GEN PHYS PHYS 21
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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 21 at University of California Santa Barbara taught by Staff in Fall. Since its upload, it has received 28 views. For similar materials see /class/227127/phys-21-university-of-california-santa-barbara in Physics 2 at University of California Santa Barbara.
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Date Created: 10/22/15
Physics 21 Final 3 hours 3 pages 10 problems Harry Nelson Friday March 18 Write your answers in a blue book Calculators and two pages of notes allowed No textbooks allowed Please make your work neat7 clear7 and easy to follow It is hard to grade sloppy work accurately Generally7 make a clear diagram7 and label quantities Make it clear what you think is known7 and what is unknown and to be solved for Except for extremely simple problems7 derive symbolic answers7 and then plug in numbers if numbers provided after a symbolic answer is available You can take the acceleration of gravity near the earth as g 10 ms27 to simplify calculations Put a box around your nal answer otherwise we may be confused about which answer you really mean and you could lose credit 1 3 9 4 You release a mass m1 from rest at the top of a ramp shaped like a quarter circle of radius R on to a horizontal table7 where m1 eventually has an elastic collision with mass mg as shown in Figure 1 You may choose any value for the mass m1 but everything else in the situation stays the same7 like R7 m2 and the acceleration of gravity 9 everything is frictionless a What is the velocity7 111 of the mass m1 just before it collides with mg in terms of the masses7 R7 and g b What choice of m1 will result in the largest velocity uz of mg after the collision7 and what is the value of that velocity 0 What choice of m1 will result in ml to losing the largest fraction of its energy in the collision A line of rain drops7 each with mass m and falling at terminal velocity 1 falls on the pan of a weight scale Each drop in the line is a distance Z from the next drop When each rain drop falls on the pan7 its water immediately comes to rest7 accumulating in a puddle on the pan At t 07 the rst rain drop hits the pan What does weight is read on the scale7 as a function of time t Neglect any jerkiness7 that arises because the drops reach the pan one at a time A particle of mass m 1 kg moves in one dimension from the origin to 00 and is subject to the potential energy z 1 2 Um a1 i 1 a 2 where a 4 Joules a l meter7 and B 4 Joulesmeterz a ls there a stable equilibrium point for the particle7 and if so7 at what value of z does it occur symbolically and numerically b Determine the circular frequency w of small oscillations about any stable equilibrium point both symbolically and numerically A bug of mass m1 sits on a bar of mass m2 and length L The midpoint of the bar is connected by a massless strut of length d to a pivot point7 as shown in Figure 2 The bar and strut sit atop a frictionless table The bug starts at t 0 from the point where the strut attaches to the bar7 and walks along the bar with velocity V with respect to the bar No net external force or torque acts on the system R Figure 1 For use in Problem 1 a Find the angular velocity of the bar and strut at t 0 when the the bug has just started walking b Find the angular velocity of the bar and strut for general time t for 0 g t g LZv when the bug is still on the bar A mass m near the earth s surface is initally at rest and is at coordinates 13 z where the origin is at the level of the ground 2 is the elevation above the ground and 1 is the horizontal distance from the z axis The mass m is dropped find the torque vector on the mass with respect to the origin of the coordinates as a function of time from the time of release to the time it hits the ground A mass of 10kg sits on a weight scale in an elevator on earth the elevator accelerates upward with an acceleration of 5 rns2 What is the reading on the weight scale A 10 kg mass is on an inclined plane that makes an angle of 450 with the horizontal near the surface of the earth The coefficient of friction between the mass and the incline is u 02 What is the component of acceleration of the block parallel to the incline A mass m is attached to the end of a spring with spring constant k the spring has negligible mass The spring is used like a rope to swing the mass in a circle of radius R at a constant angular velocity Q What is the equilibrium length of the spring You throw a dense ball from ground level vertically upward with an initial velocity of 20 rn s about 40 miles per hour Ignore air resistance
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