PHYSICS 111 SPRING FINAL EXAM: May 2, 2017; 2:15pm - 4:15pm

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1 PHYSICS 111 SPRING 2017 FINAL EXAM: May 2, 2017; 2:15pm - 4:15pm Name (printed): Recitation Instructor: Section # INSTRUCTIONS: This exam contains 30 multiple-choice question, each worth 3 points, for a nominal maximum score of 80 points plus 10 extra credit points. Choose one answer only for each question. Choose the best answer to each question. Answer all questions. Allowed material: Before turning over this page, put away all materials except for pens, pencils, erasers, rulers and your calculator. There is a formula sheet attached at the end of the exam. Other copies of the formula sheet are not allowed. Calculator: In general, any calculator, including calculators that perform graphing, is permitted. Electronic devices that can store large amounts of text, data or equations (like laptops, e-book readers, smart phones) are NOT permitted. Calculators with WiFi technology are NOT permitted. If you are unsure whether or not your calculator is allowed for the exam, ask your TA. How to fill in the bubble sheet: Use a number 2 pencil. Do NOT use ink. If you did not bring a pencil, ask for one. You will continue to use the same bubble sheet you already used for Exam 1-3. Bubble answers on the bubble sheet for this exam. Only, if for some reason you are starting a new bubble sheet, write and fill in the bubbles corresponding to: - Your last name, middle initial, and first name. - ««Your ID number (the middle 9 digits on your ISU card) ««- Special codes K to L are your recitation section. Always use two digits (e.g. 01, 09, 11, 13). Please turn over your bubble sheet when you are not writing on it. If you need to change any entry, you must completely erase your previous entry. Also, circle your answers on this exam. Before handing in your exam, be sure that your answers on your bubble sheet are what you intend them to be. You may also copy down your answers on a piece of paper to take with you and compare with the posted answers. You may use the table at the end of the exam for this. When you are finished with the exam, place all exam materials, including the bubble sheet, and the exam itself, in your folder and return the folder to your recitation instructor. No cell phone calls allowed. Either turn off your cell phone or leave it at home. Anyone answering a cell phone must hand in their work; their exam is over. Best of luck, Dr. Soeren Prell

2 64. Which two temperature changes are equivalent? A) 1 C 1 K B) 1 F 1 C C) 1 K 1 F D) None of the above E) All of the above The Celsius scale and the Kelvin scale are offset by K, but a temperature difference of 1 C is the same as a temperature difference of 1 K. 65. As shown in the figure, a bimetallic strip, consisting of metal G on the top and metal H on the bottom, is rigidly attached to a wall at the left. The coefficient of linear thermal expansion for metal G is greater than that of metal H. If the strip is uniformly heated, it will A) Remain horizontal, but get longer. B) Remain horizontal, but get shorter. C) Curve out of the page. D) Curve upward. E) Curve downward. Both metals expand when heated. However, metal G expands more than metal H. Therefore the bi-metallic strip bends down.

3 66. Some properties of a certain glass are listed here: Density 2300 kg/m 3 Specific heat capacity 840 J/(kg C) Coefficient of thermal expansion ( C) -1 Thermal conductivity 0.80 W/(m C) A glass window pane is 2.7 m high, 2.4 m wide, and 9.0 mm thick. The temperature at the inner surface of the glass is 19 C and at the outer surface 4 C. How much heat is lost each hour through the window? A) 8.6 J B) J C) J D) J E) J Q kaδt L t 0.80 W/ m K ( ) 15 K ( m) ( ( )) m 2 ( ) ( 3600 s) J 67. Object 1 has three times the specific heat capacity and four times the mass of Object 2. The two objects are given the same amount of heat Q. If the temperature of Object 1 changes by an amount ΔT, the change in temperature of Object 2 will be A) 3/4 ΔT B) 4/3 ΔT C) 6 ΔT D) 12 ΔT E) ΔT Q m 2 c 2 ΔT 2 ΔT 2 ( )( 3c 2 ) Q m c 1 1 ΔT 4m 2 m 2 c 2 m 2 c 2 m 2 c 2 ΔT 12ΔT

