Physics for Scientists and Engineers: Foundations and Connections
1st Edition
ISBN: 9781133939146
Author: Katz, Debora M.
Publisher: Cengage Learning
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Chapter 16, Problem 28PQ
We do not need the analogy in Equation 16.30 to write expressions for the translational displacement of a pendulum bob along the circular arc s(t), translational speed v(t), and translational acceleration a(t). Show that they are given by
s(t) = smax cos (ωsmpt + φ)
v(t) = −vmax sin (ωsmpt + φ)
a(t) = −amax cos(ωsmpt + φ)
respectively, where smax = ℓθmax with ℓ being the length of the pendulum, vmax = smax ωsmp, and amax = smax
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A body of mass m is suspended by a rod of length L that pivots without friction (as shown). The mass is slowly lifted along a circular arc to a height h.
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The θ integration fails if α is non-constant. There is also a type of situation where the step before the integration fails, involving ω.
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Start with the derivatives I began with, and derive this equation.
Question 2: derive θ = 1/2αt2 + ω0t + θ0.
You may use prior derived results.
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You probably need to use prior derived results.
Chapter 16 Solutions
Physics for Scientists and Engineers: Foundations and Connections
Ch. 16.1 - Prob. 16.1CECh. 16.2 - Prob. 16.2CECh. 16.2 - For each expression, identify the angular...Ch. 16.5 - Prob. 16.4CECh. 16.6 - Prob. 16.5CECh. 16.6 - Prob. 16.6CECh. 16 - Case Study For each velocity listed, state the...Ch. 16 - Case Study For each acceleration listed, state the...Ch. 16 - Prob. 3PQCh. 16 - Prob. 4PQ
Ch. 16 - Prob. 5PQCh. 16 - Prob. 6PQCh. 16 - The equation of motion of a simple harmonic...Ch. 16 - The expression x = 8.50 cos (2.40 t + /2)...Ch. 16 - A simple harmonic oscillator has amplitude A and...Ch. 16 - Prob. 10PQCh. 16 - A 1.50-kg mass is attached to a spring with spring...Ch. 16 - Prob. 12PQCh. 16 - Prob. 13PQCh. 16 - When the Earth passes a planet such as Mars, the...Ch. 16 - A point on the edge of a childs pinwheel is in...Ch. 16 - Prob. 16PQCh. 16 - Prob. 17PQCh. 16 - A jack-in-the-box undergoes simple harmonic motion...Ch. 16 - C, N A uniform plank of length L and mass M is...Ch. 16 - Prob. 20PQCh. 16 - A block of mass m = 5.94 kg is attached to a...Ch. 16 - A block of mass m rests on a frictionless,...Ch. 16 - It is important for astronauts in space to monitor...Ch. 16 - Prob. 24PQCh. 16 - A spring of mass ms and spring constant k is...Ch. 16 - In an undergraduate physics lab, a simple pendulum...Ch. 16 - A simple pendulum of length L hangs from the...Ch. 16 - We do not need the analogy in Equation 16.30 to...Ch. 16 - Prob. 29PQCh. 16 - Prob. 30PQCh. 16 - Prob. 31PQCh. 16 - Prob. 32PQCh. 16 - Prob. 33PQCh. 16 - Show that angular frequency of a physical pendulum...Ch. 16 - A uniform annular ring of mass m and inner and...Ch. 16 - A child works on a project in art class and uses...Ch. 16 - Prob. 37PQCh. 16 - Prob. 38PQCh. 16 - In the short story The Pit and the Pendulum by...Ch. 16 - Prob. 40PQCh. 16 - A restaurant manager has decorated his retro diner...Ch. 16 - Prob. 42PQCh. 16 - A wooden block (m = 0.600 kg) is connected to a...Ch. 16 - Prob. 44PQCh. 16 - Prob. 45PQCh. 16 - Prob. 46PQCh. 16 - Prob. 47PQCh. 16 - Prob. 48PQCh. 16 - A car of mass 2.00 103 kg is lowered by 1.50 cm...Ch. 16 - Prob. 50PQCh. 16 - Prob. 51PQCh. 16 - Prob. 52PQCh. 16 - Prob. 53PQCh. 16 - Prob. 54PQCh. 16 - Prob. 55PQCh. 16 - Prob. 56PQCh. 16 - Prob. 57PQCh. 16 - An ideal simple harmonic oscillator comprises a...Ch. 16 - Table P16.59 gives the position of a block...Ch. 16 - Use the position data for the block given in Table...Ch. 16 - Consider the position data for the block given in...Ch. 16 - Prob. 62PQCh. 16 - Prob. 63PQCh. 16 - Use the data in Table P16.59 for a block of mass m...Ch. 16 - Consider the data for a block of mass m = 0.250 kg...Ch. 16 - A mass on a spring undergoing simple harmonic...Ch. 16 - A particle initially located at the origin...Ch. 16 - Consider the system shown in Figure P16.68 as...Ch. 16 - Prob. 69PQCh. 16 - Prob. 70PQCh. 16 - Prob. 71PQCh. 16 - Prob. 72PQCh. 16 - Determine the period of oscillation of a simple...Ch. 16 - The total energy of a simple harmonic oscillator...Ch. 16 - A spherical bob of mass m and radius R is...Ch. 16 - Prob. 76PQCh. 16 - A lightweight spring with spring constant k = 225...Ch. 16 - Determine the angular frequency of oscillation of...Ch. 16 - Prob. 79PQCh. 16 - A Two springs, with spring constants k1 and k2,...Ch. 16 - Prob. 81PQCh. 16 - Prob. 82PQ
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