Final Exam: Wednesday, May 11, 10:05 am - 12:05 pm, BASCOM 272 The exam will cover chapters 1 14 The exam will have about 30 multiple choice questions Consultations hours the same as before. Another review sessions will be held by your TAʼs at the discussion session Read and understand the problem statement completely: Often this is helped by a diagram showing the relationships of the objects. Be sure you understand what is wanted Be sure you understand what information is available to you ( Translate the situation described to physics concepts. Be alert for clues regarding the choice of relationships (e.g. conservation of energy, conservation of momentum, rotational or linear motion,.) Be alert for detail that would qualify the use of some concepts (e.g. friction affecting conservation of energy.) If there are other unknowns involved how can you find them (or eliminate them). 5/4/11 Physics 201, Spring 2011 1 5/4/11 Physics 201, Spring 2011 2 After choosing the appropriate relationship between the concepts (equation), find the target quantities -- at first algebraically, then substitute numbers at the end. Check Does the answer make sense? Are the units consistent? Often with multiple choice questions you can round the numerical quantities and check the final choice without the calculator. Techniques and Hints Be clear and organized -- neat in your solution.you must be able to read and understand your own notes! Go through the exam completely at first and complete those questions that you are confident in solving. Then return to the others. Chapters 2, 3 (linear) 9 (rotational) 5/4/11 Physics 201, Spring 2011 3 5/4/11 Physics 201, Spring 2011 4 Page 1
Chapters 4, 5, (the 2 nd law) 6, 7, (energy and work) 10, 11 (rotational, gravity) 5/4/11 Physics 201, Spring 2011 5 Chapters 8 (linear: consequence of the 2 nd law) 10 (rotational) 5/4/11 Physics 201, Spring 2011 6 Chapters 12 (static equilibrium, elasticity) Archimedes Principle : A body wholly or partially submerged in a fluid is buoyed up by a force equal to the weight of the displaced fluid. Resonance frequency: 5/4/11 Physics 201, Spring 2011 7 5/4/11 Physics 201, Spring 2011 8 Page 2
Question (Chapt 2) An European sports car dealer claims that his product will accelerate at a constant rate from rest to a speed of 100 km/hr in 8s. What is the speed after first 5 s of acceleration? 17.4 m/s 53.2 m/s 44.4 m/s 34.7 m/s 28.7 m/s Two gliders of unequal mass m A <m B are placed on a frictionless air track. Glider A is pushed horizontally as shown so that the gliders accelerate together to the right. Let F ha represent the magnitude of the force of the hand on the glider A. Let F BA represent the magnitude of the force exerted by the glider A on the glider B. Which one of the following is true? F ha < F BA F ha = F BA F ha > F BA Newton s Second Law: Net external, F ha -F BA, is causing block A to accelerate to the right. F BA = F AB < F ha 5/4/11 Physics 201, Spring 2011 9 5/4/11 Physics 201, Spring 2011 10 Two gliders of unequal mass m A <m B are placed on a frictionless air track. Glider A is pushed horizontally as shown so that the gliders accelerate together to the right. Let F ha represent the magnitude of the force of the hand on the glider A. Let F BA represent the magnitude of the force exerted by the glider A on the glider B. Two gliders of unequal mass m A <m B are placed on a frictionless air track. Glider A is pushed horizontally as shown so that the gliders accelerate together to the right. Which one of the following is true? F BA < F AB How does the net force on glider B (F B ) compare to the magnitude of the net force on glider A (F A )? F B < F A F BA = F AB F BA > F AB Newton s Third Law F B = F A F B > F A 5/4/11 Physics 201, Spring 2011 11 5/4/11 Physics 201, Spring 2011 12 Page 3
