= y(x, t) =A cos (!t + kx)


 Natalie Gilbert
 1 years ago
 Views:
Transcription
1 A harmonic wave propagates horizontally along a taut string of length L = 8.0 m and mass M = 0.23 kg. The vertical displacement of the string along its length is given by y(x, t) = 0. m cos(.5 t x), where x is measured in meters and t in seconds.. (7 points) What is the tension, T, in the string? a. T = 0.0 N b. T = 0.2 N c. T = 0.29 N d. T = N e. T = N v prop =! k = s T µ y! 2 L =) T = µ!2 k 2 = M L k 2 = =0.0 N x 2. (7 points) What is the maximum acceleration in the ydirection of any point along the string? a. a <=> =.50 m/s 2 b. a <=> = m/s 2 c. a <=> = 0.50 m/s 2 d. a <=> = 0.05 m/s 2 e. a <=> = m/s 2 y(x, t) =A cos(!t + kx) d 2 y dt 2 = a y(x, t) =! 2 A cos(!t + kx) =) a max,y =! 2 A =(.5) 2 0. =0.225 m/s 2 3. (5 points) In which direction is the wave propagating? a. +x direction b. x direction c. +y direction y(x, t) =A cos (!t + kx) When time (t) increases, then the position (x) must decrease in order for the value of the cosine to remain constant.
2 A block (which you should treat like a point particle) has mass m =.55 kg and slides with initial speed v B in the +x direction. It collides with a rod of length L =.3 m and mass M = 30.3 kg, which is initially at rest and oriented perpendicular to the path of the block. The block hits the rod a distance D = 0.39 m from the center of the rod. After the collision, the block is at rest and the rod spins with angular velocity of ω E = 28 rad/s. Everything is on top of a horizontal frictionless table, and the rod has a fixed frictionless pivot through its center that allows it to rotate freely but keeps its center from moving. 4. (7 points) Which of the following statements best describes the collision? a. Neither the angular momentum about the pivot nor the linear (translational) momentum are conserved. b. The angular momentum about the pivot is conserved, but the linear (translational) momentum is not conserved. c. The angular momentum about the pivot and the linear (translational) momentum are both conserved. d. The linear (translational) momentum is conserved, but the angular momentum about the pivot is not conserved. e. There is not enough information provided to answer this question. The pivot exerts an external force on the block/rod system to keep the center of the rod from sliding to the right upon impact of the block. 5. (7 points) What was the initial speed of the block? a. v B = m/s b. v B = m/s c. v B = m/s d. v B = m/s e. v B = m/s L i = L f mv i D = I rod! f = =) v i = 2 ML2! f md = m/s 2 ML2! f = 2 (30.3)(.3)2 28 (.55)(0.39) 6. (5 points) Suppose the experiment is repeated using new block that has the same mass and initial speed as in the original situation, but is made of a different material so that it bounces back and ends up moving in the x direction after the collision. How would the final angular velocity of the rod in this new case, ω HIJ, compare to the final angular velocity of the rod in the original case ω E? a. ω HIJ = ω E b. ω HIJ > ω E c. ω HIJ < ω E In the second case, the block will have a negative value of angular momentum (if it had positive before the collision), so to conserve angular momentum, the rod must spin faster in the second case.
3 A block of mass M slides on a frictionless surface with a velocity V. It strikes an identical block of mass M that is at rest and is attached to an ideal spring of spring constant k. Before the collision, the spring is not compressed and the collision takes place very quickly before the spring has time to compress appreciably. After the collision, the blocks stick together. 7. (7 points) Immediately after the collision, the blocks slide to the right and the spring is compressed. By how much is the spring shortened, ΔL, before the blocks are pushed to the left? a. ΔL = 2MV P /k b. ΔL = MV P /(2k) c. ΔL = MV P /k d. ΔL = 4MV P /k P i = P f =) MV =(2M)V f =) V f = V/2 =) e. ΔL = MV P /(4k) 2 k( L)2 = 4 MV 2 r M =) L = 2k V 8. (7 points) After the collision, the blocks undergo simple harmonic motion. How much time does it take after the collision for the blocks to return to their starting position (spring at equilibrium length) for the first time? (Hint: the blocks will oscillate through this position repeatedly. The problem refers to the first occurrence.) M =) E tot = 2 (2M) V 2 V 2 = 4 MV 2 M k a. Δt = 4π 2M k b. Δt = 2π k 2M c. Δt = 2π 2M k d. Δt = 2π k 2M! =2 f = 2 r P = r Mtot k M tot =) P =2 k r 2M t = P/2= k e. Δt = π 2M k 9. (5 points) After the collision, the blocks undergo simple harmonic motion. If the initial velocity V is increased, the frequency of the oscillation a. decreases. b. stays the same. c. increases. The initial speed of the block will affect the oscillation amplitude. However, for simple harmonic motion, oscillation frequency does NOT depend on oscillation amplitude.
