Physics 211 Sample Questions for Final Chapters Spring 2011 Each Exam usually consists of 10 Multiple choice questions which are conceptual in nature. They are often based upon the assigned thought questions from the homework. There are also 4 problems in each exam, based upon the assigned homework problems. Partial credit may be awarded for the problems. Physical constants and equation sheets are provided for the exam. Part I Multiple Choice (4 points. ea.) ___ . In an equilibrium problem, the point about which torques are calculated (A) must pass through one end of the object. (B) must pass through the objects center of mass. (C) must intersect the line of action of at least one force acting on the object. (D) may be located anywhere. Pivot point ___ . A wrench is suspended by a nail through a hole in its handle as shown, and is free to rotate. The wrench is in (A) stable equilibrium. (B) neutral equilibrium. (C) unstable equilibrium. (D) non-equilibrium. (E) suspended animation. Center of gravity ___ . A meter stick is balanced on end as shown. The meter stick is in (A) stable equilibrium. (B) neutral equilibrium. (C) unstable equilibrium. (D) non-equilibrium. (E) suspended animation. F ___ . The figure at right shows a rod divided into five equal parts. The rod has negligible weight and a fixed pivot at point c. An upward force of magnitude F is applied at point b, as shown. At what point on the rod could you apply a second force with magnitude half of F, also upward and perpendicular to the rod so that the net torque on the rod about the pivot is zero? Use answer G if it is not possible to create a net torque of zero under these conditions. ___ . The figure at right shows a rod divided into five equal parts. The rod has negligible weight and a fixed pivot at point c. An upward force of magnitude F is applied at point a, and an identical force is applied at point f, as shown. At what point on the rod could you apply a third force of the same magnitude F, but downward and perpendicular to the rod so that the net torque on the rod about the pivot is zero? Use answer g if it is not possible to create a net torque of zero under these conditions. A B C D E F F F a b c d e ___ . If the sum of the torques on an object in equilibrium is zero about a certain point, it is (A) zero about all other points. (B) zero about some other points (but not all other points). (C) zero about no other points. (D) any of the above, depending upon the situation. 1 f Physics 211 Sample Questions for Final Chapters ___ . An object in equilibrium must not have (A) acceleration. (B) any forces acting on it. (C) any torques acting on it (D) all of the above. (E) none of the above. Spring 2011 ___ . The type of matter that can support (i.e. resist and spring back against) a shear stress is (A) liquid. (B) gas. (C) solid. (D) all of the above. (E) none of the above. ___ . When the stresses on an object exceed the material’s Elastic Limit, then (A) the material “fails” (i.e. breaks). (B) the material is permanently deformed. (C) the material snaps back to its original size and shape when the stress is removed. (D) the material’s strain is proportional to the stress. (E) the object undergoes hysteria. ___ . When the stresses on an object exceed the material’s Ultimate Strength, then (A) the material is permanently deformed. (B) the material “fails” (i.e. breaks). (C) the material snaps back to its original size and shape when the stress is removed. (D) the material’s strain is proportional to the stress. (E) the object collapses into a screaming mass, requiring therapy for the rest of its earthly existence. ___. When a force acts on an object producing a stress on the object, the resulting strain is the (A) relative change in its dimensions. (B) the applied force per unit area. (C) the bulk modulus. (D) the ultimate strength of the material. ___ . When a force acts on an object producing a stress on the object resulting in strain, the stress on the object is the (A) relative change in its dimensions. (B) the applied force per unit area. (C) the bulk modulus. (D) the ultimate strength of the material. ___ . When a force acts on an object producing a stress on the object resulting in strain, the elastic modulus is the (A) relative change in the object's dimensions. (B) applied force per unit area. (C) ultimate strength. (D) stress divided by the strain. 