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A metal cylinder with a mass of 1.10 kg is attached to a spring and is able to oscillate horizontally with negligible friction. The cylinder is pulled to a distance of 0.200 m from its equilibrium position, held in place with a force of 18.0 N, and then released from rest. It then oscillates in simple harmonic motion. (The cylinder oscillates along the x-axis, where x = 0 is the equilibrium position.) (a) What is the spring constant (in N/m)? 90 N/m (b) What is the frequency of the oscillations (in Hz)? 1.44 ✔ Hz (c) What is the maximum speed of the cylinder (in m/s)? 1.81 ✓ m/s (d) At what position(s) (in m) on the x-axis does the maximum speed occur? x= ± 0 m (e) What is the maximum acceleration of the cylinder? (Enter the magnitude in m/s².) 16.37 ✓ m/s² (f) At what position(s) (in m) on the x-axis does the maximum acceleration occur? x = ± 0.2 m (g) What is the total mechanical energy of the oscillating spring-cylinder system (in J)? (h) What is the speed of the cylinder (in m/s) when its position is equal to one-third of the maximum displacement from equilibrium? m/s (i) What is the magnitude of the acceleration of the cylinder (in m/s2) when its position is equal to one-third of the maximum displacement from equilibrium? m/s²

A metal cylinder with a mass of 1.10 kg is attached to a spring and is able to oscillate horizontally with negligible friction. The cylinder is pulled to a distance of 0.200 m from its equilibrium position, held in place with a force of 18.0 N, and then released from rest. It then oscillates in simple harmonic motion. (The cylinder oscillates along the x-axis, where x = 0 is the equilibrium position.) (a) What is the spring constant (in N/m)? 90 N/m (b) What is the frequency of the oscillations (in Hz)? 1.44 ✔ Hz (c) What is the maximum speed of the cylinder (in m/s)? 1.81 ✓ m/s (d) At what position(s) (in m) on the x-axis does the maximum speed occur? x= ± 0 m (e) What is the maximum acceleration of the cylinder? (Enter the magnitude in m/s².) 16.37 ✓ m/s² (f) At what position(s) (in m) on the x-axis does the maximum acceleration occur? x = ± 0.2 m (g) What is the total mechanical energy of the oscillating spring-cylinder system (in J)? (h) What is the speed of the cylinder (in m/s) when its position is equal to one-third of the maximum displacement from equilibrium? m/s (i) What is the magnitude of the acceleration of the cylinder (in m/s2) when its position is equal to one-third of the maximum displacement from equilibrium? m/s²

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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A metal cylinder with a mass of 1.10 kg is attached to a spring and is able to oscillate horizontally with negligible friction. The cylinder is pulled to a distance of 0.200 m from its equilibrium position, held in place with a force of 18.0 N, and then released from rest. It then oscillates in simple harmonic motion. (The cylinder oscillates along the x-axis, where x = 0 is the equilibrium position.) (a) What is the spring constant (in N/m)? 90 N/m ✔ (b) What is the frequency of the oscillations (in Hz)? 1.44 Hz (c) What is the maximum speed of the cylinder (in m/s)? 1.81 m/s (d) At what position(s) (in m) on the x-axis does the maximum speed occur? x = ± 0 m (e) What is the maximum acceleration of the cylinder? (Enter the magnitude in m/s².) 16.37 m/s² ✔ (f) At what position(s) (in m) on the x-axis does the maximum acceleration occur? x = ± 0.2 m (g) What is the total mechanical energy of the oscillating spring-cylinder system (in J)? J (h) What is the speed of the cylinder (in m/s) when its position is equal to one-third of the maximum displacement from equilibrium? m/s (i) What is the magnitude of the acceleration of the cylinder (in m/s2) when its position is equal to one-third of the maximum displacement from equilibrium? m/s²
Transcribed Image Text:A metal cylinder with a mass of 1.10 kg is attached to a spring and is able to oscillate horizontally with negligible friction. The cylinder is pulled to a distance of 0.200 m from its equilibrium position, held in place with a force of 18.0 N, and then released from rest. It then oscillates in simple harmonic motion. (The cylinder oscillates along the x-axis, where x = 0 is the equilibrium position.) (a) What is the spring constant (in N/m)? 90 N/m ✔ (b) What is the frequency of the oscillations (in Hz)? 1.44 Hz (c) What is the maximum speed of the cylinder (in m/s)? 1.81 m/s (d) At what position(s) (in m) on the x-axis does the maximum speed occur? x = ± 0 m (e) What is the maximum acceleration of the cylinder? (Enter the magnitude in m/s².) 16.37 m/s² ✔ (f) At what position(s) (in m) on the x-axis does the maximum acceleration occur? x = ± 0.2 m (g) What is the total mechanical energy of the oscillating spring-cylinder system (in J)? J (h) What is the speed of the cylinder (in m/s) when its position is equal to one-third of the maximum displacement from equilibrium? m/s (i) What is the magnitude of the acceleration of the cylinder (in m/s2) when its position is equal to one-third of the maximum displacement from equilibrium? m/s²
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