A body of unknown mass is attached to an ideal spring with force constant 123 N/m. It is found to vibrate with a frequency of

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1 Chapter 14 [ Edit ] Overview Suary View Diagnostics View Print View with Answers Chapter 14 Due: 11:59p on Sunday, Noveber 27, 2016 To understand how points are awarded, read the Grading Policy for this assignent. Exercise 14.2 Description: If an object on a horizontal frictionless surface is attached to a spring, displaced, and then released, it will oscillate. If it is displaced a distance ## fro its equilibriu position and released with zero initial speed. Then after a tie ## s... If an object on a horizontal frictionless surface is attached to a spring, displaced, and then released, it will oscillate. If it is displaced a distance fro its equilibriu position and released with zero initial speed. Then after a tie s its displaceent is found to be a distance on the opposite side, and it has passed the equilibriu position once during this interval. Find the aplitude. A = = Find the period. T = = 1.61 s Find the frequency. f = = Hz Exercise 14.9 Description: A body of unknown ass is attached to an ideal spring with force constant ## N/. It is found to vibrate with a frequency of ## Hz. (a) Find the period. (b) Find the angular frequency. (c) Find the ass of the body. A body of unknown ass is attached to an ideal spring with force constant 123 N/. It is found to vibrate with a frequency of 5.95 Hz. 1/12

2 Find the period. T = = s Find the angular frequency. ω = = 37.4 rad/s Find the ass of the body. Express your answer using two significant figures. = = kg Exercise Description: An object is undergoing SHM with period T and aplitude At t = 0, the object is at x = and is instantaneously at rest. (a) Calculate the tie it takes the object to go fro x = 0.320, to x = (b) Calculate the tie it... An object is undergoing SHM with period s and aplitude At t = 0, the object is at x = and is instantaneously at rest. Calculate the tie it takes the object to go fro x = 0.320, to x = Express your answer with the appropriate units. t = = /12

3 Calculate the tie it takes the object to go fro x = 0.160, to x = 0. Express your answer with the appropriate units. t = = Exercise Description: A frictionless block of ass ## kg is attached to an ideal spring with force constant ## N/. At t=0 the spring is neither stretched nor copressed and the block is oving in the negative direction at a speed of ## /s. (a) Find the aplitude. (b)... A frictionless block of ass 2.15 kg is attached to an ideal spring with force constant 260 N/. At t = 0 the spring is neither stretched nor copressed and the block is oving in the negative direction at a speed of 12.5 /s. Find the aplitude. A = = 1.14 Find the phase angle. ϕ = 1.57 rad Write an equation for the position as a function of tie. x = ( 1.14 )sin(( 11.0 rad/s )t) x = ( 1.14 )cos(( 11.0 rad/s )t) x = ( 11.0 )sin(( 1.14 rad/s)t) x = ( 11.0 )cos(( 1.14 rad/s)t) Exercise /12

4 Description: A 2.00 kg, frictionless block is attached to an ideal spring with force constant 300 N/. At t = 0 the block has velocity 4.00 /s and displaceent (a) Find (a) the aplitude and (b) the phase angle. (b)... (c) Write an equation for the... A 2.00 kg, frictionless block is attached to an ideal spring with force constant 300 N/. At t = 0 the block has velocity 4.00 /s and displaceent Find (a) the aplitude and (b) the phase angle. A = ϕ = 1.02 rad Write an equation for the position as a function of tie. Assue x (t) in eters and t in seconds. x (t) = Also accepted:, Exercise Description: A ass on a spring has displaceent as a function of tie given by the equation x( t ) = ( (7.40 ( c)) ) cos ( (( (4.16 ( rad/s) ) )t 2.42 (rad)) ). (a) Find the tie for one coplete vibration. (b) Find the force constant of the spring. (c... A 1.30 kg ass on a spring has displaceent as a function of tie given by the equation x(t) = (7.40 c) cos [(4.16 rad/s)t 2.42 rad]. Find the tie for one coplete vibration. T = 1.51 s 4/12

5 Find the force constant of the spring. k = = 22.5 N/ Find the axiu speed of the ass. v ax = /s Part D Find the axiu agnitude of force on the ass. F ax = = 1.67 N Part E Find the position of the ass at t = 1.00 s; x = Part F Find the speed of the ass at t = 1.00 s; v = /s Part G Find the agnitude of acceleration of the ass at t = 1.00 s; 5/12

6 a = /s 2 Part H Find the agnitude of force on the ass at t = 1.00 s; F = = N Also accepted: = Exercise Description: A toy of ass ## kg is undergoing SHM on the end of a horizontal spring with force constant k=## N/. When the toy is a distance ## fro its equilibriu position, it is observed to have a speed of ## /s. (a) What is the toy's total... A toy of ass kg is undergoing SHM on the end of a horizontal spring with force constant k = 350 N/. When the toy is a distance fro its equilibriu position, it is observed to have a speed of /s. What is the toy's total energy at any point of its otion? Express your answer with the appropriate units. E = = What is the toy's aplitude of the otion? Express your answer with the appropriate units. A = = What is the toy's axiu speed during its otion? Express your answer with the appropriate units. 6/12

