A mass between two springs-simple harmonic motion

AI Thread Summary
A 4kg mass is balanced between two springs on a frictionless surface, with spring 1 stretched 4 meters and spring constants of 40 N/m and 60 N/m for springs 1 and 2, respectively. The first question determines that spring 2 is stretched 8/3 meters to the left. The potential energy in spring 1 is calculated as 320 J, while spring 2's potential energy is approximately 213.33 J, leading to a total potential energy of about 553.33 J for the system. The discussion emphasizes the importance of correctly labeling forces and understanding the direction of motion in harmonic systems. Overall, the calculations and concepts of simple harmonic motion are explored in the context of the problem.
cnputhur
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Homework Statement


A 4kg mass remains at rest on a friction free surface due to equal and opposite pulls of two springs. Spring 1 is stretched 4 meters. The k in spring 1 equals 40 N/m and the k in spring 2 equals 60 N/m.

This is what the the picture looks like in words.
From left to the right, these are the objects.

Wall, spring 1, 4kg mass, spring 2, wall

1. How much is spring 2 stretched?
2. What is the potential energy stored in each spring?
3. Taken as a simple harmonic motion system, what is the potential energy stored in the system

Homework Equations


The Attempt at a Solution


Homework Statement


Homework Equations


F=ma
Restorative force=-kx perhaps?

The Attempt at a Solution


1. F=-kx=-40(4)=-160N
160=-kx=-60x
x=-8/3 meters
8/3 meters to the left?

2. PE=0.5kx^2=0.5(40)(4)^2=320J in Spring 1
PE=0.4kx^2=0.5(60)(-8/3)^2=640/3 J in Spring 2

3. 320+(640/3)=1660/3 J

I'm very unsure about these answers. To be honest, I don't understand the questions.
 
Last edited:
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Hello cnputhur, welcome to PF.

Your solution to the first question is the correct magnitude. However your minus signs may have gone awry. Try labeling the forces in future to help with these things ( a diagram will then make it very clear which way it must go).

And for question 2?...
 
cnputhur said:

Homework Statement


A 4kg mass remains at rest on a friction free surface due to equal and opposite pulls of two springs. Spring 1 is stretched 4 meters. The k in spring 1 equals 40 N/m and the k in spring 2 equals 60 N/m.

This is what the the picture looks like in words.
From left to the right, these are the objects.

Wall, spring 1, 4kg mass, spring 2, wall

1. How much is spring 2 stretched?
2. What is the potential energy stored in each spring?
3. Taken as a simple harmonic motion system, what is the potential energy stored in the system?



Homework Equations





The Attempt at a Solution


Homework Statement





Homework Equations


F=ma
Restorative force=-kx perhaps?



The Attempt at a Solution


F=-kx=-40(4)=-160N
160=-kx=-60x
x=-8/3 meters
8/3 meters to the left?

f=kx. -ve sign only indicates it is in the opp. direction.
about energy, spring p.e. =1/2kx^2
 

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