Finding Lengths of Springs with Three Identical Masses

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In summary, the three identical springs, each with a force constant of 8.50kN/m and an unstretched length of 0.11m, are supporting three identical 6.00kg masses. The length of each spring when hanging as shown is 0.1169m for the bottom spring, 0.2276m for the middle spring, and 0.33875m for the top spring. It is important to only consider the unstretched length once in the calculation for each spring.
  • #1
Moninder
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Homework Statement



Three identical 6.00kg masses are hung by three identical springs, as shown in the figure. Each spring has a force constant of 8.50kN/m and was 11.0cm long before any masses were attached to it. How long is each spring when hanging as shown? (Hint: First isolate only the bottom mass. Then treat the bottom two masses as a system. Finally, treat all three masses as a system.)

Homework Equations


F=-ma
F=-kx

The Attempt at a Solution


I started with the bottom block.
-ma=-kx
(6.00kgx9.8m/s^2)/-(8.50kN/m)=x
x=6.92m? and then i added 0.11m
and its still wrong
I also took the F=ma and divided by 1000 to get into(0.0588) kN and then divided it by 8.50kN and then dded .11m and still wrong

I need to find all three block eventually
 
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  • #2
That can't be answered without the diagram.
 
  • #3
This is how it is from top to bottom
Ceiling
-
spring
-
block
-
spring
-
block
-
spring
-
block
 
  • #4
Moninder said:

Homework Statement



Three identical 6.00kg masses are hung by three identical springs, as shown in the figure. Each spring has a force constant of 8.50kN/m and was 11.0cm long before any masses were attached to it. How long is each spring when hanging as shown? (Hint: First isolate only the bottom mass. Then treat the bottom two masses as a system. Finally, treat all three masses as a system.)

Homework Equations


F=-ma
F=-kx


The Attempt at a Solution



I also took the F=ma and divided by 1000 to get into(0.0588) kN and then divided it by 8.50kN and then dded .11m and still wrong

What was your answer from doing the calculation this way, and how do you know it was wrong?
 
  • #5
For the bottom spring I got 0.1169m
Middle Spring 0.3376m
Top spring 0.35075m

I put it in an online program
 
  • #6
Still need help
 
  • #7
Moninder said:
I started with the bottom block.
-ma=-kx
(6.00kgx9.8m/s^2)/-(8.50kN/m)=x
x=6.92m?
Note that the spring constant is in kN/m, not N/m.
 
  • #8
Doc Al said:
Note that the spring constant is in kN/m, not N/m.

Yes I know, check my 3 answers i posted, they are with converting the kN
 
  • #9
Moninder said:
For the bottom spring I got 0.1169m
Looks OK.
Middle Spring 0.3376m
Top spring 0.35075m
Show how you got these last two.
 
  • #10
Doc Al said:
Looks OK.

Show how you got these last two.

I added the weights together
Mg=kx
((6+6)9.8)/(8500N/m) + .22 m =middle spring
Top spring
((6+6+6)9.8)/(8500N/m) + 0.33m
 
  • #11
Moninder said:
I added the weights together
Mg=kx
((6+6)9.8)/(8500N/m) + .22 m =middle spring
Top spring
((6+6+6)9.8)/(8500N/m) + 0.33m
Ah... But they all start with an unstretched length of 0.11m.
 
  • #12
Doc Al said:
Ah... But they all start with an unstretched length of 0.11m.

Yes, i did add in the unstrecthed length?
 
  • #13
Moninder said:
Yes, i did add in the unstrecthed length?
For the middle spring you added in twice the unstretched length; for the top spring you added three times the unstretched length.

Each spring has a total length equal to its unstretched length (0.11m for each) plus the amount of stretch (which varies).
 
  • #14
Why would i not add in 2 lengths because the middle spring is also carrying the bottom spring
 
  • #15
Moninder said:
Why would i not add in 2 lengths because the middle spring is also carrying the bottom spring
How does that affect its unstretched length?
 
  • #16
Oh now i get it, i should just only add in 1 unstrecthed length because I am only calculating for 1 spring
 
  • #17
Moninder said:
Oh now i get it, i should just only add in 1 unstrecthed length because I am only calculating for 1 spring
Right.
 
  • #18
Thank you
 

FAQ: Finding Lengths of Springs with Three Identical Masses

How do you determine the length of a spring with three identical masses?

To find the length of a spring with three identical masses, you will need to use Hooke's Law, which states that the force applied to a spring is directly proportional to the displacement of the spring. This means that as you add mass to the spring, the length of the spring will increase proportionally. By measuring the displacement of the spring when each mass is added, you can calculate the length of the spring.

Is the length of a spring affected by the force applied?

Yes, the length of a spring is directly affected by the force applied. This is due to Hooke's Law, which states that the force applied to a spring is directly proportional to the displacement of the spring. As the force increases, the displacement of the spring will also increase, resulting in a longer length.

Can the length of a spring be measured without adding masses?

Yes, the length of a spring can be measured without adding masses. This can be done by using a ruler or measuring tape to directly measure the length of the spring. However, if you are trying to find the length of a spring with three identical masses, it is necessary to add the masses in order to calculate the length using Hooke's Law.

How do you ensure accuracy when measuring the length of a spring with three identical masses?

To ensure accuracy when measuring the length of a spring with three identical masses, it is important to use a consistent method for adding the masses and measuring the displacement of the spring. Additionally, it is helpful to take multiple measurements and calculate an average to minimize errors. Using precise measuring tools, such as a digital scale and calipers, can also improve accuracy.

Are there any other factors that can affect the length of a spring besides mass and force?

Yes, there are other factors that can affect the length of a spring. These include the material and thickness of the spring, the temperature, and any external forces acting on the spring. It is important to keep these factors in mind when conducting experiments to find the length of a spring with three identical masses.

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