2 Physics 211 Sample Questions for Final Chapters ___ . When the stresses on an object create a permanent deformation, then (A) the stress has exceeded the material's Elastic Limit. (B) the object undergoes hysteresis. (C) the deformations may also be referred to as a plastic deformation. (D) all of the above. (E) none of the above. Spring 2011 ___ . Which of the following diagrams most closely represents the gravitational forces that the earth and the moon exert on each other? (A) (C) E M (B) (E) E M E M E M (D) E M ___ . If two planets have the same average density and one has twice the mass of the other, then the more massive planet has (A) twice the radius and twice the surface gravity of the lighter. (B) 21/3 times the radius and 21/3 times the surface gravity of the lighter. (C) twice the radius and half the surface gravity of the lighter. (D) 21/3 times the radius and twice the surface gravity of the lighter. (E) 8 times the radius and 1/32 times the surface gravity of the lighter. ___ . If two planets have the same average density and one has a greater radius than the other, then compared to the smaller planet the larger planet has (A) a greater surface gravity. (B) the same surface gravity. (C) less surface e gravity. (D) more information on the details of the planets are needed to answer this question. ___ . If two planets have the same radius and one has a greater density (and hence a greater mass) than the other, then compared to the first planet the more massive planet will have (A) a greater surface gravity. (B) the same surface gravity. (C) less surface gravity. (D) more information on the details of the planets are needed to answer this question ___ . If two planets have the same mass and one has a greater radius than the other, then compared to the smaller planet the larger planet will have (A) a greater surface gravity. (B) the same surface gravity. (C) less surface gravity. (D) more information on the details of the planets are needed to answer this que 3 Physics 211 Sample Questions for Final Chapters Spring 2011 ___ . If two planets have the same radius and one has a greater mass than the other, then compared to the first planet the planet with the larger mass will have (A) a greater surface gravity. (B) a greater escape velocity. (C) a larger density. (D) all of the above (E) none of the above ___ . Pluto is in an elliptical orbit around the sun. After exactly one complete orbit, the net work done by the sun’s gravity on the Pluto is (A) positive. (B) negative. (C) zero. (D) any of the above depending upon the eccentricity of the orbit. ___. A satellite is in a circular orbit around the earth. After one complete orbit, the net work done by earth’s gravity on the satellite is (A) positive. (B) negative. (C) zero. (D) any of the above depending upon the actual radius of the orbit. ___ . A satellite is in a circular orbit around the earth. After one complete orbit, the net work done by earth’s gravity on the satellite is (A) positive. (B) negative. (C) zero. (D) any of the above depending upon the actual radius of the orbit. ___ . The gravitational force exerted on the earth by the moon (A) is greater than the gravitational force exerted on the moon by the earth. (B) is less than the gravitational force exerted on the moon by the earth. (C) is the same as the gravitational force exerted on the moon by the earth. (D) is zero. ___ . The total energy (KE +PE) of a simple harmonic oscillator is (A) a maximum when the mass is at the equilibrium position. (B) a maximum when the mass is at its maximum displacement from equilibrium. (D) constant. (D) always zero ___ . The kinetic energy of a simple harmonic oscillator is (A) a maximum when the mass is at the equilibrium position. (B) a maximum when the mass is at its maximum displacement from equilibrium. (D) constant. (D) always zero 4 Physics 211 Sample Questions for Final Chapters ___ . The potential energy of a simple harmonic oscillator is (A) a maximum when the mass is at the equilibrium position. (B) a maximum when the mass is at its maximum displacement from equilibrium. (C) constant. (D) always zero Spring 2011 ___. The amplitude of a simple harmonic oscillator does not affect its (A) frequency. (B) maximum speed. (C) maximum acceleration. (D) maximum KE. ___. The amplitude of the motion of an object undergoing Simple Harmonic Motion is (A) the total range of motion. (B) its maximum displacement on either side of the equilibrium position. (C) its minimum displacement on either side of the equilibrium position. (D) the number of cycles per second it undergoes ___ . The amplitude of a simple harmonic oscillator does not affect its (A) frequency. (B) maximum speed. (C) maximum acceleration. (D) maximum KE. ___ The frequency of oscillations of a mass on a spring do not depend upon (A) the mass. (B) the spring constant. (C) the amplitude of oscillations. (D) all of the above. (E) none of the above. ___ . A mass on a spring oscillates at a particular frequency. If the mass is replaced with a larger mass, then (A) the spring constant will be larger. (B) the frequency of oscillations will be smaller. (C) the period of oscillations will be smaller. (D) all of the above. ___ . A mass on a spring oscillates at a particular frequency. If the spring is replaced with a stiffer spring, then (A) the spring constant of the new spring is larger. (B) the frequency of oscillations will be larger. (C) the period of oscillations will be smaller. (D) all of the above. 