice sheet. Identify all the force acting on it. What is the net force acting on it? Describe its motion. Blinking Light Diagrams Describe velocity and acceleration for the following blinking light diagrams: How do the two velocities compare with each other? 2

3 Blinking Light Diagrams Describe velocity and acceleration for the following blinking light diagrams: How do the average velocities compare? v, F, a During Free Fall Draw velocity, force, and acceleration vectors for this ball at the points shown. There are no contact forces during this time. With Fan (No Friction) As you are playing air hockey, the puck is moving to the right. In the region shown, a fan is blowing the puck toward the top of the page. Identify the forces on the puck. Draw the path of the puck as it moves past the fan. Draw the velocity vector of the puck a large distance from the fan. Ice Sheet As you are playing air hockey, the puck is moving to the right. At the point shown, you hit the puck with the striker toward the top of the page. Draw the velocity vector immediate after the strike. Draw the velocity vector at a later time. Heavier Puck We repeat the last experiment with a heavier puck. Assume the force of the fan is the same. Draw the path of the puck as it moves past the fan. Draw the velocity vector of the puck a large distance from the fan. 3

4 Compare Pucks Think of force in terms of /. Describe how the experiments are different in terms of this equation. How long does it take the heavy puck to go past the fan compared to the light puck? How does the change of momentum compare? How does the change in velocity compare? 3rd Law and P Conservation Two air track carts of masses and are pushed together with a spring (attached to one cart only) in between. The spring is compressed and then the carts are released. The spring exerts a force over a time. Afterward the velocity of is and the velocity of is. What is the average force on? What is the average force on? How are these forces related? What is in terms of? Third Law Pairs What are the action-reaction pairs in each of these cases? A rabbit is running on the ground. A bird is flying through the air You push a box across the floor. A truck hits a mosquito. A satellite orbits the earth. You throw a baseball. Two air track carts are held together by a spring. A car is going up a hill. A car is going down a hill. Three Balls Three balls are thrown with the same velocity. One is thrown straight up, one is thrown straight down, and the is thrown horizontally. In what order to they reach the ground? How do their velocities compare as they hit the ground? 4

5 Two Balls Two balls are dropped, but one is dropped straight down and the other is thrown horizontally as it is released. Which reaches the ground first? How do their velocities compare as they hit the ground? How do their energies compare? How does the work done by gravity compare? How do the changes in their kinetic energies compare? Climbing Up Stairs You climb up a long flight of stairs in such a way that your center of mass moves with a constant velocity. (That may be tricky.) What forces act on you? What net force acts on you? What net work is done in climbing the stairs? Assume m and h are known. What net work does gravity do as you climb the stairs? What net work do you do? Inclined Plane Three objects have the same mass: a solid sphere, a hollow sphere, and a cube. The spheres also have the same radius. The spheres roll without slipping and the cube slides without friction down an inclined plane. In what order to they reach the bottom? What is the order of their velocities? What is the order of their kinetic energies at the bottom? Of translational kinetic energies? Climbing Down Stairs You climb down a long flight of stairs in such a way that your center of mass moves with a constant velocity. What forces act on you? What net force acts on you? What net work is done in climbing the stairs? Assume m and h are known. What net work does gravity as you climb hte stairs? What net work do you do? Work and Friction Of static, kinetic, and rolling friction, which do work? For which of these these frictions can we apply conservation of mechanical energy? 5

6 Centripetal Force What is the physical source of the centripetal force? What equation can you use to find the tension in the string? The Broken String An air hockey puck is connected to a string that is in turn tied to a fixed post. It moves in a circular path. At the instant shown in the figure, the string breaks. Sketch the path of the puck. When and Where In this room Wednesday, Dec. 20, 3:00 6:00 pm Will it take the entire time? I hope not, but don t come late! Can I take the test early? No! Section 2 Final Exam What Will It Cover There will be two parts - A comprehensive part - A part similar to the mid-term exams with from Classes There will be no group exam. 6

7 Part 1 12 taken (almost) verbatim from Mid-terms 1-3 and Basic Test Questions 1-4. About half conceptual and half computational What Information is given? - The formula for cross products - The table of moments of inertia for the book - Constants and prefixes, as on other exams Part 2 8 covering Classes About half conceptual and half computational 1 very short essay question on the Hawking material of Class 24. Equations to know Torque and angular momentum equations compare force equations: Kinetic energy Center of mass equations: 1 Moment of inertia equations: : : Parallel axis theorem: Gravity: Physical Pendulum: cos / How Much Does It Count? 15 % of your final grade 25 % of that comes from the basic test 75 % comes form the in-class test. 7

8 Cross Products Find Sphere on Incline A sphere rolls down an incline. Given,,, what is at the bottom? Point mass l l Even objects moving in straight lines have angular momentum and torque. Sphere on Incline A sphere rolls down an incline. Given,,, what is? Rolling Friction Does no work (no energy loss) Does not obey any simple formulas Solve problems using energy conservation or torque and force Pushed Box A box on a rough surface is pushed at the upper corner. How large can the applied force be increased without the box tipping? Hint: At the verge of tipping, the normal force is on the lower right corner. 8

9 Pushed Box A box on a rough surface is pushed at the upper corner. How large can the applied force be increased without the box tipping? What happens if the box is moving? Conical Pendulum Find l and about the pivot point and the center of the circle. Atwood Machine Find the angular acceleration of the pulley using torques. Merry-Go-Round You are riding a merry-go-round. You are sitting on a frictionless seat facing the center. What are the normal forces on you from the back of the seat and from the bottom of the seat? What is the angular momentum? What forces do you apply to the merry-go-round? What are names of the radial forces on you and on the merry-go-round? If you drop a ball, how does it move with respect to the ground? Yo-yo Given,, and assume is that of a cylinder, find. Find l and. Ferris Wheel You are riding a Ferris wheel. You are sitting on a seat that has a bottom that remains horizontal. What are the normal forces on you at the top of the Ferris wheel? At the bottom? Half way between? If you drop a ball when you are at the top, how does it move with respect to the ground? 9

10 Center of Mass, Moment of Inertia Three rods form an equilateral triangle of length on a side. The masses of each rod are, 2, and 3. Where is the center of mass? What is the moment of inertia about an axis passing though the vertex opposite the 3 rod and perpendicular to the plane of the triangle? Statics 2 Given:,,, What are the tensions in each cable? Statics Draw a free body diagram Identify forces Identify the center of rotation Draw lines of force Determine moment arms Sum of forces = 0 Sum of torques (+ = ccw) =0 Physical Pendulum A sphere of mass and radius is attached to a thin rod of mass and length. It swings from the end of the rod. What is the period of oscillation? Statics I Given:,,, What are the tensions in each cable? Find the distance. Section 3 Recap 10

11 Schedule Lab #12 is due Monday, Dec. 11 HW 23 is due Thursday, Dec. 14 Final Exam is on December 20 11