F2019 Final Exam PHYS 211 221

Physics 211/221 Final Examination, Fall 2019 Page 1 of 21 University of Calgary Faculty of Science PHYSICS 211/221 ALL LECTURE SECTIONS Fall 2019 Final Examination December 18, 2019, 15h30 – 18h30 Time: 180 minutes. This is a closed-book exam worth a total of 45 points. Please answer all questions. Use of a calculator is allowed. You need the following: 1. THIS MULTIPLE QUESTION BOOKLET , which includes multiple choice exam questions and the formula sheet (last page). THIS BOOKLET WILL NOT BE HANDED IN. Make sure this question paper booklet contains 21 pages (including formula sheet). If you are missing any pages, get a new booklet from the exam supervisor. 2. A BUBBLE SHEET used to answer multiple choice questions. IT WILL BE HANDED IN. IMPORTANT: START by entering your ID NUMBER, NAME and COURSE ID on the bubble sheet. Also, using pen, black out the corresponding numbers below your ID and name. DO THIS NOW . Then wait for the Exam Supervisor to signal when to start the test. Please note that you can leave the room at any time after the first 30 minutes (after the signing-in process has been completed) and before 150 minutes of the exam. Students remaining after 150 minutes must remain seated for the duration of the exam until permitted to leave by the exam supervisor.

Physics 211/221 Final Examination, Fall 2019 Page 2 of 21 Final Questions (Total: 45 marks, 1 mark for each question) 1. Which of the following represents an inertial reference frame? a) A train slowing down as it pulls into the station. b) A car driving around a corner at constant speed. c) A bus driving down a steady incline at constant speed. d) An airplane accelerating down the runway during takeoff. 2. Shown in the figure is a motion diagram for an object moving along the x -axis. The sequence of the dots is labeled and the origin of the x -axis is indicated. When the object is at the position labeled 5, what are the signs of its velocity and acceleration? a) The velocity and acceleration are both negative. b) The velocity is positive and the acceleration is negative. c) The velocity and acceleration are both positive. d) The velocity is negative and the acceleration is positive. 3. Which of the following is NOT a true statement of one of Newton’s Laws of motion? a) Interacting objects exert equal and opposite forces on each other. b) An object in motion must have a net force acting on it to keep it in motion. c) If the direction of an object’s velocity changes, there must be a net force acting on it. d) An object in equilibrium has no net force acting on it. 4. If ? ⃗ = 3?̂ − 2?̂ and ? ⃗⃗ = 1.5?̂ + 5?̂ , what is the angle between the two vectors? a) 17˚ b) 73˚ c) 233˚ d) 107˚

Physics 211/221 Final Examination, Fall 2019 Page 4 of 21 7. A plane that is taking a turn in the air has two forces acting on it, gravity and the lift force, as shown in the picture. If the plane of mass ? 𝑝 , moving at constant speed 𝑣 𝑃 takes a turn of radius 𝑅 , what is the expression for the magnitude of the lift force, ? ? ? a) ? ? = ? 𝑃 ? + ? 𝑃 𝑣 𝑃 2 𝑅 b) ? ? = ? 𝑃 ? − ? 𝑃 𝑣 𝑃 2 𝑅 c) ? ? = ? 𝑃 √ ? 2 + 𝑣 𝑃 4 𝑅 2 d) ? ? = ? 𝑃 √ ? 2 − 𝑣 𝑃 4 𝑅 2 8. Consider the car traveling at a constant speed 𝑣 along a bumpy road, as shown in the picture. At which point is the normal force exerted on the driver by the seat the largest? a) ? b) ? c) ? d) ?

Physics 211/221 Final Examination, Fall 2019 Page 5 of 21 9. A force ? ? (?) = (+9.0 × 10 5 )? 2 − (1.8 × 10 4 )? acts on an object from time ? 𝑖 = 0 ms to time ? ? = 20 ms . ? ? is measured in N when t measured in s. What is the change in the object’s momentum? a) Δ? ? = +6.0 kg ⋅ m s b) Δ? ? = +6.0 kg ⋅ m s c) Δ? ? = +1.2 kg ⋅ m s d) Δ? ? = −1.2 kg ⋅ m s 10. A small block of mass m sits atop a larger block of mass M. A force is applied to the small block causing the entire ensemble to move to the right without any slippage between m and M. There is static friction between the small and large blocks and kinetic friction between the large block and the surface. Which of the Free Body diagrams below correctly labels all the forces on block M?