4 68. If 50 g of lead (of specific heat 0.11 kcal/(kg C ) ) at 100 C is put into 75 g of water (of specific heat 1.0 kcal/(kg C ) ) at 0 C. What is the final temperature of the mixture? A) 2.0 C B) 25 C C) 6.8 C D) 50 C E) 2.0 C T m Pbc Pb T Pb,0 + m w c w T w m Pb c Pb + m w c w ( kg) 0.11 kcal/ kg K kg ( ( )) 100 o C ( ) 0.11 kcal/ ( kg K) 6.8 o C ( ) + ( kg) ( 1.0 kcal/ ( kg K) )( 0 o C) ( ) + ( kg) ( 1.0 kcal/ ( kg K) ) 69. For water, the latent heat of fusion is 334 kj/kg, the latent heat of evaporation is 2265 kj/kg, and the specific heat capacity is 4180 J/(kg K). The specific heat capacity of ice is 2050 J/(kg K). You have 1.0 kg of water at 0 C. After you remove 150 kj from the water you have A) 450 g of ice and 550 g of water at 0 C B) 1,000 g of water at 36 C C) 1,000 g of ice at 73 C D) 67 g of ice and 933 g of water at 0 C E) 550 g of ice and 450 g of water at 0 C The heat removed from the water will freeze some of the water before the temperature drops below 0 C. Only after all the water has frozen, will further heat removal result in decreasing the temperature. Removing 150 kj freezes 0.45 kg of water to ice. Q ml fusion m Q ( 150 kj) 0.45 kg L fusion 334 kj/kg ( )

5 70. A sample of an ideal gas is originally at a temperature of 10 C. What is the final temperature of the gas if both the pressure and volume are doubled? A) 10 C B) 40 C C) 120 C D) 620 C E) 860 C PV nrt PV T constant P F V F P 0V 0 T F P FV F T 0 2P 0 T F T 0 P 0 V 0 P 0 V 0 ( )( 2V 0 ) T 0 4T 0 4(283 K) 1130 K 860 o C 71. Dust particles in a grain elevator frequently have masses of the order of kg. If, to a first approximation, we model the dust particles as an ideal gas, what would be the rms speed of such a particle in air at 300 K? A) m/s B) m/s C) m/s D) m/s E) m/s v rms 3kT m ( ) 300 K ( ) J/K 10 9 kg ( ) m/s 72. An ideal Carnot engine operating between a warm reservoir of unknown temperature and a cold reservoir at 1.76 K has an efficiency of 40.0 %. What is the temperature of the warm reservoir? A) 2.93 K B) K C) K D) 106 K E) 46.4 K e ideal 1 T L T T H L 1.76 K T H 1 e ideal K

6 73. A car moves along the x-axis with zero acceleration. Which of the following graphs of either position (x) or velocity (v) versus time (t) represent the motion of the car? A) only graph a B) only graph b C) graphs a and b D) graphs c and d E) graphs b and c (Instantaneous) acceleration is the slope of velocity with time curve. An object moving with zero acceleration is represented by a velocity versus time curve with slope zero. Zero acceleration is a special case of constant acceleration. For zero acceleration, the position versus time curve has constant slope i.e. it is a straight line: x(t) x 0 + v 0 t at 2 x 0 + v 0 t

7 74. The eastward component of vector is equal to the westward component of vector and their northward components are equal. Which one of the following statements must be correct for these two vectors? A) The magnitude of vector must be equal to the magnitude of vector. B) Vector is antiparallel (in the opposite direction) to vector. C) The angle between vector and vector must be 90. D) Vector must be perpendicular to vector. E) Vector is parallel to vector. If we draw a coordinate system such that the x-axis points East and the y-axis points north, then A x B x ; A y B y! B B x 2 + B y 2 A ( ) x 2 + A y 2 A x 2 + A y 2! A 75. A woman is straining to lift a large crate, but without success because it is too heavy. We denote the forces on the crate as follows: P is the magnitude of the upward force being exerted on the crate by the person, C is the magnitude of the vertical contact force on the crate by the floor, and W is the weight of the crate. How are the magnitudes of these forces related while the person is trying unsuccessfully to lift the crate? A) P C B) P + C W C) P + C > W D) P + C < W E) P C W In the free-body diagram, C and P point up and W points down. Thus from Newton s 2 nd law: C + P W m a 0 and therefore C + P W

