found the answer on quizlet but i cannot understand the Us part. it says k=mg/2A but when it was substituted to equation 9, it was just mg/A it says Us= mgh yet there is a times 2 before 0.05 (check picture for context)

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)...
icon
Related questions
icon
Concept explainers
Topic Video
Question

A thrill-seeking cat with mass 4.00 kg is attached by a harness to an ideal spring of negligible mass and oscillates vertically in SHM. The amplitude is 0.050 m, and at the highest point of the motion the spring has its natural unstretched length. Calculate the elastic potential energy of the spring (take it to be zero for the unstretched spring), the kinetic energy of the cat, the gravitational potential energy of the system relative to the lowest point of the motion, and the sum of these three energies when the cat is  (b) at its lowest point

 

found the answer on quizlet but i cannot understand the Us part.

it says k=mg/2A but when it was substituted to equation 9, it was just mg/A

it says Us= mgh yet there is a times 2 before 0.05 (check picture for context)

 

please explain it to me. thanks

(b) When the cat is at its lowest point, then at the lowest
point of the motion the spring has its maximum stretched length i.e. a = 2A, so from equation (1), the elastic
potential energy of the spring will be
Us = k (24)
(8)
= 2k A?
But here we know
mg = kr
= 2kA
From the above, we get
mg
k =
2A
! ??
Hence equation (8) becomes
ng
Us = 2
= mg A
= 4 kg x 9.8 ms
= 3.92 J
(9)
-2
2 0.05 m
Transcribed Image Text:(b) When the cat is at its lowest point, then at the lowest point of the motion the spring has its maximum stretched length i.e. a = 2A, so from equation (1), the elastic potential energy of the spring will be Us = k (24) (8) = 2k A? But here we know mg = kr = 2kA From the above, we get mg k = 2A ! ?? Hence equation (8) becomes ng Us = 2 = mg A = 4 kg x 9.8 ms = 3.92 J (9) -2 2 0.05 m
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Knowledge Booster
Simple Harmonic Motion
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
College Physics
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
Physics for Scientists and Engineers
Physics for Scientists and Engineers
Physics
ISBN:
9781337553278
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
Lecture- Tutorials for Introductory Astronomy
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:
9780321820464
Author:
Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:
Addison-Wesley
College Physics: A Strategic Approach (4th Editio…
College Physics: A Strategic Approach (4th Editio…
Physics
ISBN:
9780134609034
Author:
Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:
PEARSON