Physics 211/221 Final Examination, Fall 2019 Page 7 of 21 13. Buddy the Elf has a toy airplane ( m = 0.5 kg) on a string that he whirls around his head in a circle at a constant speed of 10 m/s. The circle is 80 cm in radius and is perfectly parallel to the ground. The figure to the right shows a top-down view of the situation. How much work does the force of tension do on the airplane to keep it moving in a circular path? a) ? = 0 J b) ? = 62.5 J c) ? = 25 J d) ? = 2.5 J 14. On a cold day you rub your hands together to warm them up. With each pass, you press your hands together with a force of 30 N over a distance of 10 cm while moving at constant velocity of 1.5 m/s. How much thermal energy do you put into your hands in one pass (i.e. one rub)? The coefficient of kinetic friction between your palms is 0.40. a) ∆? ?ℎ = 1.2 J b) ∆? ?ℎ = 120 J c) ∆? ?ℎ = 3.0 J d) ∆? ?ℎ = 45 J 15. The potential energy for a particle moving in one dimension in some region of space is given by the function ?(?) = 8? 4 − 3? 2 + 2? − 5 , where the units of U are in joules when x is measured in metres. What is the force acting on the particle when it is at the position x = 3.50 m? a) ? ? = −1350 N b) ? ? = −333 N c) ? ? = +1350 N d) ? ? = +333 N

Physics 211/221 Final Examination, Fall 2019 Page 8 of 21 16. A snail has the position vs time graph seen to the right. At what time or times does the snail have an instantaneous velocity of 0 mm/s? a) t = 0.5 s, 5.0 s, and 9.0 s b) t = 2.5 s and 7.0 s c) t = 0 s d) t = 1.5 s and 9.5 s 17. Santa is standing on an icy (frictionless) roof that has a 37˚ angle. If he slips when he is 15 m from the edge, how long does it take for him to fall off the roof? a) Δ? = 2.3 s b) Δ? = 5.1 s c) Δ? = 3.8 s d) Δ? = 2.0 s 18. The Martian Rover watches a rock with an initial velocity of -1.5 m/s ?̂ fall 43 m down a cliff face on Mars. If it takes 4.4 seconds for the rock to hit the ground, what is the acceleration due to gravity on Mars? a) ? ⃗ = −5.1 ?̂ m/s 2 b) ? ⃗ = −1.9 ?̂ m/s 2 c) ? ⃗ = −3.8 ?̂ m/s 2 d) ? ⃗ = −4.3 ?̂ m/s 2

Physics 211/221 Final Examination, Fall 2019 Page 10 of 21 22. Shown below is the position vs time graph for an object moving in the x -direction. In each of t he motion diagrams, the time between dots is ∆ t = 1 s. Which motion diagram corresponds to this position vs time graph? a) b) c) d) 23. A car stopped at a stoplight accelerates forward at a = 5.0 m/s 2 for 6.0 s, after which it drives at constant speed for another 4.0 s. What is the magnitude of the car’s displacement after the 10 s of motion? a) |∆? ⃗| = 110 m b) |∆? ⃗| = 170 m c) |∆? ⃗| = 210 m d) |∆? ⃗| = 250 m

Physics 211/221 Final Examination, Fall 2019 Page 11 of 21 24. Shown in the diagram are two forces acting on an object, where each division on the graph represents 1 N. A third force is applied to the object so that the net force acting on it is zero. What is the third force ? ⃗ 3 ? a) ? ⃗ 3 = −4?̂ − 3?̂ N b) ? ⃗ 3 = −4?̂ + 3?̂ N c) ? ⃗ 3 = +4?̂ + 3?̂ N d) ? ⃗ 3 = +4?̂ − 3?̂ N 25. A car is driving without skidding up a hill at constant speed on a windy day. Which of the following forces is NOT acting on the car? a) Gravity b) Drag force c) Normal force d) Kinetic friction 26. A high-speed drill reaches its peak angular velocity of 2500 rpm in 0.450 s. How many revolutions does it go through in that time, assuming its angular acceleration is constant? a) ∆𝜃 = 4.22 rev b) ∆𝜃 = 9.38 rev c) ∆𝜃 = 13.0 rev d) ∆𝜃 = 18.8 rev