4 A Tshaped object is made by combining two identical, uniform rods of equal mass M and length L. The thickness of each rod is negligible. The object can be rotated around the four different axes shown by the dashed lines. 20. (5 points) Rank in increasing order the moments of inertia, I T to I U for rotation about the dashed lines. a. I P < I T < I U < I V b. I T < I P < I U < I V c. I T < I P < I V < I U 2. (7 points) Now consider the situation depicted above in diagram #2 and imagine that the object is oscillating as a pendulum around the axis shown. Gravity acts downward as indicated. What is the correct expression for the oscillation frequency, ω? a. ω = 3g 2L b. ω = 2g 3L I = 2 ML2 I 2 = 3 ML2 ~g I 3 = 3 ML2 + ML 2 = 4 3 ML2 I 4 = 3 ML2 + M(L/2) 2 = 7 2 ML2 Rod at top of T does not contribute to oscillation frequency because it has no moment of inertia about the given axis (width of each rod is neglected). c. ω = 2g L d. ω = 2 g L e. ω = 2 g L 22. (7 points) Now consider the situation depicted above in diagram #3. If the mass of each rod is M = 2. kg and each has a length of L =.7 m, what is the moment of inertia of the object around the axis shown? a. I V = 5. kg m 2 b. I V = 6. kg m 2 c. I V = 8. kg m 2 d. I V = 7.4 kg m 2 e. I V = 4.0 kg m 2 I 3 = I top,3 + I vert,3 = 0+MD ML2 D = L =) I 3 = ML ML2 = 4 3 ML2 = 4 3 (2. kg)(.7 m)2 =8. kgm 2
5 A uniform rod of length d and mass M is inclined at 45 with respect to the horizontal. On one end of the rod is an ideal pivot. A massless string is attached to the other end of the rod. The string runs vertically upward, then over a frictionless pulley, and a block of mass m is hung from the other end of the string. In this configuration, the system is in equilibrium. 23. (7 points) What is the mass of the block, m? a. m = 3M b. m = 2M c. m = 2M/3 d. m = M/2 e. m = M/4 24. (5 points) What is the horizontal force on the pivot? a. 0 b. Mg/ 2 c. Mg d Mg cos 45 = T (d cos 45 ) 2 d T = mg =) Mg cos 45 = mg (d cos 45 ) 2 =) m = M/2 The tension in the rope acts vertically, so the rope exerts no horizontal force on the rod. Thus, the pivot can exert no horizontal force or the rod s CM would accelerate horizontally. d 45 M g m 25. (7 points) Consider the case where the mass of the rod is M = 30 kg, and its length is d = 3 m. At a particular moment, the string is cut and the rod is free to rotate about the pivot. What is the angular acceleration, α, of the beam immediately after the string is cut? a. α = 3.9 rad/s 2 b. α = 3.47 rad/s 2 c. α = 4.9 rad/s 2 d. α = 6.94 rad/s 2 e. α = 2.45 rad/s 2 = = Mg d 2 cos 45 I rod,end 3 Md2 = 3g 2 p 2 d = p 3g = d 3 p 8 =3.47 rad/s 2
6 Mass m T initially has a speed of V \ in the +x direction along a frictionless horizontal floor. It collides with mass m P, which is initially at rest. Immediately after the collision m T is moving in the x direction with speed V TE = V \ /4 and m P is moving in the +x direction with speed V PE = V \ / (5 points) Is this collision elastic? a. There is not enough information provided to determine whether the collision is elastic. b. No, the collision is not elastic. c. Yes, the collision is elastic. 27. (7 points) Which of the following correctly expresses the relationship between the masses? a. m T = 2m P b. m T = m P /2 c. m T = (4/3)m P V approach = V 0 V separate = V 0 /4+V 0 /2=3V 0 /4 =)V approach >V separate m V 0 = m 2 V 0 /2 m V 0 /4=) 5 4 m = 2 m 2 d. m T = (3/4)m P e. m T = (2/5)m P =) m = 2 5 m (7 points) Mass m P continues to the right and slides up a frictionless ramp. It momentarily comes to rest at a maximum height h above its starting height on the floor before sliding back down. Which of the following correctly expresses the maximum height h reached by m P? a. h = V \ P /(2g) b. h = 4V \ P /(3g) c. h = V \ P /(8g) d. h = 3V \ P /(4g) e. h = V \ P /(4g) E m2,after collision = E m2,top of ramp 2 2 m V0 2 = m 2 gh 2 =) h = V 2 0 8g
7 Block A has mass M^ = 4 kg and slides on a frictionless inclined plane. It is connected to a hanging block B of mass M _ by a massless string that runs over a frictionless pulley. The incline makes an angle of θ = 30 with horizontal. The acceleration of block A up the incline is a = 2. m/s (7 points) As block A moves a distance.3 m along the incline, what is the work done on it by the tension in the string, W^,b? a. W^,b = J b. W^,b = 4.59 J c. W^,b = 55. J d. W^,b = 0.92 J e. W^,b = 0 J T M A g sin = M A a =) T = M A (a + g sin ) = (4 kg)( sin 30 ) m/s 2 = kg m/s 2 W A,T = T d = = J 30. (5 points) As block A moves a distance.3 m up the incline, how does the magnitude of the work done on it by the tension in the string W^,b, compare to magnitude of the work done on it by gravity, W^,d? a. W^,b = W^,d b. W^,b > W^,d c. W^,b < W^,d W net = W A,T W A,g = K>0 =) W A,T >W A,g 3. (7 points) Now assume that there is friction between block A and the plane and that both blocks have the same mass M^ = M _ = M. For the geometry shown, what is the minimum coefficient of static friction, μ f, needed to hold block A stationary if it is initially released from rest? a. μ g = 0.74 b. μ g = 0.67 c. μ g = 0.82 d. μ g = 0.58 e. μ g = 0.49 Block B: T = Mg Block A: T = Mgsin + f s =) f s = Mg( sin ) µ s N = µ s Mgcos = Mg( sin ) =) µ s = sin cos = =0.58
