Calculating Energy Required to Rotate a Spiral Spring by 180 Degrees

In summary, the conversation discusses a spiral spring and the energy required to turn it through 180 degrees from its relaxed state. The solution involves finding the work done by integrating the torque from 0 to 180 degrees, which is equal to the moment of inertia times the angular displacement squared, divided by 2. The correct answer, after converting from degrees to radians, is 4.93*10^-4 joules.
  • #1
KiNGGeexD
317
1
A spiral spring exerts a restoring torque on an axis proportional to the angle through which the axis is turned. If it provides a torque of 10-5 Nmrad-1, find the energy required to turn it through 180degrees from its relaxed state?

My solution was simple

Work done = torque* the angle theta but I seemed to get the wrong answer!
 
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  • #2
Hi KiNGGeexD! :smile:

(try using the X2 button just above the Reply box :wink:)

I think you're misunderstanding the question …

the torque isn't constant, it's 10-5*θ Nm, depending on the instantaneous angle θ. :wink:
 
  • #3
So how would I go about solving the problem?:(
 
  • #4
linear work done = ∫ F·ds

circular work done = ∫ τ dθ :wink:
 
  • #5
Ah so I need to integrate τ dθ for 0-180 degrees?:)
 
  • #6
yup! :biggrin:
 
  • #7
Haha cheers friend!
 
  • #8
Maybe I'm getting confused but would the answer not just be the same?:)
 
  • #9
no

show us your integral​
 
  • #10
I'm clearly integrating wrong haha

I had

W= τ dθ

From 0-180 ok I'm not 100% lol
 
  • #11
show us your integral! :rolleyes:
 
  • #12
W=τ dθ

So

W= τ*180 + c
 
  • #13
an integral should have an ∫ in it :confused:

(and limits)

and what is τ ?​
 
  • #14
τ= Iα ?

And yea I know about the imetrgral sign and limits I just can't do it on my phone:(!
 
  • #15
KiNGGeexD said:
And yea I know about the imetrgral sign and limits I just can't do it on my phone:(!

try typing two #, then \int, then two more # :wink:

tiny-tim said:
the torque isn't constant, it's 10-5*θ Nm, depending on the instantaneous angle θ. :wink:
 
  • #16
For a non constant torque W= ταθ
 
  • #17
That tau was supposed to be I, moment of inertia
 
  • #18
I am integrating

τ from 0-180

Or τθ from 0-180?
 
  • #19
If soW= τ*θ^2 all divided by 2?
 
  • #20
hmm :redface: … what you mean is correct, but that's certainly not the correct way to write it
 
  • #21
Yea I know sorry :(But is that correct?
 
  • #22
if it means what i think it means, yes

what result do you get?​
 
  • #23
1.62 j
 
  • #24
you forgot to convert from degrees to radians
 
  • #25
Haha ok in that case4.93*10^-4 :)
 
  • #26
-4 ? :confused:
 
  • #27
Haha sorry where do you get this notation from? Lol!
 
  • #28
[NOPARSE]type -4[/NOPARSE] :wink:
 
  • #29
Is my wrong answer right though? Lol
 
  • #30
Wait never mind the dimensions are spot on haha!
 

1. How do you calculate the energy required to rotate a spiral spring by 180 degrees?

To calculate the energy required to rotate a spiral spring by 180 degrees, you will need to use the formula E = 1/2 * k * θ^2, where E is the energy in joules, k is the spring constant, and θ is the angle of rotation in radians. You can find the spring constant by dividing the force applied to the spring by the distance it is stretched or compressed.

2. What is the spring constant and how does it affect the energy required to rotate a spiral spring?

The spring constant is a measure of how stiff the spring is. It is represented by the letter k and is measured in units of force per unit distance (N/m). The higher the spring constant, the more energy is required to rotate the spiral spring by 180 degrees.

3. Can you use the same formula to calculate the energy required for any type of spiral spring?

Yes, the formula E = 1/2 * k * θ^2 can be used to calculate the energy required for any type of spiral spring as long as the spring constant and angle of rotation are known. However, it is important to note that the formula assumes that the spring is being rotated in a uniform circular motion.

4. How does the angle of rotation affect the energy required to rotate a spiral spring?

The angle of rotation, represented by θ in the formula E = 1/2 * k * θ^2, directly affects the amount of energy required to rotate a spiral spring. The greater the angle of rotation, the more energy is required to overcome the resistance of the spring and complete the rotation.

5. Is there a limit to the amount of energy that can be stored in a spiral spring?

Yes, there is a limit to the amount of energy that can be stored in a spiral spring. This limit is known as the elastic limit and is determined by the material and design of the spring. Once the elastic limit is reached, the spring will permanently deform and lose its ability to store energy.

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