University Physics with Modern Physics (14th Edition)
14th Edition
ISBN: 9780321973610
Author: Hugh D. Young, Roger A. Freedman
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Question
Chapter 42, Problem 42.33P
(a)
To determine
The force constant of the spring.
(b)
To determine
The number of vibrations per second the molecule making.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Suppose a large spherical object, such as a planet, with
radius R and mass M has a narrow tunnel passing
diametrically through it. A particle of mass m is inside the
tunnel at a distance x ≤R from the center. It can be
shown that the net gravitational force on the particle is due
entirely to the sphere of mass with radius r x.
Find an expression for the magnitude of the gravitational force on the particle, assuming the object has uniform density.
Express your answer in terms of the variables x, R, m, M, and gravitational constant G.
► View Available Hint(s)
(a) An oscillating object repeats its motion every 3.3 seconds. (i) What is the period of this oscillation?
(ii) What is its frequency? (iii) What is its phase rate (i.e. angular frequency)?
(b) A magnesium atom (mass of 24 proton masses) in a crystal is measured to oscillate with a frequency
of roughly 10l3 Hz. What is the effective spring constant of the forces holding that atom in the crystal?
(c) Sitting on a trampoline, a person with mass m sinks a distance Az below the trampoline's normal
level surface. (i) If the person gently bounces on the trampoline (without leaving its surface), what
would be the person's period of oscillation T?
(You should not need the person's mass, but if you think you do, assume and state a value.)
(ii) Find T for Az = 45 cm.
Check: For Az = 20 cm you should find T = 0.90 s.
Note: Make sure your calculator is in radian mode for this problem, and that you switch it back after this problem. There are two particles (1 and 2) that are moving around in space. The force that particle 2 exerts on 1 is given by:
F→21(t)=Fxe−(t/T)ı^+Fysin(2πt/T)ȷ^
Where the parameters have the values: Fx=14.2 N, Fy=89 N, T=55 s.We will consider a time interval that begins at ti=0 s and ends at tf=96 s.
Find the x component of the impulse from 2 on 1 between ti and tf.
Chapter 42 Solutions
University Physics with Modern Physics (14th Edition)
Ch. 42.1 - If electrons obeyed the exclusion principle but...Ch. 42.2 - Prob. 42.2TYUCh. 42.3 - Prob. 42.3TYUCh. 42.4 - One type of thermometer works by measuring the...Ch. 42.5 - Prob. 42.5TYUCh. 42.6 - Prob. 42.6TYUCh. 42.7 - Suppose a negative charge is placed on the gate of...Ch. 42 - Van der Waals bonds occur in many molecules, but...Ch. 42 - Prob. 42.2DQCh. 42 - The H2+ molecule consists of two hydrogen nuclei...
Ch. 42 - The moment of inertia for an axis through the...Ch. 42 - Prob. 42.5DQCh. 42 - Prob. 42.6DQCh. 42 - Prob. 42.7DQCh. 42 - The air you are breathing contains primarily...Ch. 42 - Prob. 42.9DQCh. 42 - Prob. 42.10DQCh. 42 - What factors determine whether a material is a...Ch. 42 - Prob. 42.12DQCh. 42 - Prob. 42.13DQCh. 42 - Prob. 42.14DQCh. 42 - Prob. 42.15DQCh. 42 - Prob. 42.16DQCh. 42 - Prob. 42.17DQCh. 42 - Prob. 42.18DQCh. 42 - Prob. 42.19DQCh. 42 - Prob. 42.20DQCh. 42 - Prob. 42.21DQCh. 42 - Prob. 42.22DQCh. 42 - Prob. 42.23DQCh. 42 - Prob. 42.24DQCh. 42 - If the energy of the H2 covalent bond is 4.48 eV,...Ch. 42 - An Ionic Bond, (a) Calculate the electric...Ch. 42 - Prob. 42.3ECh. 42 - Prob. 42.4ECh. 42 - Prob. 42.5ECh. 42 - Prob. 42.6ECh. 42 - Prob. 42.7ECh. 42 - Two atoms of cesium (Cs) can form a Cs2 molecule....Ch. 42 - Prob. 42.9ECh. 42 - Prob. 42.10ECh. 42 - A lithium atom has mass 1.17 1026 kg, and a...Ch. 42 - Prob. 42.12ECh. 42 - When a hypothetical diatomic molecule having atoms...Ch. 42 - The vibrational and rotational energies of the CO...Ch. 42 - Prob. 42.15ECh. 42 - Prob. 42.16ECh. 42 - Prob. 42.17ECh. 42 - Prob. 42.18ECh. 42 - Prob. 42.19ECh. 42 - Prob. 42.20ECh. 42 - Prob. 42.21ECh. 42 - Prob. 42.22ECh. 42 - Prob. 42.23ECh. 42 - Prob. 42.24ECh. 42 - Prob. 42.25ECh. 42 - Prob. 42.26ECh. 42 - Prob. 42.27ECh. 42 - Prob. 42.28ECh. 42 - Prob. 42.29ECh. 42 - Prob. 42.30ECh. 42 - Prob. 42.31ECh. 42 - Prob. 42.32ECh. 42 - Prob. 42.33PCh. 42 - Prob. 42.34PCh. 42 - Prob. 42.35PCh. 42 - The binding energy of a potassium chloride...Ch. 42 - (a) For the sodium chloride molecule (NaCl)...Ch. 42 - Prob. 42.38PCh. 42 - Prob. 42.39PCh. 42 - Prob. 42.40PCh. 42 - Prob. 42.41PCh. 42 - Prob. 42.42PCh. 42 - Prob. 42.43PCh. 42 - Prob. 42.44PCh. 42 - Prob. 42.45PCh. 42 - Prob. 42.46PCh. 42 - Prob. 42.47PCh. 42 - Prob. 42.48PCh. 42 - Prob. 42.49PCh. 42 - Prob. 42.50PCh. 42 - Prob. 42.51PCh. 42 - Prob. 42.52PCh. 42 - Prob. 42.53CPCh. 42 - Prob. 42.54CPCh. 42 - Prob. 42.55CPCh. 42 - Prob. 42.56PPCh. 42 - Prob. 42.57PPCh. 42 - Prob. 42.58PP