Physics 211/221 Final Examination, Fall 2019 Page 13 of 21 Questions 29-30 are all related to the following situation: A boy and his dad are throwing snowballs in Bowness Park, trying to hit a tree. The boy throws his snowballs with speed 𝑣 𝑖? = 4.55 m/s at an angle of 0 o above the horizontal from height ? 𝑖? = 0.95 m while his dad throws them with a speed of 𝑣 𝑖? = 10.7 m/s at the angle of 65 o above horizontal from a height of ? 𝑖? = 1.50 m . 29. How long is the ball thrown by the dad in the air, assuming it does not hit the tree and lands on the ground ? a) Δ? = 1.18 s b) Δ? = 1.98 s c) Δ? = 2.12 s d) Δ? = 2.31 s 30. The boy hits the tree at height ? ? = 0.25 m above the ground. How far away from the tree is he standing? a) Δ? = 2.00 m b) Δ? = 1.72 m c) Δ? = 1.22 m d) Δ? = 1.03 m

Physics 211/221 Final Examination, Fall 2019 Page 14 of 21 Questions 31-33 are all related to the following situation: An 𝛼 -particle ( ? 𝛼 = 6.65 × 10 −27 kg) , moving with initial velocity of 𝑣 ⃗ 𝑖 𝛼 = 9.81 × 10 6 m s ?̂ collides perfectly elastically with an atom ? , initially at rest. The 𝛼 -particle bounces back and its velocity is measured to be 𝑣 ⃗ ? 𝛼 = −8.77 × 10 6 m s ?̂ . 31. What is the magnitude of the initial momentum of the system? a) ? 𝑖 = 6.92 × 10 −21 kg m s b) ? 𝑖 = 6.52 × 10 −20 kg m s c) ? 𝑖 = 5.83 × 10 −20 kg m s d) ? 𝑖 = 1.24 × 10 −19 kg m s 32. What is the impulse delivered to the atom ? ? a) ? ⃗ = +6.92 × 10 −21 kg m s ?̂ b) ? ⃗ = +6.52 × 10 −20 kg m s ?̂ c) ? ⃗ = +5.83 × 10 −20 kg m s ?̂ d) ? ⃗ = +1.24 × 10 −19 kg m s ?̂ 33. Which of the following is true about the system during the collision? a) The total momentum is conserved, the total mechanical energy is not conserved. b) Both the total momentum and the total mechanical energy are conserved. c) The total momentum is not conserved, the total mechanical energy is conserved. d) Neither the total momentum nor the total mechanical energy are conserved.

Physics 211/221 Final Examination, Fall 2019 Page 16 of 21 Questions 37-38 are all related to the following situation: Max the dog is forced to pull the Grinch’s sled laden with stolen presents (mass = 1500 kg) up a 10˚ incline. The coefficients of static and kinetic friction between the sled and the snow are  s = 0.27 and  k = 0.15 respectively. 37. When the sled is stationary and Max is not pulling on the rope, what is the magnitude and direction of the static friction force on the sled? a) ? ? = 2550 N up the slope b) ? ? = 2550 N down the slope c) ? ? = 3910 N up the slope d) ? ? = 3910 N down the slope 38. With how much force does Max have to pull on the sled to just get it to start moving uphill, assuming Max pulls it straight up the slope? a) ? = 2550 N b) ? = 1360 N c) ? = 6470 N d) ? = 3910 N

Physics 211/221 Final Examination, Fall 2019 Page 17 of 21 Questions 39-40 are all related to the following situation: Bumble the Abominable Snowbeast is pushing an 800 kg block of ice over a rocky surface (  k = 0.31) at a constant velocity. He is pushing with a constant force at a 30˚ angle downward (since he’s taller than the block). 39. How much work does Bumble do to push the block 100 m across the surface? a) ? = 3.4 × 10 3 J b) ? = 2.4 × 10 3 J c) ? = 3.0 × 10 5 J d) ? = 2.4 × 10 5 J 40. Sometime later, Bumble starts pushing the block with a constant force of 3000 N (at the same angle) and the block moves at a constant velocity of 1.5 m/s. How much power does Bumble supply? a) 𝑃 = 4500 W b) 𝑃 = 3900 W c) 𝑃 = 2300 W d) 𝑃 = 1500 W