8 A child is playing with a new toy that consists of a ball of mass m = 0.87 kg tied to the end of a string of length ll = 0.3 m. The child swings the toy above her head so that it moves with uniform circular motion in a horizontal plane. The string makes an angle of 63 with respect to the vertical arm of the child. The ball should be treated as a point particle. 32. (7 points) What is the tension in the string? a. T = 8.8 N b. T = N c. T = 8.53 N d. T = 4.35 N e. T = 9.58 N F y =0=) T cos = mg T = mg = cos cos 63 = 8.8 N 33. (5 points) Say the speed of the ball in the original problem is V \. Suppose we increase mass of the ball but keep the length of the string the same. If we want the angle that the string makes with the vertical to be the same as in the original problem, what would the new speed of the ball have to be? a. V HIJ > V \ b. V HIJ < V \ c. V HIJ = V \ F x = ma cent =) T sin = m V 2 R =) mg tan = m V 2 ` sin V 2 = `g sin tan (independent of m) 34. (7 points) Now consider once again the geometry shown in the figure above. Assuming the ball travels with tangential speed V \ as it travels along the circular path shown, what is the magnitude of the angular momentum of the ball as it orbits the central vertical axis? a. L = m ll V \ sin θ b. L = m ll V \ cos θ c. L = < ll V \ P sin θ d. L = < ll V \ P tan θ e. L = m ll V \ tan θ ~L = ~p ~ R =) L = mv 0 R = mv 0` sin
9 Two houses are located on opposite sides of a river as shown. The width of the river is W = 247 m, and the river flows in the +y direction with speed V m,n =.3 m/s relative to the houses. A boat sets off from the left house, moving with velocity V _,m relative to the river. The xcomponent of V _,m is 2. m/s and the ycomponent of V _,m is 3. m/s. 35. (7 points) What is the speed of the boat as measured in the reference frame of the houses? a. V _,n = 3.74 m/s b. V _,n = 2.77 m/s c. V _,n = 4.88 m/s d. V _,n = 4.4 m/s e. V _,n = 2.47 m/s ~V B,H = ~ V B,R + ~ V R,H x : (V B,H ) x =(V B,R ) x +(V R,H ) x =2. m/s + 0 y : (V B,H ) y =(V B,R ) y +(V R,H ) y =3. m/s +.3 m/s = 4.4 m/s V B,H = p =4.88 m/s 36. (7 points) When the boat reaches the other side of the river, how far is it from the nearest house? a m b m c. 2.7 m d m e m t cross = W = 247 (V B,H ) x 2. = 7.62 s D downstream =(V B,H ) y t cross = = m 37. (5 points) Say the time it takes the boat to get to the other side in the above scenario is T \. Now suppose the driver of the boat steers in such a way that the boat moves along the xaxis, directly from the house on the left to the house on the right. If the speed of the boat relative to the water is the same as in the original problem, compare the time it takes the boat to get across the river in the new case, T HIJ, to T \. a. T HIJ > T \ b. T HIJ < T \ c. T HIJ = T \ The time it takes for the boat to cross the river is dictated by the xcomponent of its velocity relative to the houses (or river, since the water flows in the ydirection). In the first scenario, the xcomponent of the boat s velocity relative to the river is 2. m/s and the ycomponent is 3. m/s. In the second scenario, the boat travels directly across the river, which means the ycomponent of the boat s velocity relative to the water is only.3 m/s. Since the ycomponent of the boat s velocity relative to the water is smaller than in the first case, but its total speed relative to the water is the same as before, then its xcomponent of velocity must be larger and it crosses the river more quickly.
10 A football is kicked across a level field. The ball spends Δt = 4.8 seconds in the air and lands a distance X = 30 meters from the point where it was kicked. The initial speed of the ball is V \. You should ignore air resistance. 38. (7 points) What is the speed of the ball at the top of its trajectory? a. v = m/s b. v = 3.06 m/s c. v = m/s V x = X t d. v = 6.25 m/s e. There is not enough information given to determine this. = 30/4.8 =6.25 m/s 39. (7 points) What is the maximum height reached by the ball? a. h = m b. h = 7.5 m c. h = 56.5 m d. h = 5 m e. h = 0 m t peak = V y (V 0 ) y = gt peak =) (V 0 ) y = gt peak h =(V 0 ) y t peak 2 gt2 peak = gt 2 peak t 2 =) h = g t 2 8 = m 2 gt2 peak = 2 gt2 peak 40. (5 points) After the kick, but before the ball hits the ground, which of the following statements best describes the acceleration vector of the ball? a. It always points toward the right. b. It points upward before the ball reaches its maximum height, then downward. c. It always points downward.
Exam 3 Practice Solutions
Exam 3 Practice Solutions Multiple Choice 1. A thin hoop, a solid disk, and a solid sphere, each with the same mass and radius, are at rest at the top of an inclined plane. If all three are released at
More informationAP Physics. Harmonic Motion. Multiple Choice. Test E
AP Physics Harmonic Motion Multiple Choice Test E A 0.10Kg block is attached to a spring, initially unstretched, of force constant k = 40 N m as shown below. The block is released from rest at t = 0 sec.
More informationSummer Physics 41 Pretest. Shorty Shorts (2 pts ea): Circle the best answer. Show work if a calculation is required.
