The natural length of a spring

In summary, the problem involves a block fixed on an ideal spring and two different lengths of the spring, 50 cm and 80 cm, resulting in two different forces, 5 N and 10 N. The natural length of the spring and the spring constant are unknown. The relevant equations are used to write a system of two equations for the forces, which includes the two unknowns. The problem does not require complex algebra or a calculator.
  • #1
astrololo
200
3

Homework Statement



A block is fixed on the extremity of a mobile ideal spring that is horizontal and which has the other side of it fixed (Non mobile). When the length of the spring is 50 cm, the block has a force of 5 N on the right; When the length of the spring is 80 cm, the block has a force of 10 N vers the left. What is the natural length of the spring and what is the spring constant?

Image of the situation : http://imgur.com/RN7Hv3T

Homework Equations


e=L-Lnat
F=k*Absolutevalue(e)

The Attempt at a Solution


I know that the natural length is going to be between 50 and 80 cm and that the natural length is going to be closer to 50 cm because the force is 5 N which indicates that we don't put a lot of pressure on it. Other than that, I have no idea where to go next.
 
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  • #2
astrololo said:

Homework Statement



A block is fixed on the extremity of a mobile ideal spring that is horizontal and which has the other side of it fixed (Non mobile). When the length of the spring is 50 cm, the block has a force of 5 N on the right; When the length of the spring is 80 cm, the block has a force of 10 N vers the left. What is the natural length of the spring and what is the spring constant?

Image of the situation : http://imgur.com/RN7Hv3T

Homework Equations


e=L-Lnat
F=k*Absolutevalue(e)

The Attempt at a Solution


I know that the natural length is going to be between 50 and 80 cm and that the natural length is going to be closer to 50 cm because the force is 5 N which indicates that we don't put a lot of pressure on it. Other than that, I have no idea where to go next.

Whats the work done for each displacement?
 
  • #3
Student100 said:
Whats the work done for each displacement?
You mean what have I done so far ? Nothing...
 
  • #4
astrololo said:
You mean what have I done so far ? Nothing...

No I mean what's the work required to compress the string to 50 cm or stretch it to 80 cm?
 
  • #5
Student100 said:
No I mean what's the work required to compress the string to 50 cm or stretch it to 80 cm?
Oh, I guess that if we want to maintain it stable, then it's going to be -5 N on the left and 10 N on the right. So it's the inverse.
 
  • #6
astrololo said:
Oh, I guess that if we want to maintain it stable, then it's going to be -5 N on the left and 10 N on the right. So it's the inverse.

Remember that work is ##w=\vec{F}\cdot\vec{R}##, one dimensional (this problem) we can write ##w=F_xR_x##

The spring is compressed in the first case from some natural length, and stretched in the second. We can write work in terms of some variable, L.
 
  • #7
Student100 said:
Remember that work is ##w=\vec{F}\cdot\vec{R}##, one dimensional (this problem) we can write ##w=(F_x)(R_x)##
Sorry but we didn't see this yet. Also, my problem sindicates that this exercice's solution doesn't any complex/hard algebra or a calculator.
 
  • #8
astrololo said:
Sorry but we didn't see this yet. Also, my problem sindicates that this exercice's solution doesn't any complex/hard algebra or a calculator.

Then the rabbit hole I'm going to lead you down probably isn't the easiest way to do this problem. If no one else has responded when I get home I'll take a second look.
 
  • #9
Student100 said:
Then the rabbit hole I'm going to lead you down probably isn't the easiest way to do this problem. If no one else has responded when I get home I'll take a second look.
Thank you, I got some other things to do so I'm patient with this.
 
  • #10
Use your "Relevant equations" to write a system of two equations for the forces. It will involve two unknowns, the spring's constant and the spring's rest length.
 
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  • #11
Nathanael said:
Use your "Relevant equations" to write a system of two equations for the forces. It will involve two unknowns, the spring's constant and the spring's rest length.
Thank you ! I didn't realize that it was a system of equation. The worse is that I was able to get the two equations previously but I didn't realize that I had a system ! Thank you again !
 
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1. What is the natural length of a spring?

The natural length of a spring is the length of the spring when it is not being stretched or compressed by any external forces. This is also known as the equilibrium length.

2. How is the natural length of a spring determined?

The natural length of a spring is determined by the material it is made of, the thickness of the wire used, and the number of coils in the spring.

3. Can the natural length of a spring change over time?

Yes, the natural length of a spring can change over time due to factors such as fatigue, corrosion, and temperature changes. This can lead to a decrease in the spring's elasticity and stiffness.

4. How does the natural length of a spring affect its performance?

The natural length of a spring is an important factor in determining its performance. If a spring is stretched or compressed beyond its natural length, it may not return to its original length and can lose its elasticity. This can affect its ability to absorb and release energy effectively.

5. Is the natural length of a spring the same as its resting length?

No, the resting length of a spring is the length when it is not under any external forces, but it may not necessarily be its natural length. The natural length is the length at which the spring is in equilibrium and has no tension or compression.

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