Physics 105 Final Practice Exam

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1 Physics 105 Final Practice Exam LAST Name (print)*: FIRST Name (print)*: Signature*: UIN #*: * Please fill in all required fields PROBLEM POINTS SCORE TOTAL 100 Giving or receiving aid in any examination is cause for dismissal from the University. Any other violation of academic honesty can have the same effect. Perform the necessary calculations in the space provided ALL WORK MUST BE CLEARLY SHOWN TO RECEIVE FULL CREDIT; NO CREDIT WILL BE GIVEN IF NO WORK IS SHOWN. 1

2 Question 1: Torque, Static Equilibrium (15 points) A uniform pole of mass M = 1 kg is at rest on an incline of angle θ = 30 o, secured by a horizontal rope as shown in Figure. a) [3 points] Show all the forces acting on the pole. b) [5 points] Find the tension in the rope. b) [7 points] What is the minimum coefficient of friction that will keep the pole from slipping? 2

Question 2: Rotational Dynamics, Angular Momentum (15 points) Two disks of moments of inertia I 1 and I 2, and with angular velocities ω 1 and ω 2, respectively, are brought in contact with each

3 Question 2: Rotational Dynamics, Angular Momentum (15 points) Two disks of moments of inertia I 1 and I 2, and with angular velocities ω 1 and ω 2, respectively, are brought in contact with each other face to face such that their axis of rotation coincides. The situation is as shown in the Figure just before the contact. Then, the disks acquire a common angular velocity due to friction operating between the surfaces in contact. a) [5 points] Find an expression for the common angular velocity of the combined system of two rotating disks b) [10 points] Find the expression for the energy dissipated due to the friction (i.e. an expression for the work done by friction) 3

4 Question 3: Gravity (15 points) A geosynchronous satellite, A, is a satellite that rotates around the Earth with a period of 24 hours, equal to the period of Earth s rotation around its axis. Viewed from the point on the Earth, a geosynchronous satellite appears to be stationary in the sky. Assume satellite orbits are circles and centered on Earth. Note that Earth rotates around its axis from West to East. Use: G = N m 2 /kg 2, 1 mi = 1609 m, 1 day = 24 h = s, R E = m, M E = kg. a) [5 points] If the altitude, h A, above Earth s surface is mi, what is the orbital speed of the satellite A? b) [5 points] A second satellite B is placed on orbit at an altitude of h B = mi above Earth s surface. What is the period of rotation, T B, of satellite B? c) [5 points] As viewed from Earth, does satellite B move eastward or westward? Explain the relationship of T B with respect to T A (larger, smaller or equal) based on the relationship between the altitudes h A and h B. 4

5 Question 4: Sound Waves (15 points) a) The wave speed on a taut wire is 320 m/s. The wire is 80 cm long and is vibrating at 800 Hz. [5 points] How far apart are the nodes? b) You are standing by the roadside as a truck approaches, and you measure the dominant frequency in the truck noise at 1100 Hz. As the truck passes the frequency drops to 950 Hz. [10 points] What is the truck s speed? 5

6 Question 5: Interference and Diffraction (15 points) a) [5 points] A two-slit experiment with slits separated by m produces a second-order maximum at a angle of o. Find the wavelength of the light used in this experiment. b) [5 points] Two sources of light that both have wavelengths equal to 750 nm are separated by a horizontal distance x. They are 5.00 m from a vertical slit of width mm. What is the smallest value of x for which the diffraction pattern of the sources can be resolved? c) [5 points] A drop of oil (n oil = 1.22) floats on water (n water = 1.33). When reflected light is observed from above, what is the thickness of the drop at the point where the second red fringe, counting from the edge of the drop, is observed? Assume green light has a wavelength λ = 532 nm. 6

7 Question 6: Special Relativity (25 points) Two pieces of space debris are on a head-on collision course. The one on the left has a relativistic speed v and the one on the right has a speed (2/3)v according to an outside observer. This observer notes that the initial distance between between the pieces is D and each has length L. a) [5 points] Find the velocity of the piece on the left according to the piece on the right. b) [5 points] Find the proper length of the piece on the right. c) [5 points] Find the length of the piece on the right according to the left piece. d) [5 points] Find the initial separation distance between the pieces according to the right piece. e) [5 points] Find the time before collision according to the right piece. 7

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Physics 218 Exam III

Physics 218 Exam III Spring 2017 (all sections) April 17 th, 2017 Rules of the exam: Please fill out the information and read the instructions below, but do not open the exam until told to do so. 1. You