Summer Physics 41 Pretest Name: Shorty Shorts (2 pts ea): Circle the best answer. Show work if a calculation is required. 1. An object hangs in equilibrium suspended by two identical ropes. Which rope
More informationPHY218 SPRING 2016 Review for Final Exam: Week 14 Final Review: Chapters 111, 1314
Final Review: Chapters 111, 1314 These are selected problems that you are to solve independently or in a team of 23 in order to better prepare for your Final Exam 1 Problem 1: Chasing a motorist This
More informationWritten Homework problems. Spring (taken from Giancoli, 4 th edition)
Written Homework problems. Spring 014. (taken from Giancoli, 4 th edition) HW1. Ch1. 19, 47 19. Determine the conversion factor between (a) km / h and mi / h, (b) m / s and ft / s, and (c) km / h and m
More informationPHYS 1303 Final Exam Example Questions
PHYS 1303 Final Exam Example Questions (In summer 2014 we have not covered questions 3035,40,41) 1.Which quantity can be converted from the English system to the metric system by the conversion factor
More informationSolution Only gravity is doing work. Since gravity is a conservative force mechanical energy is conserved:
8) roller coaster starts with a speed of 8.0 m/s at a point 45 m above the bottom of a dip (see figure). Neglecting friction, what will be the speed of the roller coaster at the top of the next slope,
More informationChapter 12. Recall that when a spring is stretched a distance x, it will pull back with a force given by: F = kx
Chapter 1 Lecture Notes Chapter 1 Oscillatory Motion Recall that when a spring is stretched a distance x, it will pull back with a force given by: F = kx When the mass is released, the spring will pull
More informationREVISING MECHANICS (LIVE) 30 JUNE 2015 Exam Questions
REVISING MECHANICS (LIVE) 30 JUNE 2015 Exam Questions Question 1 (Adapted from DBE November 2014, Question 2) Two blocks of masses 20 kg and 5 kg respectively are connected by a light inextensible string,
More informationVersion A (01) Question. Points
Question Version A (01) Version B (02) 1 a a 3 2 a a 3 3 b a 3 4 a a 3 5 b b 3 6 b b 3 7 b b 3 8 a b 3 9 a a 3 10 b b 3 11 b b 8 12 e e 8 13 a a 4 14 c c 8 15 c c 8 16 a a 4 17 d d 8 18 d d 8 19 a a 4
More informationUse the following to answer question 1:
Use the following to answer question 1: On an amusement park ride, passengers are seated in a horizontal circle of radius 7.5 m. The seats begin from rest and are uniformly accelerated for 21 seconds to
More information4) Vector = and vector = What is vector = +? A) B) C) D) E)
1) Suppose that an object is moving with constant nonzero acceleration. Which of the following is an accurate statement concerning its motion? A) In equal times its speed changes by equal amounts. B) In
More information(A) I only (B) III only (C) I and II only (D) II and III only (E) I, II, and III
1. A solid metal ball and a hollow plastic ball of the same external radius are released from rest in a large vacuum chamber. When each has fallen 1m, they both have the same (A) inertia (B) speed (C)
More informationConcept Question: Normal Force
Concept Question: Normal Force Consider a person standing in an elevator that is accelerating upward. The upward normal force N exerted by the elevator floor on the person is 1. larger than 2. identical
More informationName: AP Physics C: Kinematics Exam Date:
Name: AP Physics C: Kinematics Exam Date: 1. An object slides off a roof 10 meters above the ground with an initial horizontal speed of 5 meters per second as shown above. The time between the object's
More informationt = g = 10 m/s 2 = 2 s T = 2π g
Annotated Answers to the 1984 AP Physics C Mechanics Multiple Choice 1. D. Torque is the rotational analogue of force; F net = ma corresponds to τ net = Iα. 2. C. The horizontal speed does not affect the
More informationExtra credit assignment #4 It can be handed in up until one class before Test 4 (check your course outline). It will NOT be accepted after that.
Extra credit assignment #4 It can be handed in up until one class before Test 4 (check your course outline). It will NOT be accepted after that. NAME: 4. Units of power include which of the following?
More informationTwo Hanging Masses. ) by considering just the forces that act on it. Use Newton's 2nd law while
Student View Summary View Diagnostics View Print View with Answers Edit Assignment Settings per Student Exam 2  Forces [ Print ] Due: 11:59pm on Tuesday, November 1, 2011 Note: To underst how points are
More informationEquilibrium & Elasticity
PHYS 101 Previous Exam Problems CHAPTER 12 Equilibrium & Elasticity Static equilibrium Elasticity 1. A uniform steel bar of length 3.0 m and weight 20 N rests on two supports (A and B) at its ends. A block
More informationWhich, if any, of the velocity versus time graphs below represent the movement of the sliding box?
Review Packet Name: _ 1. A box is sliding to the right along a horizontal surface with a velocity of 2 m/s. There is friction between the box and the horizontal surface. The box is tied to a hanging stone
More informationW = 750 m. PHYS 101 SP17 Exam 1 BASE (A) PHYS 101 Exams. The next two questions pertain to the situation described below.
PHYS 101 Exams PHYS 101 SP17 Exa BASE (A) The next two questions pertain to the situation described below. A boat is crossing a river with a speed to the water. The river is flowing at a speed W = 750
More informationfrictionless horizontal surface. The bullet penetrates the block and emerges with a velocity of o
AP Physics Free Response Practice Momentum and Impulse 1976B2. A bullet of mass m and velocity v o is fired toward a block of mass 4m. The block is initially at rest on a v frictionless horizontal surface.