5 Physics 211 Sample Questions for Final Chapters Spring 2011 ___ The maximum speed of a mass on a spring undergoing simple harmonic oscillations will depend upon (A) the mass. (B) the spring constant. (C) the amplitude of oscillations. (D) all of the above. (E) none of the above. ___ . Suppose a uniform spring is cut in half. The force constant for each half of the spring would be (A) half the spring constant for the original spring. (B) the same as the spring constant for the original spring. (C) twice the spring constant for the original spring. (D) 2 times the spring constant for the original spring. (E) 1 2 times the spring constant for the original spring. ___ . A mass on a spring oscillates at a particular frequency. If the spring is replaced with a stiffer spring, then (A) the spring constant of the new spring is larger. (B) the frequency of oscillations will be larger. (C) the period of oscillations will be smaller. (D) all of the above. ___ . A pendulum clock, which keeps correct time on earth, is taken to the surface of the moon. The clock will (A) run fast (i.e. clock’s “seconds” are shorter than real seconds). (B) run slow (i.e. clock’s “seconds” are longer than real seconds). (C) still run correctly. (D) will not run at all because there is no gravity on the moon. ___ . A pendulum clock, which keeps correct time on earth, is taken to the surface a planet with a much stronger surface gravity than earth. The clock will (A) run fast (i.e. clock’s “seconds” are shorter than real seconds). (B) run slow (i.e. clock’s “seconds” are longer than real seconds). (C) still run correctly. (D) will not run at all because there is no gravity on the moon. ___ . A pendulum clock that is placed in an elevator that is accelerating at a constant rate upwards will (A) run fast (i.e. clock’s “seconds” are shorter than real seconds). (B) run slow (i.e. clock’s “seconds” are longer than real seconds). (C) still run correctly. (D) will not run at all because there is no gravity on the moon. ___ . In order to double the period of a simple pendulum, the length of the string must be (A) shortened to ½ of its original length. (B) shortened to ¼ times its original length. (C) lengthened to 2 times its original length. (D) lengthened to 4 times its original length. 6 Physics 211 Sample Questions for Final Chapters Spring 2011 ___ . Of the following procedures, which will lower the pitch (fundamental frequency of vibration) in a guitar string? (A) decrease the tension. (B) lengthen the string. (C) use a heavier string. (D) all of the above. ___. The speed of a wave on a stretched string depends upon (A) the tension in the string. (B) the wavelength of the wave. (C) the amplitude of the wave. (D) all of the above. ___ . The speed of a wave on a stretched string does not depend upon (A) the amplitude of the wave. (B) the density (or heaviness) of the string. (C) the tension in the string. (D) all of the above. ___ . The lower the frequency of a wave, (A) the lower its speed. (B) the longer its wavelength. (C) the greater its amplitude. (D) the shorter its period. ___ . Wave motion in a medium transfers (A) neither mass nor energy. (B) energy, only. (C) both mass and energy. (D) mass, only. 7 Physics 211 Sample Questions for Final Chapters Spring 2011 Part II Problems Show all work. No work = no credit! (15 points each) A box of weight w1 is suspended from the end of a (hinged) horizontal uniform beam of length L and weight w2, as shown. Note that the hinged connection of the beam to the wall does not exert any torque on the beam about the hinge. (A freebody diagram will be essential to the successful completion of this problem.) (A) Find expressions for tension in the cable and the x and y components of the 30o reaction force exerted on the strut by the hinge. Suppose that L is 2.00 m, w1 is 500. N and w2 is 100. N. (B) What is the tension in the cable and the x and y components of the reaction w1 w2 force exerted on the strut by the hinge? (C) What is the maximum weight w1 that can be suspended from this system as shown if the cable is not to permanently stretch? The cable has a cross section of 1.6E-5 m2, and is made of a material with Young’s modulus 11 x 1010 N/m2, Elastic Limit 1.5 x 108 N/m2, and Ultimate Strength 3.4 x 108 N/m2. _______________________________________________________ A box of weight w1 is suspended from the end of a (hinged) uniform beam of length L and weight w2, as shown. Note that the hinged connection of the beam to the wall does 30o w1 not exert any torque on the beam about the hinge. The top cable connecting the beam to the wall is horizontal. (A free-body diagram will be essential to the successful w2 completion of this problem.) (A) Find expressions for tension in the cable and the x and y components of the reaction force exerted on the strut by the hinge in terms of w1 and w2. Suppose that L is 2.00 m, w1 is 500. N and w2 is 100. N. (B) What is