Midterm 1

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University of Illinois, Urbana Champaign *

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102

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Physics

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Apr 3, 2024

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pdf

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This question will ask about how you would solve the problem described below. You wish to pilot a small boat across a rapidly flowing river as shown in the diagram. The river flows in the +z-direction with a velocity of Uyiyer = 4 m/s and is dyiyer = 150 m across. You know your boat travels with a speed |Upoq:| = 8 m/s. Your destination is the dock straight across from your boat's starting position. This problem-solving plan has a missing step: 1. Label the diagram with the quantities given in the problem. 2. Draw a velocity vector diagram that will steer the boat to the dock. 3. Missing Step Which option best fills in the missing step to steer the boat to the dock? (a) Vector add the velocity vectors to find the net velocity of the boat. (b) Use only the boat speed to find the net velocity of the boat. (c) Add the magnitudes of the velocity vectors to find the net velocity of the boat. Select all possible options that apply. There is exactly 1 correct option in the list above. @ This question is complete and cannot be answered again. = (a) Vector add the velocity vectors to find the net velocity of the boat.

Aballis thrown at an angle 6 with initial velocity vp. Which plot best represents the y-component of the ball's velocity as it travels through the air? Define positive , to point upward. A B c D E +,/ +v,/ +v,/ +vy/ +,/ (@) Plot A (b) Plot B () PlotC (d) Plot D (e) Plot E Select all possible options that apply. There is exactly 1 correct option in the list above. @ Which is a correct equation to describe the x-component of the ball's motion? Assume o = 0 and vy,; is the x-component of the initial velocity. (@) @ = vyt Select all possible options that apply. There is exactly 1 correct option in the list above. @ This question is complete and cannot be answered again. r I EEEEEE—————————. (d) Plot D (a) z = ozt

_ Two identical balls are thrown from a tower at the same time, at the same height, H, and with the same initial speed. Ball A s thrown horizontally. Ball B at an angle 6 = 45° above the horizontal as shown. Which one hits the ground first? (a) Ball B (b) Ball A (c) Both balls hit the ground at the same time. Select all possible options that apply. There is exactly 1 correct option in the list above. @ While traveling through the air, Ball B reaches a maximum height of 7.5 m above the ground. The height of the tower it was thrown from is H = 6 m. What was the initial y-component of Ball B's velocity? (@) voy = 12.12mjs (b) vgy = 3.83m/s (c) voy = 5.42mfs Select all possible options that apply. There is exactly 1 correct option in the list above. @ This question is complete and cannot be answered again. (b) Ball A (©) voy = 5.42mfs

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Andie s riding a bicycle at 4 m/s. She then speeds up at a steady rate of 4 m/s? until her speed is 10 m/s. For how much time was Andie’s speed changing? (@0.25s (b)35s ©1s d)25s (©)15s Select all possible options that apply. There is exactly 1 correct option in the list above. @ Which distance-time plot best represents Andie's position while she speeds up? H i @ im 3 3 ®) ime © ime Select all possible options that apply. There is exactly 1 correct option in the list above. @

_ A student in PHYS 101 pulls a crate that weighs 800 N across a floor that has friction. The crate slides across the floor at a constant speed of 5.5 m /s. The student applies the force, F' = 450 N at an angle of § = 30° with respect to the horizontal, as shown on the diagram. What is the magnitude of the kinetic frictional force acting on the crate? (@) F; = 225N (b) Cannot be determined without knowing the coefficient of kinetic friction () F;=389.TN Select all possible options that apply. There is exactly 1 correct option in the list above. @ Which Free Body Diagram below best describes this situation? /F' |4N g |>’ Fiic l I Fric Frec l w w w A B c (a) Figure A (b) Figure B (c) Figure C Select all possible options that apply. There is exactly 1 correct option in the list above. @ This question is complete and cannot be answered again. () Fy = 389.7TN (o) Figure C

_ Three blocks, each of mass m = 40 kg are pushed across a frictionless floor as shown in the figure. With what force must you push the blocks to achieve an acceleration of a = 3.5 m/s*? (a) F=280N (b) F = 420N (c) F=11IN (d) F=140N (e) F = 34N Select all possible options that apply. There is exactly 1 correct option in the list above. @ What is the magnitude of the force exerted on box B by box A? (@) F4 = 420N (b) F 4 = 140N (c) Fga=0N (d) Fp 4 = 34N (e) Fp4 = 280N Select all possible options that apply. There is exactly 1 correct option in the list above. @ This question is complete and cannot be answered again. (b) F = 420N (e) Fpu = 280N