Knowledge Booster
Similar questions
- 15. A planet orbits a star in an elliptical orbit. The distance at point A (aphelion) is 2r and at point B (perihelion) is r. What is the ratio of speeds at point B to point A? A) 1 B) 2 3 D) 1.718 E) 2.718 16. Let , be the properly-normalized nth energy eigenfunction of the harmonic oscillator, and let = â âton, which of the following is equal to ? Α) ΦΩ B) n on-1 C) n Pn+1 D) (n + 1)on E) None of these dä 4= darrow_forwardA mass of 458 g stretches a spring by 7.2 cm. The damping constant is c = 0.34. External vibrations create a force of F(t)= 0.4 sin 5t Newtons, setting the spring in motion from its equilibrium position with zero velocity. What is the imaginary part v, m of the complex root of the homogeneous equation? Use g= 9.8- .Express your answer in two decimal places.arrow_forwardSuppose a large spherical object, such as a planet, with radius R and mass M has a narrow tunnel passing diametrically through it. A particle of mass m is inside the tunnel at a distance x ≤R from the center. It can be shown that the net gravitational force on the particle is due entirely to the sphere of mass with radius r x. ΓΆΠΗ Find an expression for the magnitude of the gravitational force on the particle, assuming the object has uniform density. Express your answer in terms of the variables x, R, m, M, and gravitational constant G. ► View Available Hint(s) F= GmMx R³ Submit Part B ✓ Correct Previous Answers You should have found that the gravitational force is a linear restoring force. Consequently, in the absence of air resistance, objects in the tunnel will oscillate with SHM. Suppose an intrepid astronaut exploring a 180-km-diameter, 3.5 x 10¹8 kg asteroid discovers a tunnel through the center. If she jumps into the hole, how long will it take her to fall all the way through…arrow_forward
- (b) A magnesium atom (mass of 24 proton masses) in a crystal is measured to oscillate with a frequency of roughly 10¹3 Hz. What is the effective spring constant of the forces holding that atom in the crystal? (c) Sitting on a trampoline, a person with mass m sinks a distance Az below the trampoline's normal level surface. (i) If the person gently bounces on the trampoline (without leaving its surface), what would be the person's period of oscillation T? Check: For Az = 20 cm you should find T 0.90 s. (You should not need the person's mass, but if you think you do, assume and state a value.) (ii) Find T for Az = 45 cm. =arrow_forwardA uniform rod of mass M and length L is free to swing back and forth by pivoting a distance x from its center. It undergoes harmonic oscillations by swinging back and forth under the influence of gravity.Randomized Variables M = 2.4 kgL = 1.6 mx = 0.38 m a) In terms of M, L, and x, what is the rod’s moment of inertia I about the pivot point. b) Calculate the rod’s period T in seconds for small oscillations about its pivot point. c) In terms of L, find an expression for the distance xm for which the period is a minimum.arrow_forwardProblem 2: A fisherman has caught a fish on his pole, and to keep the pole steady he has to apply an upward force of F2 = 255 N at an angle of 51.5° with respect to the pole (see figure). The length of his pole is 3.1 m, and he is holding it a distance 0.45 m from the end, where he is applying a downward force F1. Randomized Variables F2 = 255 Nθ = 51.5°L = 3.1 md = 0.45 m Part (a) With how much force, F1, in newtons, does he have to push straight downward on the end of his pole to keep the pole from moving? You may assume the pole is massless.Numeric : A numeric value is expected and not an expression.F1 = __________________________________________Part (b) What is the mass of the fish on the end of the pole, in kilograms?Numeric : A numeric value is expected and not an expression.m = __________________________________________arrow_forward