8 76. A 50.0-kg crate is being pulled along a horizontal frictionless surface. The pulling force is 10.0 N and is directed 20.0 above the horizontal. What is the magnitude of the acceleration of the crate? A) m/s 2 B) m/s 2 C) m/s 2 D) m/s 2 E) m/s 2 F x ma x a x F ( x m 10.0 N )cos 20.0o 50.0 kg ( ) ( ) m/s An object attached to a spring is pulled across a horizontal frictionless surface. If the force constant (spring constant) of the spring is 45 N/m and the spring is stretched by 0.88 m when the object is accelerating at 1.4 m/s 2, what is the mass of the object? A) 36 kg B) 24 kg C) 31 kg D) 28 kg E) 44 kg F ma kx m kx a ( )( 0.88 m) 45 N/m 1.4 m/s 2 ( ) 28 kg 78. How much kinetic energy does a 0.30-kg stone have if it is thrown at 44 m/s? A) 580 J B) 290 J C) 510 J D) 440 J E) 370 J KE 1 2 mv2 1 ( 0.30 kg) ( 44 m/s 2 )2 290 J

9 79. A block slides down a frictionless inclined ramp and experiences no significant air resistance. If the ramp angle is 17.0 above the horizontal and the length of the surface of the ramp is 20.0 m, find the speed of the block as it reaches the bottom of the ramp, assuming it started sliding from rest at the top. A) 115 m/s B) 7.57 m/s C) 19.6 m/s D) 10.7 m/s E) 87.4 m/s KE f + PE f KE 0 + PE 0 KE f PE mv2 mgh v 2gh 2( 9.8 m/s 2 )( 20.0 m)sin( 17 o ) 10.7 m/s 80. A block of mass m 34 kg and speed V is behind a block of mass M 81 kg and speed of 0.50 m/s as shown in the figure. The surface is frictionless and the blocks collide and couple. After the collision, the blocks have a common speed of 0.90 m/s. What is the magnitude of the impulse on the 34-kg block due to the collision? A) 32 N s B) 41 N s C) 73 N s D) 57 N s E) 14 N s Momentum is conserved in the collision. Therefore, the magnitude of the impulse on the lighter block is the same as the magnitude of the impulse on the heavier block. J Δp m Δv ( ) ( 81 kg) ( 0.90 m/s 0.50 m/s) 32 kg m/s

10 81. A Ferris wheel rotating at 20 rad/s slows down with a constant angular acceleration of magnitude 5.0 rad/s 2. How many revolutions does it make while slowing down before coming to rest? A) 6.4 B) 20 C) 3.2 D) 40 E) 99 ω 2 ω 0 2 2αΔθ Δθ ω 2 ω 0 2 2α ( 20 rad/s) rad 1 rev 6.4 rev 2 5 rad/s 2 2π rad ( ) 82. Let the orbital radius of a planet be R and let the orbital period of the planet be T. What quantity is constant for all planets orbiting the sun, assuming circular orbits? A) T/R 2 B) T 2 /R C) T/R D) T 2 /R 3 E) T 3 /R 2 Kepler s 3 rd law: T 2 R 3 4π 2 GM 83. A 0.25 kg harmonic oscillator has a total mechanical energy of 4.1 J. If the oscillation amplitude is 20.0 cm, what is the oscillation frequency? A) 1.4 Hz B) 2.3 Hz C) 4.6 Hz D) 3.2 Hz E) 0.96 Hz KE max 1 2 mv 2 max v max 2KE max m ; v max Aω f ω 2π 2KE max m 2π A 4.6 Hz

11 84. A 1.1-kg uniform bar of metal is 0.40 m long and has a diameter of m. When someone bangs one end of this bar, a Hz shock wave travels along the length of the bar and reaches the other end in s. What is the wavelength of the shock wave in the metal? A) 3.8 mm B) 2.2 mm C) 3.0 mm D) 3.4 mm E) 2.6 mm λ v f L / t f ( 0.40 m) Hz ( )( s) m 85. A block of wood is floating in a bathtub. A second block of the same type of wood sits on top of the first block, and does not touch the water. If the top block is taken off and placed in the water, what happens to the water level in the tub? A) It goes up. B) It goes down. C) It does not change. D) It cannot be determined without knowing the volumes of the two pieces of wood. E) It cannot be determined without knowing the density of the wood. The two pieces of wood have the same density. The buoyant force is equal to the weight of the two blocks and also equal to the weight of the displaced water. The weight of the blocks does not change when the second block is put in the water. Neither does the volume of the displaced water.

