Consider having 2-D Cartesian coordinate xy-plane, a block connected to a spring

Braylon Lester 2022-07-19 Answered
Let's consider having 2-D Cartesian coordinate xy-plane, a block connected to a spring (placed horizontally on negative part of x-axis and having natural length L) sitting at the origin point with the spring at natural length.It is allowed to oscillate back and forth about the origin. From the equation that relates the work done by conservative force and the potential energy, U ( x a ) U ( x b ) = x b x a F x d x. If we define the zero point at x=0, we can express its potential energy for 0 < x < L, with
U ( x ) U ( x = 0 ) = 0 x k x d x U ( x ) = 1 2 k x 2
while for −L<x<0, we have (the restoring force switch sign as it now points to the positive x- direction):
U ( x ) U ( x = 0 ) = 0 x k x d x U ( x ) = 1 2 k x 2
My question: Is my idea and this approach for the energy of the system correct? Because I saw from some reference books, they simply say that it is just 1 2 k x 2 for both of the conditions.
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Answers (1)

neobuzdanio
Answered 2022-07-20 Author has 13 answers
For L < x < 0, a spring force of + k x would point in the negative direction (since k>0 and x<0.) This would not be a restoring force, as it would point away from the origin.
On the other hand, a force of F = k x for all x points in the negative direction for positive x (F<0 and x>0), but points in the positive direction for negative x (F>0 and x<0). This is the correct function to model the force, and leads to a potential energy of 1 2 k x 2 for all x
Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

You might be interested in

asked 2021-02-25

A 1000 kg safe is 2.0 m above a heavy-duty spring when the rope holding the safe breaks. The safe hits the spring and compresses it 50 cm. What is the spring constant of the spring?

asked 2021-01-24

A sled with rider having a combined mass of 120 kg travels over the perfectly smooth icy hill shown in the accompanying figure. How far does the sled land from the foot of the cliff (in m)?
image

asked 2021-03-20

Find the tension in each cord in Figure if the weight ofthe suspended object is w. 
a)  
b)

asked 2020-12-15

A 2.0- kg piece of wood slides on the surface. The curved sides are perfectly smooth, but the rough horixontal bottom is 30 m long and has a kinetic friction coefficient of 0.20 with the wood. The iece of wood starts fromrest 4.0 m above the rough bottom (a) Where will this wood eventually come to rest? (b) For the motion from the initial release until the piece of wood comes to rest, what is the total amount of work done by friction?

asked 2022-07-22
What is the gravitational force between two identical 50,000 kg asteroids whose centers of mass are separated by 1000 m?
asked 2022-07-17
Assume that you weigh 500 N. If you are falling down through the air at constant speed, the force of the air against your body is
a) zero
b) more than 0 but less than 500 N
c) 500 N
d) more than 500 N
e) need more information
Explain with thorough reasoning.
asked 2022-05-20
Meaning of acceleration due to gravity
I found article in which it is said that it would be incorrect to say that g is not acceleration due to gravity but local gravitational field as there is no acceleration on a block placed on a table. Please can you explain this as I am in a school and I have read only that g is acceleration due to gravity and textbooks say this too.

New questions