- A sphere, of radius a, is suspended by a fine wire from a fixed point at a distance I from its centre show that the time of a small oscilation is given by 2x - √ ( ² ; ²² ) {₁ + | Sin² (;)}. 2π 51² +20² 581 1 where a represents the ar "tude of the vibration.arrow_forward(a) An oscillating object of mass m, obeys the governing equation my" + cy' + ky = F(t) subject to an external driving force F(t) = F, sin(Nt), where n represents angular frequency and c, k are constants. Find the general solution y as a %3D %3D function of time t.arrow_forwardThe equation of motion of an MSQ object of mass m attached with a spring of spring constant K is oscillating in medium of damping constant b is written as m(d²x)/dt2 +b dx/dt+Kx=D0 if wo is the 35 natural angular frequency of the free oscillator thus which of the following are true? (a) The critical damping occurs when b = v2mK (b) Non-oscillatory, a periodic motion occurs when b >2mwo (c) Oscillations about equilibrium with exponentially decaying amplitude occurs when b<2mwo an (d) Non-oscillatory equilibriums occurs when b = 2vmK and faster return to a b Carrow_forward
- Problem 11: A small block of mass M= 350 g is placed on top of a larger block of mass 3M which is placed on a level frictionless surface and is attached to a horizontal spring of spring constant k = 1.9 N/m. The coefficient of static friction between the blocks is μ =0.2. The lower block is pulled until the attached spring is stretched a distance D = 2.5 cm and released. Randomized Variables M = 350 g D = 2.5 cm k = 1.9 N/m Part (a) Assuming the blocks are stuck together, what is the maximum magnitude of acceleration amax of the blocks in terms of the variables in the problem statement? amax = k D/(3 M+M ) ✓ Correct! Part (b) Calculate a value for the magnitude of the maximum acceleration amax of the blocks in m/s². ✓ Correct! | @mar= 0.03390 Part (c) Write an equation for the largest spring constant kmax for which the upper block does not slip. Kmax = μ (M +M) g/klarrow_forwardScientists have developed a clever way to measure a mass of virus using a spring. A cantilever beam in the scanning electron microscope image below is like a diving board, except that it is extremely small (a couple of micrometer). The cantilever beam with mass m can oscillate (imagine a vibrating diving board) and it can be modeled as a spring with a spring constant k. What you can measure experimentally is the frequency of oscillation of the cantilever first without the virus (f1) and after the virus had attached itself to the cantilever (f2). (a) Find the mass of virus from f1 and f2 (assume that we don’t know the spring constant k) (b) Suppose the mass of cantilever is 10.0 * 10^-16 g and a frequency of 2.00 * 10^15 Hz without the virus and 2.87 * 10^14 Hz with the virus. What is the mass of the virus?arrow_forwardA uniform rod of mass M and length L is free to swing back and forth by pivoting a distance x from its center. It undergoes harmonic oscillations by swinging back and forth under the influence of gravity. Randomized Variables M = 2.8 kg L = 1.7 m x = 0.29 m Part (a) In terms of M, L, and x, what is the rod's moment of inertia I about the pivot point. I= ((ML²)/12) + Mx² ✓ Correct! Part (b) Calculate the rod's period I' in seconds for small oscillations about its pivot point. Part (c) In terms of L, find an expression for the distance xm for which the period is a minimum.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage Learning
Classical Dynamics of Particles and SystemsPhysicsISBN:9780534408961Author:Stephen T. Thornton, Jerry B. MarionPublisher:Cengage Learning
Principles of Physics: A Calculus-Based Text
Physics
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Physics for Scientists and Engineers: Foundations...
Physics
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Cengage Learning
Classical Dynamics of Particles and Systems
Physics
ISBN:9780534408961
Author:Stephen T. Thornton, Jerry B. Marion
Publisher:Cengage Learning