GEN PHYS PHYS 22
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This 2 page Class Notes was uploaded by Hailey Halvorson on Thursday October 22, 2015. The Class Notes belongs to PHYS 22 at University of California Santa Barbara taught by Staff in Fall. Since its upload, it has received 13 views. For similar materials see /class/227143/phys-22-university-of-california-santa-barbara in Physics 2 at University of California Santa Barbara.
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Date Created: 10/22/15
Physics 22 Practice Midterm 50 minutes 3 pages Harry Nelson Monday April 25 Write your answers in a blue book Calculators and one page of notes allowed No textbooks allowed Please make your work neat clear and easy to follow It is hard to grade sloppy work accurately Generally make a clear diagram and label quantities Make it clear what you think is known and what is unknown and to be solved for Except for extremely simple problems derive symbolic answers and then plug in numbers if necessary after a symbolic answer is available Put a box around your nal answer otherwise we may be confused about which answer you really mean and you could lose credit Mass m radius R I moment I n 7mm H a rd Floor Figure 1 For use in problem 1 1 A ball with initial velocity 39u U vyj is about to hit the oor as shown in Fig 1 The ball has mass m radius R and moment of inertia I The reduced moment of inertia is de ned by c E ImR2 Just 3 9 7 before the bounce the velocity makes an angle 04 with the vertical as shown in Fig 1 Neglect gravity because the time between what is shown in Fig 1 and the bounce is so small that gravity has no chance to make a difference The bounce of the ball off the oor is elastic meaning that the magnitude of the vertical component of the velocity after the bounce is the same as that before the bounce but opposite in direction The ball is initially not spinning at all There is a lot of friction between the ball and the oor so spin in uences the outcome of the bounce The ball never slips during the bounce so friction does no work on the ball and the balls nal total energy equals its initial total energy Denote the nal velocity of the ball by s smi syj and the nal angular velocity of the ball by 14 Use the yz coordinate system shown in Fig 1 a The impulse on the ball in the z direction from friction with the oor during the bounce is Jm medt ls J1 gt 0 J1 0 or J1 lt 0 where the positive x direction is shown in the gure State the equation that describes the change in horizontal linear momentum due to J1 State the equation that describes the change in angular momentum due to J1 be careful to state the point about which you evaluate angular momenta i lt State the equation that describes conservation of energy before and after the bounce A C7 V Describe the direction of the angular velocity of the ball after the bounce as a vector using the unit vectors shown What is the nal angular velocity vector w in terms of the quantities that specify this problem AA CLO VV What is tan 6 in terms of the quantities that specify this problem A person rides a unicycle in a circle of radius R as shown in Fig 2 The total mass of the unicycle and the person is M and the center of mass of the whole system is a distance h above the bottom of the tire They go at speed The radius of the wheel is b its mass is m and its moment of inertia for spinning about its axis is I mbz The acceleration of gravity is 9 Find the angle b that the unicycle is tipped at as shown on Fig 2 in terms of the other quantities that specify the problem When a certain spaceship of mass m is extremely far from a planet of mass MI gt m and radius RP the ships aims itself to miss the edge of the planet by a distance h and has speed 1 On the surface of the planet the acceleration of gravity is 9 GMpRg As the ship nears the planet the ship slows itself by bouncing a tractor beam aimed at the center of the planet this is very ef cient since the ship slows down once by ring the tractor beam at the planet and then gets a bonus on the rebound when the tractor beam bounced off the planet hits the ship Eventually the ship ends up in a circular orbit what is the radius r0 of this circular orbit in terms of the other quantities that specify the problem Eliminate GMp in favor of 97 and The following problems all involve the manipulation of complex numbers where cartesian form is z z W and polar form is z ref a Put in cartesian form 2 171 239 b Put in polar form 2 73 7 3xgz39 c Put in polar form 2 d Put in the form Asinwt B cos wt Re z39ei t 4
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