More information= o + t = ot + ½ t 2 = o + 2
Chapters 89 Rotational Kinematics and Dynamics Rotational motion Rotational motion refers to the motion of an object or system that spins about an axis. The axis of rotation is the line about which the
More informationInstructor: Biswas/Ihas/Whiting PHYSICS DEPARTMENT PHY 2053 Exam 3, 120 minutes December 12, 2009
77777 77777 Instructor: Biswas/Ihas/Whiting PHYSICS DEPARTMENT PHY 2053 Exam 3, 120 minutes December 12, 2009 Name (print, last first): Signature: On my honor, I have neither given nor received unauthorized
More informationGood Vibes: Introduction to Oscillations
Good Vibes: Introduction to Oscillations Description: Several conceptual and qualitative questions related to main characteristics of simple harmonic motion: amplitude, displacement, period, frequency,
More informationFALL TERM EXAM, PHYS 1211, INTRODUCTORY PHYSICS I Saturday, 14 December 2013, 1PM to 4 PM, AT 1003
FALL TERM EXAM, PHYS 1211, INTRODUCTORY PHYSICS I Saturday, 14 December 2013, 1PM to 4 PM, AT 1003 NAME: STUDENT ID: INSTRUCTION 1. This exam booklet has 14 pages. Make sure none are missing 2. There is
More informationP8.14. m 1 > m 2. m 1 gh = 1 ( 2 m 1 + m 2 )v 2 + m 2 gh. 2( m 1. v = m 1 + m 2. 2 m 2v 2 Δh determined from. m 2 g Δh = 1 2 m 2v 2.
. Two objects are connected by a light string passing over a light frictionless pulley as in Figure P8.3. The object of mass m is released from rest at height h. Using the principle of conservation of
More informationUniversity of Houston Mathematics Contest: Physics Exam 2017
Unless otherwise specified, please use g as the acceleration due to gravity at the surface of the earth. Vectors x, y, and z are unit vectors along x, y, and z, respectively. Let G be the universal gravitational
More informationPractice Problems for Exam 2 Solutions
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics Physics 8.01 Fall Term 008 Practice Problems for Exam Solutions Part I Concept Questions: Circle your answer. 1) A springloaded toy dart gun
More informationPHYS 101 Previous Exam Problems. Force & Motion I
PHYS 101 Previous Exam Problems CHAPTER 5 Force & Motion I Newton s Laws Vertical motion Horizontal motion Mixed forces Contact forces Inclines General problems 1. A 5.0kg block is lowered with a downward
More informationSolution Derivations for Capa #12
Solution Derivations for Capa #12 1) A hoop of radius 0.200 m and mass 0.460 kg, is suspended by a point on it s perimeter as shown in the figure. If the hoop is allowed to oscillate side to side as a
More informationExam 2: Equation Summary
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics 8.01 Physics Fall Term 2012 Exam 2: Equation Summary Newton s Second Law: Force, Mass, Acceleration: Newton s Third Law: Center of Mass: Velocity
More informationHATZIC SECONDARY SCHOOL
HATZIC SECONDARY SCHOOL PROVINCIAL EXAMINATION ASSIGNMENT VECTOR DYNAMICS MULTIPLE CHOICE / 45 OPEN ENDED / 75 TOTAL / 120 NAME: 1. Unless acted on by an external net force, an object will stay at rest
More informationName: Class: Date: so sliding friction is better so sliding friction is better d. µ k
Name: Class: Date: Exam 2PHYS 101F08 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. You put your book on the seat next to you. When the bus stops,
More informationPHYSICS FORMULAS. A. B = A x B x + A y B y + A z B z = A B cos (A,B)
PHYSICS FORMULAS A = A x i + A y j Φ = tan 1 A y A x A + B = (A x +B x )i + (A y +B y )j A. B = A x B x + A y B y + A z B z = A B cos (A,B) linear motion v = v 0 + at x  x 0 = v 0 t + ½ at 2 2a(x  x
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Exam Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) A 4.8kg block attached to a spring executes simple harmonic motion on a frictionless
More informationPRACTICE TEST for Midterm Exam
South Pasadena AP Physics PRACTICE TEST for Midterm Exam FORMULAS Name Period Date / / d = vt d = v o t + ½ at 2 d = v o + v 2 t v = v o + at v 2 = v 2 o + 2ad v = v x 2 + v y 2 = tan 1 v y v v x = v cos
More informationExam. Name. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Exam Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) You want to swim straight across a river that is 76 m wide. You find that you can do
More informationPhysics 2210 Homework 18 Spring 2015
Physics 2210 Homework 18 Spring 2015 Charles Jui April 12, 2015 IE Sphere Incline Wording A solid sphere of uniform density starts from rest and rolls without slipping down an inclined plane with angle
More informations_3x03 Page 1 Physics Samples
Physics Samples KE, PE, Springs 1. A 1.0kilogram rubber ball traveling east at 4.0 meters per second hits a wall and bounces back toward the west at 2.0 meters per second. Compared to the kinetic energy
More informationGood Vibes: Introduction to Oscillations
Chapter 14 Solutions Good Vibes: Introduction to Oscillations Description: Several conceptual and qualitative questions related to main characteristics of simple harmonic motion: amplitude, displacement,
More informationAAPT UNITED STATES PHYSICS TEAM AIP 2008
8 F = ma Exam AAPT UNITED STATES PHYSICS TEAM AIP 8 8 F = ma Contest 5 QUESTIONS  75 MINUTES INSTRUCTIONS DO NOT OPEN THIS TEST UNTIL YOU ARE TOLD TO BEGIN Use g = N/kg throughout this contest. You may
More informationHealy/DiMurro. Vibrations 2016
Name Vibrations 2016 Healy/DiMurro 1. In the diagram below, an ideal pendulum released from point A swings freely through point B. 4. As the pendulum swings freely from A to B as shown in the diagram to
More informationFall 2007 RED Barcode Here Physics 105, sections 1 and 2 Please write your CID Colton
Fall 007 RED Barcode Here Physics 105, sections 1 and Exam 3 Please write your CID Colton 3669 3 hour time limit. One 3 5 handwritten note card permitted (both sides). Calculators permitted. No books.