the tension in the cable and the x and y components of the reaction force exerted on the strut by the hinge? (C) What is the minimum cross sectional area of the horizontal cable if the cable is not to permanently stretch? The cable is made of a material with Young’s modulus 11 x 1010 N/m2, Elastic Limit 1.5 x 108 N/m2, and Ultimate Strength 3.4 x 108 N/m2. _______________________________________________________ Sir Robin makes a mad dash for the drawbridge which is supported at one end by a frictionless hinge and the other end by a vertical cable. The bridge is 8.00 m long and has a mass of 100 kg. Sir Robin has a mass of 60.0 kg (in armor, soaking wet). At the instant Sir Robin has made it three fourths of the way across the bridge (as shown) x (A) use the conditions of equilibrium to determine the tension in the cable and the components of the reaction force at the hinge. (B) given the tension you found in (A), what is the minimum cross sectional area of the cable, given that it did not break. The cable is made of a material with Young’s modulus 11 x 1010 N/m2, Elastic Limit 1.5 x 108 N/m2, and Ultimate Strength 3.4 x 108 N/m2. 8 Physics 211 Sample Questions for Final Chapters Spring 2011 Dr Mic rides his motorcycle across a drawbridge as shown at right. The bridge is 8.00 m long and has a mass of 400 kg. Rider and motorcycle have a combined mass of 350 kg. At the instant the motorcycle has made it three fourths of the way across the bridge (as shown) hinge (A) use the conditions of equilibrium to determine the tension in x the cable and the components of the reaction force at the hinge. (B) given the tension you found in (A), what is the minimum cross sectional area of the cable, given that it was not permanently stretched. The cable is made of a material with Young’s modulus 11 x 1010 N/m2, Elastic Limit 1.5 x 108 N/m2, and Ultimate Strength 3.4 x 108 N/m2. Dr Mic rides his motorcycle across a drawbridge as shown at right. The bridge is 6.00 m long and has a mass of 200 kg. Rider and motorcycle have a combined mass of 400 kg. The cable is made of a material with Young’s modulus 1.1E11 N/m2, Elastic Limit 1.5E8 hinge N/m2, and Ultimate Strength 3.0E8 N/m2. (A) What is the maximum force the cable on the right side can x withstand without breaking, if it has a cross sectional area of 1.00E-5 m2 ? (B) use the conditions of equilibrium to relate the actual tension in the cable to the position of the motorcycle at a distance x from the hinge side of the drawbridge. (Hint: look at the torques about the left end of the bridge) (B) How far from the hinge side of the drawbridge does Dr Mic get before he plunges into the abyss because of a snapped cable? ___________________________________________________________________ Dr Mic rides his motorcycle across a drawbridge as shown at right. The bridge is 6.00 m long and has a mass of 400 kg. Rider and motorcycle have a combined mass of 350 kg. (A) What is the maximum force the cable on the right side can withstand without breaking, if it has a cross sectional area of 1.50x10-5 m2 ? (B) use the conditions of equilibrium to relate the actual tension in the cable to the position of the motorcycle at a distance x from the hinge side of the drawbridge. (Hint: look at the torques about the left end of the bridge) (B) How far from the hinge side of the drawbridge does Dr Mic get before he plunges into the abyss because of a snapped cable? The cable is made of a material with Young’s modulus 11 x 1010 N/m2, Elastic Limit 1.5 x 108 N/m2, and Ultimate Strength 3.0 x 108 N/m2. 9 Physics 211 Sample Questions for Final Chapters Spring 2011 A brave and trustworthy (and 90.0 kg) physics professor is being forced to walk the (3.00m, 50.0 kg) plank by a horde of angry students. The plank is supported one meter from the left end, and another force is applied downwards at the very end. The instructor is .500 meters from the right end of the board. (A) Draw a free body diagram, indicating all the forces on the plank. (B) Determine the forces exerted by the two supports. A 4.00 m uniform beam of mass 40.0 kg is suspended by vertical ropes at each end. A 120 Kg mass sits on the beam 1.00 m from the left end of the beam. Determine the tension in each rope. B A Planets can be used to determine the mass of the star they orbit. Venus has a nearly circular orbit about the sun with an orbit radius of 1.08E11 m and an orbital period 225 days. It also has a mass of 4.87E24kg. Determine (A) Venus’s orbital speed, (B) Centripetal acceleration, (C) the necessary centripetal force required to keep Venus in orbit, and (D) the necessary mass of the sun so that the sun’s gravitational attraction can create the centripetal force required to keep Venus in orbit. (E) Could (D) have been determined solely from the orbit radius and orbital period if the mass of Venus were unknown? (Yes or No) _______________________________________________________ Planet Hollywood has