7 v ax = = Exercise Description: A certain alar clock ticks four ties each second, with each tick representing half a period. The balance wheel consists of a thin ri with radius r, connected to the balance staff by thin spokes of negligible ass. The total ass of the balance... A certain alar clock ticks four ties each second, with each tick representing half a period. The balance wheel consists of a thin ri with radius 0.56 c, connected to the balance staff by thin spokes of negligible ass. The total ass of the balance wheel is 0.95 g. What is the oent of inertia of the balance wheel about its shaft? Express your answer using two significant figures. I = = kg 2 What is the torsion constant of the hairspring? Express your answer using two significant figures. κ = = N /rad Exercise Description: A certain siple pendulu has a period on the earth of T. (a) What is its period on the surface of Mars, where g = 3.71 ( /s)^2? A certain siple pendulu has a period on the earth of 2.00 s. What is its period on the surface of Mars, where g = 3.71 /s 2? 7/12

8 T M = = 3.25 s Exercise Description: A 1.80 kg onkey wrench is pivoted fro its center of ass and allowed to swing as a physical pendulu. The period for sall angle oscillations is s. (a) What is the oent of inertia of the wrench about an axis through the pivot? (b)... A 1.80 kg onkey wrench is pivoted fro its center of ass and allowed to swing as a physical pendulu. The period for sall angle oscillations is s. What is the oent of inertia of the wrench about an axis through the pivot? I = kg 2 If the wrench is initially displaced rad fro its equilibriu position, what is the angular speed of the wrench as it passes through the equilibriu position? Ω ax = 2.66 rad/s Exercise Description: A holiday ornaent in the shape of a hollow sphere with ass ## kg and radius ## is hung fro a tree lib by a sall loop of wire attached to the surface of the sphere. If the ornaent is displaced a sall distance and released, it swings back and... A holiday ornaent in the shape of a hollow sphere with ass kg and radius is hung fro a tree lib by a sall loop of wire attached to the surface of the sphere. If the ornaent is displaced a sall distance and released, it swings back and forth as a physical pendulu. Calculate its period. (You can ignore friction at the pivot. The oent of inertia of the sphere about the pivot at the tree lib is 5M R 2 /3.) Take the free fall acceleration to be 9.80 /s 2. Express your answer using two significant figures. 8/12

9 T = = 0.61 s Proble Description: A block with ass M rests on a frictionless surface and is connected to a horizontal spring of force constant k. The other end of the spring is attached to a wall (the figure ). A second block with ass rests on top of the first block. The... A block with ass M rests on a frictionless surface and is connected to a horizontal spring of force constant k. The other end of the spring is attached to a wall (the figure ). A second block with ass rests on top of the first block. The coefficient of static friction between the blocks is. μ s Find the axiu aplitude of oscillation such that the top block will not slip on the botto block. Express your answer in ters of the variables, M, k, μ s, and appropriate constants. Proble Description: An object with ass ## kg is acted on by an elastic restoring force with force constant ## N/. The object is set into oscillation with an initial potential energy of ## J and an initial kinetic energy of ## J. (a) What is the aplitude of... An object with ass kg is acted on by an elastic restoring force with force constant 10.7 N/. The object is set into oscillation with an initial potential energy of J and an initial kinetic energy of J. What is the aplitude of oscillation? 9/12

10 A = = What is the potential energy when the displaceent is one half the aplitude? U = = J At what displaceent are the kinetic and potential energies equal? x = = Part D What is the value of the phase angle ϕ if the initial velocity is positive and the initial displaceent is negative? ϕ = = 3.73 rad Also accepted: = 2.55 Proble Description: A partridge of ass ## kg is suspended fro a pear tree by an ideal spring of negligible ass. When the partridge is pulled down below its equilibriu position and released, it vibrates with a period of ## s. (a) What is its speed as it... A partridge of ass 5.10 kg is suspended fro a pear tree by an ideal spring of negligible ass. When the partridge is pulled down below its equilibriu position and released, it vibrates with a period of 4.25 s. What is its speed as it passes through the equilibriu position? 10/12

11 v = = /s What is its acceleration when it is above the equilibriu position? a = = /s 2 When it is oving upward, how uch tie is required for it to ove fro a point below its equilibriu position to a point above it? t = = s Part D The otion of the partridge is stopped, and then it is reoved fro the spring. How uch does the spring shorten? Δl = = 4.48 Proble Description: A rifle bullet with ass and initial horizontal velocity v strikes and ebeds itself in a block with ass _b that rests on a frictionless surface and is attached to one end of an ideal spring. The other end of the spring is... A rifle bullet with ass 7.00 g and initial horizontal velocity 250 /s strikes and ebeds itself in a block with ass kg that rests on a frictionless surface and is attached to one end of an ideal spring. The other end of the spring is attached to the wall. The ipact copresses the spring a axiu distance of 14.0 c. After the ipact, the block oves in SHM. Calculate the period of this otion. Express your answer with the appropriate units. 11/12

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