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_ == In your hand you are holding a book that has a weight of 530 N. While your hand moves the book upward, the normal force of your hand supporting the book is 590 N. What are the magnitude and direction of the book's acceleration? Assume the -+y direction points upward. (a)a=9.8m/s (b)a = +6.1 m/s” ©a=+L1m/s’@ (da=-11m/s* @ a=—6.1m/s* Select all possible options that apply. There is exactly 1 correct option in the list above. @ Which of the following is the correct Newton's Third Law reaction force pair with the force your hand exerts on the book? (a) The weight of your hand. (b) The weight of the book. (c) The normal force of the book on the hand. Select all possible options that apply. There is exactly 1 correct option in the list above. @ This question is complete and cannot be answered again. (c)a=+11m/s® (c) The normal force of the book on the hand.

| A block of mass M = 8 kg is on a rough, horizontal table. A rope pulls the block by applying a horizontal force F' = 2 N. The block remains stationary. F ¥ >+X The coefficient of static friction for the block on this table is ;15 = 0.35. What are the magnitude and direction of the static friction force F's acting on the block? (a) F'y = 27.4 N to the right (b) F, = 2 N to the left (@ (c) F's = 2 N to the right (dFs=0N (e) F's = 27.4 N to the left Select all possible options that apply. There is exactly 1 correct option in the list above. @ This question is complete and cannot be answered again. = (b) Fy = 2 N to the left

Block 1 with mass m; is on a frictionless inclined plane of angle 8 and is connected by a cord over a small frictionless pulley to a Block 2 of mass m;, hanging vertically. We find that, when released, block 1 moves up the incline and block 2 moves downward. Which two equations below are an appropriate application of Newton's Second Law for the two blocks? The coordinate system used for Block 1 has the x-axis along the incline and the y-axis perpendicular to the incline; The coordinate system for Block 2 has the y-axis pointing vertically. (@) Block 1: T +mygeosf = mia Block 2: T~mag = —maa (b) Block 1: T'—mygsinf = mya @ Block 2: T~mag = —maa (c) Block 1: T—mygsind = Block 2: T~mpg = maa —ma Select all possible options that apply. There is exactly 1 correct option in the list above. @ Suppose that m; = 7.5 kg and & = 60°. What must be the mass of Block 2 (mn3) for the two block system to be in equilibrium (ie., a = 0)? (@) my = 8.66 kg (b)my = 3.75 kg (©)my = 248 kg (d)ymy = 6.5kg @ (e)my =T.5kg Select all possible options that apply. There is exactly 1 correct option in the list above. @ This question is complete and cannot be answered again. r- - 000000n0nn0n0nnnnnnnnnnnnn] (b) Block 1: T—mygsinf = mya Block 2: T—mag = —maa (d)my = 6.5kg

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A steel sphere islaunched horizontallyfrom a smallspring- launcher. The launcher sit on a platiorm and the sphoro islaunched from a height A; = 1.6 m above the floor The sphere ands n a bucket siting on a box located an unknown distance d from the end of the platiorm and By = 0.9 m above the foor as shown i the figure. How long does it take the sphere toustreach the top of the bucket? @ 0085 (0)035s@ ©0s5s Select all possile option that appy. Thera s xactly 1 coractapton n th st above. @ Now the systamis adusted so the spring launcher st aims upward at an e & = 60° from hrizonta. The sphere s launched from the same hight ; = 1.5 m above the floc. Th buck is moved 0.2 new locaton,digesy = 2 m rom the end o theplatform and is hy = 0.9 m above th floor a5 shown i the Faure. What must be the launch velocity g of the ball bearings from the launcher so that they land n the bucket? (@2 = 6.86ms @ (b)vo = 8.08mis ©w=632ms@ @ =361 mis ©) v =5.23ms Select all possile ostions that apoy. Thers s xacty 1 corect ogtion nth st sbove. @ This question i complete and cannot be answered again ©0355 (@) % = 5.23ms Ertor in question 2; fulcredit given to all students for the vO question only.

Consider two masses, connected by a massless string over a massless, frictionless pulley as shown in the diagram. The masses are m; = 2 kg and my, = 6 kg. The system is released from rest in the position shown in the figure. After the system has been released, which relationship for the magnitude of the tension in the string, T, is correct? @T <myg (b) T =mg ©T>myg@ Select all possible options that apply. There is exactly 1 correct option in the list above. @ After the system is released, how long does it take for 7 to travel a vertical distance y = 3 m? (@)1.107s (6)0.782s (©)1.245 Select all possible options that apply. There is exactly 1 correct option in the list above. @ This question is complete and cannot be answered again. - | - 000000000000 ] ©T >mg (a)1.107s

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