Question (Chapt. 6) How much power is needed to lift a 75-kg student vertically upward at a constant speed of 0.33 m/s? 25 W 12.5 W 243 W 115 W 230 W A block is placed on a planar sheet that is pivoted at one end. The free side of the sheet is then raised very slowly, as shown. When the sheet is first raised, friction between block and sheet keeps the block from moving. At a certain angle, however, the block begins to slide down the inclined sheet. If the sheet is kept at this angle, will the acceleration of the block be zero, constant, or neither? 12/10/07 Physics 103, Fall 2007, U. Wisconsin 13 12/10/07 Physics 103, Fall 2007, U. Wisconsin 14 Question (Chapt 8) A moving object collides with an object initially at rest. Is it possible for both objects to be at rest after the collision? Can one of them be at rest after the collision? v m M A block of mass m moving at to the right with speed v hits a block of mass M that is at rest. If the surface is frictionless and the collision is elastic, what are the final velocities of the two blocks? If the objects stick together after the collision, is the kinetic energy conserved? 5/4/11 Physics 201, Spring 2011 15 5/4/11 Physics 201, Spring 2011 16 Page 4
v m M v m M A block of mass m moving at to the right with speed v hits a block of mass M that is at rest. If the surface is frictionless and the collision is elastic, what are the final velocities of the two blocks? In the center of mass frame, velocities reverse after an elastic collision v CM = mv/(m+m) m v-v CM -v CM M Now find velocity of each block in lab frame: Velocity of m = v CM - (v-v CM ) = 2v CM v = (m-m)v/(m+m) Velocity of M = 2v CM = 2mv/(m+M) v CM = mv/(m+m) -(v-v CM ) m M v CM 5/4/11 Physics 201, Spring 2011 17 5/4/11 Physics 201, Spring 2011 18 A boy is whirling a stone around his head by means of a string. The string makes one complete revolution every second. The boy then speeds up the stone, keeping the radius of the circle unchanged, so that the string makes two complete revolutions every second. What happens to the tension in the string? The tension increases to four times its original value. The tension increases to two times its original value. The tension is unchanged. The tension reduces to one half its original value. The tension reduces to one fourth its original value. Is there a net force acting on the system? Yes, the direction of velocity is changing. Centripetal acceleration is provided by the tension in the string. The centripetal acceleration is different in the two cases presented, therefore, the tension will be different Note that the radius has not changed in the two conditions Note also that angular velocity is given (in words). 5/4/11 Physics 201, Spring 2011 19 5/4/11 Physics 201, Spring 2011 20 Page 5
Centripetal force for the two situations: Need to write in terms of change to angular velocity because that is what is specified Some of the quantities are not given but we are comparing situations, I.e., take ratios and cancel common factors! The picture below shows three different ways of using a wrench to loosen a stuck nut. Assume the applied force F is the same in each case. In which case is the torque on the nut the biggest? Case 1 Case 2 Case 3 = F d sin θ Longest lever arm, d at 90 o angle Tension goes up by a factor of 4! 5/4/11 Physics 201, Spring 2011 21 12/10/07 Physics 103, Fall 2007, U. Wisconsin 22 A sign of mass M is hung 1 m from the end of a 4 m long uniform beam of mass m, as shown in the diagram. The beam is hinged at the wall. What is the tension in the guy wire? Determine the tension T, and the contact force F at the hinge. 3 m wire θ = 30 SIGN 5/4/11 Physics 201, Spring 2011 23 1 m Is there a net force acting on the system? Is there a net torque acting on the system? Draw the free body diagram. How many forces are acting on the system? 2 3 4 mg, Mg, tension, force from hinge 5 What is the direction of the contact force at the hinge between the wall and the beam? Vertical Horizontal It has both vertical and horizontal components 5/4/11 Physics 201, Spring 2011 24 wire θ = 30 SIGN 1 m Page 6