More informationKinematics and Dynamics
AP PHYS 1 Test Review Kinematics and Dynamics Name: Other Useful Site: http://www.aplusphysics.com/ap1/ap1 supp.html 201516 AP Physics: Kinematics Study Guide The study guide will help you review all
More informationChapter Four Holt Physics. Forces and the Laws of Motion
Chapter Four Holt Physics Forces and the Laws of Motion Physics Force and the study of dynamics 1.Forces  a. Force  a push or a pull. It can change the motion of an object; start or stop movement; and,
More informationPhysics 221. Exam III Spring f S While the cylinder is rolling up, the frictional force is and the cylinder is rotating
Physics 1. Exam III Spring 003 The situation below refers to the next three questions: A solid cylinder of radius R and mass M with initial velocity v 0 rolls without slipping up the inclined plane. N
More informationPotential energy functions used in Chapter 7
Potential energy functions used in Chapter 7 CHAPTER 7 CONSERVATION OF ENERGY Conservation of mechanical energy Conservation of total energy of a system Examples Origin of friction Gravitational potential
More informationUnit 2: Vector Dynamics
Multiple Choice Portion Unit 2: Vector Dynamics 1. Which one of the following best describes the motion of a projectile close to the surface of the Earth? (Assume no friction) Vertical Acceleration Horizontal
More informationWork and kinetic Energy
Work and kinetic Energy Problem 66. M=4.5kg r = 0.05m I = 0.003kgm 2 Q: What is the velocity of mass m after it dropped a distance h? (No friction) h m=0.6kg mg Work and kinetic Energy Problem 66. M=4.5kg
More information1982B1. The first meters of a 100meter dash are covered in 2 seconds by a sprinter who starts from rest and accelerates with a constant
1982B1. The first meters of a 100meter dash are covered in 2 seconds by a sprinter who starts from rest and accelerates with a constant acceleration. The remaining 90 meters are run with the same velocity
More informationDistance travelled time taken and if the particle is a distance s(t) along the xaxis, then its instantaneous speed is:
Chapter 1 Kinematics 1.1 Basic ideas r(t) is the position of a particle; r = r is the distance to the origin. If r = x i + y j + z k = (x, y, z), then r = r = x 2 + y 2 + z 2. v(t) is the velocity; v =
More informationTranslational vs Rotational. m x. Connection Δ = = = = = = Δ = = = = = = Δ =Δ = = = = = 2 / 1/2. Work
Translational vs Rotational / / 1/ Δ m x v dx dt a dv dt F ma p mv KE mv Work Fd / / 1/ θ ω θ α ω τ α ω ω τθ Δ I d dt d dt I L I KE I Work / θ ω α τ Δ Δ c t s r v r a v r a r Fr L pr Connection Translational
More informationPHYS 131 MIDTERM October 31 st, 2008
PHYS 131 MIDTERM October 31 st, 2008 The exam comprises two parts: 8 shortanswer questions, and 4 problems. Calculators are allowed, as well as a formula sheet (oneside of an 8½ x 11 sheet) of your own
More informationAP Physics C: Rotation II. (Torque and Rotational Dynamics, Rolling Motion) Problems
AP Physics C: Rotation II (Torque and Rotational Dynamics, Rolling Motion) Problems 1980M3. A billiard ball has mass M, radius R, and moment of inertia about the center of mass I c = 2 MR²/5 The ball is
More informationFind the value of λ. (Total 9 marks)
1. A particle of mass 0.5 kg is attached to one end of a light elastic spring of natural length 0.9 m and modulus of elasticity λ newtons. The other end of the spring is attached to a fixed point O 3 on
More informationTHE TWENTYSECOND ANNUAL SLAPT PHYSICS CONTEST SOUTHERN ILLINOIS UNIVERSITY EDWARDSVILLE APRIL 21, 2007 MECHANICS TEST. g = 9.
THE TWENTYSECOND ANNUAL SLAPT PHYSICS CONTEST SOUTHERN ILLINOIS UNIVERSITY EDWARDSVILLE APRIL 21, 27 MECHANICS TEST g = 9.8 m/s/s Please answer the following questions on the supplied answer sheet. You
More informationVersion PREVIEW Semester 1 Review Slade (22222) 1
Version PREVIEW Semester 1 Review Slade () 1 This printout should have 48 questions. Multiplechoice questions may continue on the next column or page find all choices before answering. Holt SF 0Rev 10A
More informationPhys 270 Final Exam. Figure 1: Question 1
Phys 270 Final Exam Time limit: 120 minutes Each question worths 10 points. Constants: g = 9.8m/s 2, G = 6.67 10 11 Nm 2 kg 2. 1. (a) Figure 1 shows an object with moment of inertia I and mass m oscillating
More informationUnit 2 Energy and Momentum Test
Name: Class: Date: ID: A Unit 2 Energy and Momentum Test Multiple Choice Identify the choice that best completes the statement or answers the question.. Which of the following is not a unit of energy?
