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Assume that a physical pendulum can be modeled as a long, thin cylindrical rod, pivoting around one end. The mass of the pendulum is 630. g. Its period is 2.444 s. If its moment of inertia can be calculated by I = 1/3mL2, what is the length, L, of the rod? (The answer it’s supposed to be 1.06m) in the image there are two possible formulas

Assume that a physical pendulum can be modeled as a long, thin cylindrical rod, pivoting around one end. The mass of the pendulum is 630. g. Its period is 2.444 s. If its moment of inertia can be calculated by I = 1/3mL2, what is the length, L, of the rod? (The answer it’s supposed to be 1.06m) in the image there are two possible formulas

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Assume that a physical pendulum can be modeled as a long, thin cylindrical rod, pivoting around one end. The mass of the pendulum is 630. g. Its period is 2.444 s. If its moment of inertia can be calculated by I = 1/3mL2, what is the length, L, of the rod? (The answer it’s supposed to be 1.06m) in the image there are two possible formulas
Period of a Pendulum-Your Leg What is the natural period of a human leg? This is an important consider- ation for "smart" prosthetic legs that adjust to the motion of the user. Solution: First, model an average human leg as a thin solid rod of length L and mass m 16.0 kg. From Appendix F, the moment of inertia for a thin solid rod is I mL/3. The pendulum arm is the distance from the pivot point to the center of mass. Assume for this example that the mass is uni- formly distributed throughout the leg; then L/2. = 1.5 m Use Equation 12.10 to determine the period of a human leg. Substitute the known information into the formula and solve for T.. T= 2m mgle V lg|/2) = 2T T-2V3191 2L 3|g| 2(1.5 m) 31-9.81 m/s T 2.00 s= 2.0 s The natural period for an entire human leg is about 2 seconds.
Transcribed Image Text:Period of a Pendulum-Your Leg What is the natural period of a human leg? This is an important consider- ation for "smart" prosthetic legs that adjust to the motion of the user. Solution: First, model an average human leg as a thin solid rod of length L and mass m 16.0 kg. From Appendix F, the moment of inertia for a thin solid rod is I mL/3. The pendulum arm is the distance from the pivot point to the center of mass. Assume for this example that the mass is uni- formly distributed throughout the leg; then L/2. = 1.5 m Use Equation 12.10 to determine the period of a human leg. Substitute the known information into the formula and solve for T.. T= 2m mgle V lg|/2) = 2T T-2V3191 2L 3|g| 2(1.5 m) 31-9.81 m/s T 2.00 s= 2.0 s The natural period for an entire human leg is about 2 seconds.
EXAMPLE 12-1 SHM in a Spring-Mass System A 0.190 kg mass is hung from an ideal spring with a spring constant k 76.0 N/m. It is set in motion by displacing it 3.00 cm downward, then releasing it. (a) What is the period of its motion? (b) What is the frequency? Solution: a. Use Equation 12.6 to solve for period: T= 2TTK 0.190 kg 76.0 N/m =2T kg (kg-m.)/(m-s) (unit cancellation) T 0.3141. A, T 0.314 s b. Take the reciprocal of the period to find the frequency: f==0.3141 s f= 3.183 s = 3.18 Hz Notice that the initial displacement, or amplitude, of the mass has no effect on period (T) or frequency (f).
Transcribed Image Text:EXAMPLE 12-1 SHM in a Spring-Mass System A 0.190 kg mass is hung from an ideal spring with a spring constant k 76.0 N/m. It is set in motion by displacing it 3.00 cm downward, then releasing it. (a) What is the period of its motion? (b) What is the frequency? Solution: a. Use Equation 12.6 to solve for period: T= 2TTK 0.190 kg 76.0 N/m =2T kg (kg-m.)/(m-s) (unit cancellation) T 0.3141. A, T 0.314 s b. Take the reciprocal of the period to find the frequency: f==0.3141 s f= 3.183 s = 3.18 Hz Notice that the initial displacement, or amplitude, of the mass has no effect on period (T) or frequency (f).
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