12 86. In a hydraulic garage lift, the small piston has a radius of 5.0 cm and the large piston has a radius of 15 cm. What force must be applied on the small piston in order to lift a car weighing 20,000 N on the large piston? Assume the pistons each have negligible weight. A) N B) N C) N D) N E) N F L F S F S A S F L π R 2 S A L A S A L π R F R 2 S 5.0 cm 2 L F L L 15 cm R L 2 ( 20 kn) 2.2 kn 87. You are using a wrench to loosen a rusty nut. Rank the arrangements from most effective to least effective in loosening the nut? A) 2 4, 1 3 B) 3 4, 1 2 C) 2, D) 2, 1 4, 3 E) 2 4, 1, 3 Because the forces are all the same, the only difference is the lever arm. The arrangement with the largest lever arm ( b) will provide the largest torque. The lever arm, between line of action and rotation axis, for (a) and (d) is the same and larger as for (c), since in (c) the force F is not perpendicular to the wrench.

13 88. You stand a distance d away from a speaker and you hear a certain intensity I of sound. If you decrease your distance from the speaker to d/3, what is the sound intensity at your new position? A) 3I B) 6I C) 9I D) 4I E) does not change at all For a source of power P, the intensity is given by I P/(4πd2). If the distance decreases by a factor of 3, the intensity must increase to 9 times its original value. 89. A mass attached to a vertical spring causes the spring to stretch and the mass to move downwards. What can you say about the spring s potential energy (PES) and the gravitational potential energy (PEG) of the mass during that process? A) B) C) D) E) both PES and PEG decrease PES increases and PEG decreases both PES and PEG increase PES decreases and PEG increases PES increases and PEG is constant The spring is stretched, so its elastic PE increases, because PES ½ kx2. The mass moves down to a lower position, so its gravitational PE decreases, because PEG mgh.

14 Laboratory final exam 90. In a certain experiment, we know that the magnitude of the velocity of a puck can be between 40 and 50 cm/s. We also know that the angle between the x axis and direction of this velocity can vary between 30 and 40 degrees. Find the maximum value of the x component of the velocity allowed by these ranges. A. 31 cm/s B. 32 cm/s C. 38 cm/s D. 43 cm/s E. 45 cm/s The x component of the velocity is v v cosθ. Therefore, the maximum value is: x ( ) ( ) v v cosθ 50 cm/s cos cm/s x,max max min 91. According to Kepler s third law, the relation between the period T of a satellite orbiting the Earth on a circular trajectory and the radius r of the orbit is: T πr Gm 2 4 If we measure the period and the radius for several such satellites, which of the following plots is expected to display a linear dependence? 3 Earth A. T versus r 2 B. T versus C. T versus r D. T versus r r E. T versus r 3 4πr 4π The equation above can be rewritten as T Gm Gm Earth straight line that goes through the origin and with slope Earth 4π r 3 2 Gm Earth, so T vs r 3/2 is a

15 92. A cart moves along a track. Its position is measured with an ultrasound motion detector clamped to one end of the track. The position and time data is fed onto a computer, and numerical derivatives are used to estimate the instantaneous velocity of the cart as a function of time. The results are shown in the graph below. What is the acceleration of the cart in the portion of the motion at t 4.0 s? A. 1.0 m/s 2 B. 1.5 m/s 2 C. 1.0 m/s 2 D. 1.5 m/s 2 E. 4.0 m/s 2 The acceleration of the cart is the slope of this graph. In the interval between 2 s and 6 s, the slope, and thus the acceleration, are constant: ( ) ( ) Δv 2 8 m/s a 1.5 m/s Δt 6 2 s 2

16 93. The following apparatus was used in experiment SF Static friction. A block of mass M rests on a horizontal ramp. Two light strings are attached to the block as shown. The strings go through a system of pulleys that have very little friction, and weights of masses m1 and m2 hang at the other end of the strings. When the following values are used, the block is at rest: M 25 g m1 4.5 g m2 4.0 g What is the magnitude of the static friction between the block and the ramp? A N B N C N D N E. This cannot be answered without the coefficient of static friction between the block and the ramp. The free body diagram of the block is shown to the right. The only two forces in the horizontal direction are T1 and the static friction, fs. Since the block is at rest, they must have equal magnitude. On the other hand, T1 must be equal to m1g because hanger 1, with mass m1, is also at rest. Mg Therefore, fs m1g N.

17 Physics 111 Final Exam KEY 64 A 74 A 84 B 65 E 75 B 85 C 66 D 76 C 86 D 67 D 77 D 87 D 68 C 78 B 88 C 69 A 79 D 89 B 70 E 80 A 90 D 71 C 81 A 91 E 72 A 82 D 92 B 73 C 83 C 93 D