Physics 211/221 Final Examination, Fall 2019 Page 19 of 21 Questions 44-45 are all related to the following situation: Two children, Alice and Bob, are playing on a see-saw in a park of total length L = 7.60 m. Bob’s mass is m B = 32.7 kg and Alice’s mass is m A = 30.8 kg. Each child is sitting at the end of the see- saw and the fulcrum (pivot point) is directly in the centre, as shown in the diagram. 44. What is the torque on the see-saw about the fulcrum from Alice 𝜏⃗ ? when she is at the location shown in the diagram (i.e., when Bob is at the ground)? a) 𝜏⃗ ? = (+199 N⋅m) 𝑘 ̂ b) 𝜏⃗ ? = (+1130 N⋅m) 𝑘 ̂ c) 𝜏⃗ ? = (−199 N⋅m) 𝑘 ̂ d) 𝜏⃗ ? = (−1130 N⋅m) 𝑘 ̂ 45. In order to balance the see-saw, the children use a sandbag of mass m = 10.0 kg. Where must they place the sandbag so that the see-saw will be in static equilibrium with both children on either end? a) 0.241 m to the right of the fulcrum b) 0.241 m to the left of the fulcrum c) 0.722 m to the right of the fulcrum d) 1.44 m to the right of the fulcrum

Physics 211/221 Final Examination, Fall 2019 Page 20 of 21 FORMULA SHEET K INEMATIC EQUATIONS FOR CONSTANT ACCELERATION : K INEMATIC EQUATIONS FOR CONSTANT ANGULAR ACCELERATION : ? ? = ? 𝑖 + 𝑣 𝑖? ∆? + 1 2 ? ? ∆? 2 ; ∆? = ? ? − ? 𝑖 𝜃 ? = 𝜃 𝑖 + 𝜔 𝑖 ∆? + 1 2 𝛼∆? 2 ; ∆? = ? ? − ? 𝑖 𝑣 ?? = 𝑣 𝑖? + ? ? ∆? 𝜔 ? = 𝜔 𝑖 + 𝛼∆? 𝑣 ?? 2 = 𝑣 𝑖? 2 + 2? ? ∆? ; ∆? = ? ? − ? 𝑖 𝜔 ? 2 = 𝜔 𝑖 2 + 2𝛼∆𝜃 ; ∆𝜃 = 𝜃 ? − 𝜃 𝑖 S OLUTIONS TO A QUADRATIC EQUATION : I NTEGRALS : ?? 2 + ?? + ? = 0  ? = −?±√? 2 −4?? 2? Derivatives: ? ?? (? ? ) = ?? ?−1 ? ?? (? + ?) = ?? ?? + ?? ?? ? ?? (??) = ? ?? ?? (? = constant) ∫ ? ? ?? ? 𝑓 ? 𝑖 = ? ?+1 ? + 1 ] ? 𝑖 ? 𝑓 = ? ? ?+1 ? + 1 − ? 𝑖 ?+1 ? + 1 (? ≠ −1) ∫(? + ?)?? ? 𝑓 ? 𝑖 = ∫ ? ?? ? 𝑓 ? 𝑖 + ∫ ? ?? ? 𝑓 ? 𝑖 ∫(??)?? ? 𝑓 ? 𝑖 = ? ∫ ? ?? ? 𝑓 ? 𝑖 (? = constant) T RIGONOMETRY : Law of Cosines: ? 2 = ? 2 + ? 2 − 2?? cos ? Law of Sines: sin ? ? = sin ? ? = sin ? ? Pythagorean Theorem: ? 2 = ? 2 + ? 2 ; sin 𝜃 = opp hyp ; cos 𝜃 = adj hyp ; tan 𝜃 = opp adj V ECTOR A LGEBRA IN 2D For 𝑅 ⃗⃗ = 𝑅 ? ?̂ + 𝑅 ? ?̂ |𝑅| = √𝑅 x 2 + 𝑅 ? 2 , tan 𝜃 = 𝑅 ? 𝑅 ? For ? ⃗ = ? ? ?̂ + ? ? ?̂ , ? ⃗⃗ = ? ? ?̂ + ? ? ?̂ A ⃗⃗ ⋅ ? ⃗⃗ = ?? cos(𝜃) ? ⃗ ⋅ ? ⃗⃗ = ? ? ? ? + ? ? ? ? |? ⃗ × ? ⃗⃗ | = ?? sin(𝜃) ? ⃗ × ? ⃗⃗ = (? ? ? ? − ? ? ? ? )𝑘 ̂ G RAVITY ? ? = ?𝑀? ? 2 Near the Earth ’s surface: ? ? = ??? Outside a spherically symmetric mass distribution: ? ? = − 𝐺?? ? E LASTICITY ? ? = −𝑘∆? ? ?𝑝 = 1 2 𝑘(∆?) 2 F ORCES ? 𝑘 = 𝜇 𝑘 ? ? ? ? ≤ 𝜇 ? ? ? ? ? = ?? ? ???? = 1 2 ???𝑣 2