A solid metal block with a mass of 1.30 kg is attached to a spring and is able to oscillate horizontally with negligible friction. The block is pulled to a distance of 0.200 m from its equilibrium position, held in place with a force of 19.0 N, and then released from rest. It then oscillates in simple harmonic motion. (The block oscillates along the x-axis, where x = 0 is the equilibrium position.) (a) What is the spring constant (in N/m)? 95 N/m (b) What is the frequency of the oscillations (in Hz)? 1.36 Hz (c) What is the maximum speed of the block (in m/s)? 1.71 m/s (d) At what position(s) (in m) on the x-axis does the maximum speed occur? m X = ± (e) What is the maximum acceleration of the block? (Enter the magnitude in m/s².) m/s² (f) At what position(s) (in m) on the x-axis does the maximum acceleration occur? m X = + (g) What is the total mechanical energy of the oscillating spring-block system (in J)? J (h) What is the speed of the block (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 block (in m/s2) when its position is equal to one-third of the maximum displacement from equilibrium? m/s²

Classical Dynamics of Particles and Systems
5th Edition
ISBN:9780534408961
Author:Stephen T. Thornton, Jerry B. Marion
Publisher:Stephen T. Thornton, Jerry B. Marion
Chapter2: Newtonian Mechanics-single Particle
Section: Chapter Questions
Problem 2.52P: A particle of mass m moving in one dimension has potential energy U(x) = U0[2(x/a)2 (x/a)4], where...
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A solid metal block with a mass of 1.30 kg is attached to a spring and is able to oscillate horizontally with negligible friction. The block is pulled to a distance of
0.200 m from its equilibrium position, held in place with a force of 19.0 N, and then released from rest. It then oscillates in simple harmonic motion. (The block
oscillates along the x-axis, where x = 0 is the equilibrium position.)
(a) What is the spring constant (in N/m)?
95
N/m
(b) What is the frequency of the oscillations (in Hz)?
1.36
Hz
(c) What is the maximum speed of the block (in m/s)?
1.71
m/s
(d) At what position(s) (in m) on the x-axis does the maximum speed occur?
X = +
m
(e) What is the maximum acceleration of the block? (Enter the magnitude in m/s².)
m/s²
(f) At what position(s) (in m) on the x-axis does the maximum acceleration occur?
X = +
m
(g) What is the total mechanical energy of the oscillating spring-block system (in J)?
J
(h) What is the speed of the block (in m/s) when its position is equal to one-third of the maximum displacement from equilibrium?
m/s
(1) What is the magnitude of the acceleration of the block (in m/s²) when its position is equal to one-third of the maximum displacement from equilibrium?
m/s²
Transcribed Image Text:A solid metal block with a mass of 1.30 kg is attached to a spring and is able to oscillate horizontally with negligible friction. The block is pulled to a distance of 0.200 m from its equilibrium position, held in place with a force of 19.0 N, and then released from rest. It then oscillates in simple harmonic motion. (The block oscillates along the x-axis, where x = 0 is the equilibrium position.) (a) What is the spring constant (in N/m)? 95 N/m (b) What is the frequency of the oscillations (in Hz)? 1.36 Hz (c) What is the maximum speed of the block (in m/s)? 1.71 m/s (d) At what position(s) (in m) on the x-axis does the maximum speed occur? X = + m (e) What is the maximum acceleration of the block? (Enter the magnitude in m/s².) m/s² (f) At what position(s) (in m) on the x-axis does the maximum acceleration occur? X = + m (g) What is the total mechanical energy of the oscillating spring-block system (in J)? J (h) What is the speed of the block (in m/s) when its position is equal to one-third of the maximum displacement from equilibrium? m/s (1) What is the magnitude of the acceleration of the block (in m/s²) when its position is equal to one-third of the maximum displacement from equilibrium? m/s²
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