Calculating Energy Required to Rotate a Spiral Spring by 180 Degrees

[KiNGGeexD]

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!

 

[tiny-tim]

Hi KiNGGeexD!

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

I think you're misunderstanding the question …

the torque isn't constant, it's 10^-5*θ Nm, depending on the instantaneous angle θ. ​

 

[KiNGGeexD]

So how would I go about solving the problem?:(

 

[tiny-tim]

linear work done = ∫ F·ds

circular work done = ∫ τ dθ

 

[KiNGGeexD]

Ah so I need to integrate τ dθ for 0-180 degrees

 

[tiny-tim]

yup!

 

[KiNGGeexD]

Haha cheers friend!

 

[KiNGGeexD]

Maybe I'm getting confused but would the answer not just be the same

 

[tiny-tim]

no

show us your integral​

 

[KiNGGeexD]

I'm clearly integrating wrong haha

I had

W= τ dθ

From 0-180 ok I'm not 100% lol

 

[tiny-tim]

show us your integral!

 

[KiNGGeexD]

W=τ dθ

So

W= τ*180 + c

 

[tiny-tim]

an integral should have an ∫ in it

(and limits)

and what is τ ?​

 

[KiNGGeexD]

τ= Iα ?

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

 

[tiny-tim]

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 #

the torque isn't constant, it's 10^-5*θ Nm, depending on the instantaneous angle θ. ​

 

[KiNGGeexD]

For a non constant torque W= ταθ

 

[KiNGGeexD]

That tau was supposed to be I, moment of inertia

 

[KiNGGeexD]

I am integrating

τ from 0-180

Or τθ from 0-180?

 

[KiNGGeexD]

If soW= τ*θ^2 all divided by 2?

 

[tiny-tim]

hmm … what you mean is correct, but that's certainly not the correct way to write it

 

[KiNGGeexD]

Yea I know sorry :(But is that correct?

 

[tiny-tim]

if it means what i think it means, yes

what result do you get?​

 

[KiNGGeexD]

1.62 j

 

[tiny-tim]

you forgot to convert from degrees to radians

 

[KiNGGeexD]

Haha ok in that case4.93*10^-4 :)

 

[tiny-tim]

^-4 ? ​

 

[KiNGGeexD]

Haha sorry where do you get this notation from? Lol!

 

[tiny-tim]

[NOPARSE]type ^-4[/NOPARSE]

 

[KiNGGeexD]

Is my wrong answer right though? Lol

 

[KiNGGeexD]

Wait never mind the dimensions are spot on haha!