decided to place a hotel/space-station in circular orbit about Jupiter (mass = 1.90E27 kg) so that the Jupiter's Great Red Spot will always be in view. As a result, the time for one orbit must match the rotation rate of Jupiter (which is 9.90 hours for one rotation). Use your knowledge of Centripetal Acceleration, Newton's Laws and Universal Gravitation to determine the radius of the desired circular orbit. It will be helpful to relate the speed of the station along its orbit to the circumference of the orbit and the time for one orbit. _______________________________________________________ A pendulum clock designed for use on the Earth is transported to Mercury (mass 3.30E23 kg, radius 6.05E6 m, orbital distance 5.79E10 m), where it is used without modification or adjustment. The clock’s primary timing mechanism is a simple pendulum. The period for the simple pendulum is designed to be 1.00 s on Earth. A) What is the length of the pendulum’s string? B) What is the acceleration of gravity on the surface of the Mercury? C) What is the period of the pendulum on Mercury? Does the clock run fast or slow? _______________________________________________________ 10 Physics 211 Sample Questions for Final Chapters Three masses each exert a gravitational force on a fourth. M1 is located at M1 m (0,4m) and has a mass of 5.00 kg. M2 is located at (0,0) and has a mass of 8.00 kg. M3 is located at (3m, 0) and has a mass of 4.00 kg. a) Calculate the net gravitational force (x and y components) on the mass m (mass of 2.00 kg) located at the point (3m, 4m). b) Calculate the gravitational potential M2 M3 energy of the mass m due to the other three masses. Spring 2011 The moon orbits the earth at a distance of 3.84E8m. Each orbit takes 27.3 days. The mass of the moon has been determined to be 7.35E22 kg and the mass of the earth has been determined to be 5.97E24kg. Determine: (A) the speed of the moon as it orbits the earth, (B) the centripetal acceleration of the moon, (C) the force necessary to keep the moon in its circular path, and (D) the gravitational attraction of the earth for the moon using Newton's Law of Universal Gravitation (compare your result for part D to your answer to part C) _______________________________________________________ A spring with a spring constant of 500 N/m is attached to a .800 kg mass. The mass undergoes simple harmonic motion with an amplitude of .0500 m. Determine (A) the frequency of oscillations (in Hz), (B) the mechanical energy of the system, (C) the maximum speed of the mass, (D) the speed of the mass when it is .0200 m from equilibrium, (E) the acceleration of the mass when it is 0.200 m from equilibrium. _______________________________________________________ A spring with a spring constant of 400 N/m is attached to a .250 kg mass. The mass undergoes simple harmonic motion with an initial speed of 2.00 m/s at the equilibrium position. Determine (A) the frequency of oscillations (in Hz), (B) the mechanical energy of the system, (C) the amplitude of the oscillations, (D) the speed of the mass when it is .0125 m from equilibrium, (E) the acceleration of the mass when it is 0.0125 m from equilibrium. _______________________________________________________ . A spring with an unknown spring constant is attached to a .5 kg mass. The mass undergoes simple harmonic motion with an amplitude of 0.200 m at a frequency of 0.500 Hz. Determine (A) the force constant of the spring (B) the mechanical energy of the system, (C) the maximum speed of the mass, (D) the speed of the mass when it is 0.100 m from equilibrium, (E) the acceleration of the mass when it is 0.100 m from equilibrium. 11 Physics 211 Sample Questions for Final Chapters Spring 2011 A spring with a spring constant of 400 N/m is attached to an unknown mass. The mass undergoes simple harmonic motion with an amplitude of 0.200 m at a frequency of 0.500 Hz. Determine (A) the mass attached to the spring (B) the mechanical energy of the system, (C) the maximum speed of the mass, (D) the speed of the mass when it is 0.100 m from equilibrium, (E) the acceleration of the mass when it is 0.100 m from equilibrium. _______________________________________________________ A steel wire 2.00 m long and 4.00 g in mass is under a tension of 160 N. (A) What is the velocity of waves on the wire? (B) What is wavelength of the fundamental mode of vibration? (C) What is the frequency of the fundamental mode of vibration? (D) What is the frequency of the first overtone (aka the second harmonic)? (E) What must the tension be changed to in order to double the fundamental frequency? _______________________________________________________ A steel wire 1.50 m long and 2.00 g in mass is to be tuned to a frequency of 440 Hz. (A) What is wavelength of the fundamental mode of vibration? (B) What is the velocity of waves on the wire? (C) What is the required tension? 12

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