More informationNewton s 3 Laws of Motion
Newton s 3 Laws of Motion 1. If F = 0 No change in motion 2. = ma Change in motion Fnet 3. F = F 1 on 2 2 on 1 Newton s First Law (Law of Inertia) An object will remain at rest or in a constant state of
More informationGeneral Physics I Work & Energy
General Physics I Work & Energy Forms of Energy Kinetic: Energy of motion. A car on the highway has kinetic energy. We have to remove this energy to stop it. The brakes of a car get HOT! This is an example
More informationRevolve, Rotate & Roll:
I. WarmUP. Revolve, Rotate & Roll: Physics 203, Yaverbaum John Jay College of Criminal Justice, the CUNY Given g, the rate of freefall acceleration near Earth s surface, and r, the radius of a VERTICAL
More informationP211 Spring 2004 Form A
1. A 2 kg block A traveling with a speed of 5 m/s as shown collides with a stationary 4 kg block B. After the collision, A is observed to travel at right angles with respect to the initial direction with
More informationAAPT UNITED STATES PHYSICS TEAM AIP 2011
2011 F = ma Exam 1 AAPT UNITED STATES PHYSICS TEAM AIP 2011 2011 F = ma Contest 25 QUESTIONS  75 MINUTES INSTRUCTIONS DO NOT OPEN THIS TEST UNTIL YOU ARE TOLD TO BEGIN Use g = 10 N/kg throughout this
More informationAP Physics Multiple Choice Practice Torque
AP Physics Multiple Choice Practice Torque 1. A uniform meterstick of mass 0.20 kg is pivoted at the 40 cm mark. Where should one hang a mass of 0.50 kg to balance the stick? (A) 16 cm (B) 36 cm (C) 44
More informationOscillatory Motion SHM
Chapter 15 Oscillatory Motion SHM Dr. Armen Kocharian Periodic Motion Periodic motion is motion of an object that regularly repeats The object returns to a given position after a fixed time interval A
More informationPage 1. Chapters 2, 3 (linear) 9 (rotational) Final Exam: Wednesday, May 11, 10:05 am  12:05 pm, BASCOM 272
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
More informationAP Physics 1 Waves and Simple Harmonic Motion Practice Test
AP Physics 1 Waves and Simple Harmonic Motion Practice Test MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) An object is attached to a vertical
More informationEXAMPLE 2: CLASSICAL MECHANICS: Worked examples. b) Position and velocity as integrals. Michaelmas Term Lectures Prof M.
CLASSICAL MECHANICS: Worked examples Michaelmas Term 2006 4 Lectures Prof M. Brouard EXAMPLE 2: b) Position and velocity as integrals Calculate the position of a particle given its time dependent acceleration:
More informationMultiple Choice  TEST III
Multiple Choice Test IIIClassical Mechanics Multiple Choice  TEST III 1) n atomic particle whose mass is 210 atomic mass units collides with a stationary atomic particle B whose mass is 12 atomic mass
More informationRotational Kinetic Energy
Lecture 17, Chapter 10: Rotational Energy and Angular Momentum 1 Rotational Kinetic Energy Consider a rigid body rotating with an angular velocity ω about an axis. Clearly every point in the rigid body
More information(a) On the dots below that represent the students, draw and label freebody diagrams showing the forces on Student A and on Student B.
2003 B1. (15 points) A rope of negligible mass passes over a pulley of negligible mass attached to the ceiling, as shown above. One end of the rope is held by Student A of mass 70 kg, who is at rest on
More informationAAPT UNITED STATES PHYSICS TEAM AIP 2016
216 F = ma Exam 1 AAPT UNITED STATES PHYSICS TEAM AIP 216 216 F = ma Contest 25 QUESTIONS  75 MINUTES INSTRUCTIONS DO NOT OPEN THIS TEST UNTIL YOU ARE TOLD TO BEGIN Use g = 1 N/kg throughout this contest.
More informationLecture 18: Work and Energy. Today s Agenda
Lecture 18: Work and Energy Work and Energy Definition of work Examples Today s Agenda Definition of Mechanical Energy Conservation of Mechanical Energy Conservative forces Physics 201: Lecture 10, Pg
More informationPhysicsMC Page 1 of 29 Inertia, Force and Motion 1.
PhysicsMC 20067 Page 1 of 29 Inertia, Force and Motion 1. 3. 2. Three blocks of equal mass are placed on a smooth horizontal surface as shown in the figure above. A constant force F is applied to block
More informationThe Pendulum. Goals and Introduction
The Pendulum Goals and Introduction In this experiment, we will examine the relationships between the period, frequency and length of a simple pendulum. The oscillation of a pendulum swinging back and
More informationFriction is always opposite to the direction of motion.
6. Forces and MotionII Friction: The resistance between two surfaces when attempting to slide one object across the other. Friction is due to interactions at molecular level where rough edges bond together:
More informationDynamics II Motion in a Plane. Review Problems
Dynamics II Motion in a Plane Review Problems Problem 1 A 500 g model rocket is on a cart that is rolling to the right at a speed of 3.0 m/s. The rocket engine, when it is fired, exerts an 8.0 N thrust
More informationUnit 4 Work, Power & Conservation of Energy Workbook
Name: Per: AP Physics C Semester 1  Mechanics Unit 4 Work, Power & Conservation of Energy Workbook Unit 4  Work, Power, & Conservation of Energy Supplements to Text Readings from Fundamentals of Physics
More informationGeneral Physics (PHY 2130)
General Physics (PHY 130) Lecture 0 Rotational dynamics equilibrium nd Newton s Law for rotational motion rolling Exam II review http://www.physics.wayne.edu/~apetrov/phy130/ Lightning Review Last lecture:
More informationAP physics B  Webreview ch 13 Waves
Name: Class: _ Date: _ AP physics B  Webreview ch 13 Waves Multiple Choice Identify the choice that best completes the statement or answers the question. 1. A large spring requires a force of 150 N to
More informationChapter 13, Vibrations and Waves. 1. A large spring requires a force of 150 N to compress it only m. What is the spring constant of the spring?