3m F y 2m T 30 0 F x Forces Torques mg Mg Hint: Choose axis of rotation at support because F x & F y are not known A rock is thrown straight up from the Earth s surface. Which one of the following statements concerning the net force acting on the rock at the top of its path is true? It is equal to zero for an instant. It is equal to the force used to throw it up but in opposite direction It is equal to the weight of the rock Its direction changes from up to down Its magnitude is equal to the sum of the force used to throw it up and its weight 5/4/11 Physics 201, Spring 2011 25 12/10/07 Physics 103, Fall 2007, U. Wisconsin 26 A mass of 100 tons (10 5 kg) is lifted on a steel rod two cm in diameter and 10 m in length. (Young s modulus of steel is 210 10 9 N/m 2 ) (a) How long does the rod stretch? A mass of 100 tons (10 5 kg) is lifted on a steel rod two cm in diameter and 10 m in length. (Young s modulus of steel is 210 10 9 N/m 2 ) (a) How long does the rod stretch? F = force A = area of rod L = length of rod ΔL = change of length of the rod 5/4/11 Physics 201, Spring 2011 27 5/4/11 Physics 201, Spring 2011 28 Page 7
Question (Chapt 13) 1) The pressure on the roof of a tall building is 0.985 10 5 Pa and the pressure on the ground is 1.000 10 5 Pa. The density of air is 1.29 kg/m 3. What is the height of the building? A. 100 m B. 118 m C. 135 m D. 114 m E. None of the above A venturi tube may be used as the inlet to an automobile carburetor. If the 2.0-cm diameter pipe narrows to a 1.0-cm diameter, what is the pressure drop in the constricted section for an airflow of 3.0 m/s in the 2.0-cm section? (fuel density = 1.2 kg/m 3.)? Velocity is faster in constricted section because mass flow is conserved (mass that flows into constriction must also flow out). 5/4/11 Physics 201, Spring 2011 29 Pressure drops because of Bernoulli principle: (applies to incompressible, frictionless fluid) 5/4/11 Physics 201, Spring 2011 30 Question, continued Fluid flow without friction Volume flow rate: ΔV/Δt = A Δx/Δt = Av (m 3 /s) Continuity: A 1 v 1 = A 2 v 2 i.e., mass that flows in must then flow out A venturi tube may be used as the inlet to an automobile carburetor. If the 2.0-cm diameter pipe narrows to a 1.0-cm diameter, what is the pressure drop in the constricted section for an airflow of 3.0 m/s in the 2.0-cm section? (fuel density = 1.2 kg/m 3.)? 70 Pa 85 Pa 100 Pa 115 Pa 81 Pa 5/4/11 Physics 201, Spring 2011 31 5/4/11 Physics 201, Spring 2011 32 Page 8
Question (Chapt 13) The water level in identical bowls, A and B, is exactly the same. A contains only water; B contains ice as well as water. When we weigh the bowls, we find that W A < W B W A = W B W A > W B W A < W B if the volume of the ice cubes is greater than one-ninths the volume of the water. W A < W B if the volume of the ice cubes is greater than one-ninths the volume of the water. 1) A block of aluminum (density 3041 kg/m 3 ) is lifted very slowly but at constant speed from the bottom of a tank filled with water. If it is a cube 20 cm on each side, the tension in the cord is: A. 160 N T B. 4 N Fb C. 80 N D. 8 N E. None of the above W Eureka! Archimedes Principle. Weight of the water displaced = Bouyant Force 5/4/11 Physics 201, Spring 2011 33 5/4/11 Physics 201, Spring 2011 34 Question (Chapt 13) A wind with velocity 10 m/s is blowing through a wind generator with blade radius 5.0 meters. What is the maximum power output if 30% of the wind s energy can be extracted? (air density = 1.25 kg/m 3.) 7.2 kw 14.7 kw 21.3 kw 29.4 kw 39.6 kw Firemen connect a hose (8 cm in diameter) to a fire hydrant. When the nozzle is open, the pressure in the hose is 2.35 atm. (1 atm. = 10 5 Pa). The firemen hold the nozzle at the same height of the hydrant and at 45 o to the horizontal. The stream of water just barely reaches a window 10 m above them. The diameter of the nozzle is about: A. 8 cm B. 6 cm C. 4 cm D. 2 cm E. None of the above Point 3 10m Point 2 Point 1 5/4/11 Physics 201, Spring 2011 35 5/4/11 Physics 201, Spring 2011 36 Page 9
At t=0, a 795-g mass at rest on the end of a horizontal spring (k=127 N/m) is struck by a hammer, giving it an initial speed of 2.76 m/s. The position of the mass is described by, with What is period of the motion? period = 2π/ω 0.497 s What is the frequency of the motion? What is the maximum acceleration? 2.01 Hz 34.9 m/s 2 Question (Chapt 14) The amplitude of a system moving with simple harmonic motion is doubled. The total energy will then be 4 times larger 2 times larger the same as it was half as much quarter as much What is the total energy? 3.03 J 5/4/11 Physics 201, Spring 2011 37 5/4/11 Physics 201, Spring 2011 38 Page 10