CHAPTER 13 1. A large spring requires a force of 150 N to compress it only 0.010 m. What is the spring constant of the spring? a. 125 000 N/m b. 15 000 N/m c. 15 N/m d. 1.5 N/m 2. A 0.20kg object is attached
More information(1) (3)
1. This question is about momentum, energy and power. (a) In his Principia Mathematica Newton expressed his third law of motion as to every action there is always opposed an equal reaction. State what
More informationA+B. Scalar quantities are described by magnitude only (examples: distance, speed, temperature, energy, and mass).
Honors Physics Examination I Review Questions #1#11  Vectors & Measurements vector quantity is specified by magnitude and direction (examples: displacement, velocity, acceleration, momentum, and weight).
More informationM1 January Immediately after the collision Q moves with speed 5 m s 1. Calculate. the speed of P immediately after the collision,
M1 January 2003 1. railway truck P of mass 2000 kg is moving along a straight horizontal track with speed 10 m s 1. The truck P collides with a truck Q of mass 3000 kg, which is at rest on the same track.
More informationAP Physics 1 Review. On the axes below draw the horizontal force acting on this object as a function of time.
P Physics Review. Shown is the velocity versus time graph for an object that is moving in one dimension under the (perhaps intermittent) action of a single horizontal force. Velocity, m/s Time, s On the
More informationPhysics Mechanics. Lecture 11 Newton s Laws  part 2
Physics 170  Mechanics Lecture 11 Newton s Laws  part 2 Newton s Second Law of Motion An object may have several forces acting on it; the acceleration is due to the net force: Newton s Second Law of
More informationPhysics 131: Lecture 21. Today s Agenda
Physics 131: Lecture 21 Today s Agenda Rotational dynamics Torque = I Angular Momentum Physics 201: Lecture 10, Pg 1 Newton s second law in rotation land Sum of the torques will equal the moment of inertia
More informationAP Physics. Chapters 7 & 8 Review
AP Physics Chapters 7 & 8 Review 1.A particle moves along the x axis and is acted upon by a single conservative force given by F x = ( 20 4.0x)N where x is in meters. The potential energy associated with
More informationName: M1  Dynamics. Date: Time: Total marks available: Total marks achieved:
Name: M1  Dynamics Date: Time: Total marks available: Total marks achieved: Questions Q1. A railway truck P, of mass m kg, is moving along a straight horizontal track with speed 15 ms 1. Truck P collides
More information1 of 6 10/21/2009 6:33 PM
1 of 6 10/21/2009 6:33 PM Chapter 10 Homework Due: 9:00am on Thursday, October 22, 2009 Note: To understand how points are awarded, read your instructor's Grading Policy. [Return to Standard Assignment
More informationGround Rules. PC1221 Fundamentals of Physics I. Force. Zero Net Force. Lectures 9 and 10 The Laws of Motion. A/Prof Tay Seng Chuan
PC1221 Fundamentals of Physics I Lectures 9 and 10 The Laws of Motion A/Prof Tay Seng Chuan 1 Ground Rules Switch off your handphone and pager Switch off your laptop computer and keep it No talking while
More informationPhysics 131: Lecture 21. Today s Agenda
Physics 131: Lecture 1 Today s Agenda Rotational dynamics Torque = I Angular Momentum Physics 01: Lecture 10, Pg 1 Newton s second law in rotation land Sum of the torques will equal the moment of inertia
More informationChapter 5. Force and MotionI
Chapter 5 Force and MotionI 5.3 Newton s First Law Newton s First Law: If no force acts on a body, the body s velocity cannot change The purpose of Newton s First Law is to introduce the special frames
More informationTopic 4 Forces. 1. Jan 92 / M1  Qu 8:
Topic 4 Forces 1. Jan 92 / M1  Qu 8: A particle of mass m lies on a smooth plane inclined at α. It is held in equilibrium by a string which makes an angle θ with the plane. The tension in the string is
More informationExam II: Solutions. UNIVERSITY OF ALABAMA Department of Physics and Astronomy. PH 125 / LeClair Spring 2009
UNIVERSITY OF ALABAMA Department of Physics and Astronomy PH 15 / LeClair Spring 009 Exam II: Solutions 1. A block of mass m is released from rest at a height d=40 cm and slides down a frictionless ramp
More informationNewton s Laws and FreeBody Diagrams General Physics I
Newton s Laws and FreeBody Diagrams In the next few sections, we will be exploring some of the most fundamental laws of our universe, laws that govern the relationship actions and motion. These laws are
More informationPractice Test 3. Name: Date: ID: A. Multiple Choice Identify the choice that best completes the statement or answers the question.
Name: Date: _ Practice Test 3 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. A wheel rotates about a fixed axis with an initial angular velocity of 20
More informationAP1 WEP. Answer: E. The final velocities of the balls are given by v = 2gh.
1. Bowling Ball A is dropped from a point halfway up a cliff. A second identical bowling ball, B, is dropped simultaneously from the top of the cliff. Comparing the bowling balls at the instant they reach
More information