How Does Mass Affect the Oscillation Frequency of a Spider's Web?

[toothpaste666]

Homework Statement

A small fly of mass 0.29g is caught in a spider's web. The web oscillates predominately with a frequency of 4.4Hz .

a) What is the value of the effective spring stiffness constant k for the web?

b) At what frequency would you expect the web to oscillate if an insect of mass 0.50g were trapped?

Homework Equations

f = (1/2Pi)(k/m)^.5

The Attempt at a Solution

a) rearranging the equation

k =m(2Pif)^2 = (.00029kg)(2Pi*4.4Hz)^2 = .22 N/m

mastering physics says I am right on this one. So I figured for part b I just rearrange the equation for f and plug in .0005 for m and .22 for k

f=(1/2Pi)(k/m)^.5 = (1/2Pi)(.22N/m/.0005kg)^.5 = 33Hz

but mastering physics says i am wrong. Where is my mistake?

 

[BvU]

The expression is correct. An estimate (sqrt(2000/5) = 20) yields 20/π, around 3.
As expected: twice as heavy, 1.4 times lower freq.

 

[BiGyElLoWhAt]

Hmm... I'm not sure, looks like right to me. using w = root(k/m) and w = 2pif i get the same thing. Did you try 32.9hz?

 

[toothpaste666]

it said 32.9 was wrong also. and it says in the question it wants 2 sig figs =[

 

[BiGyElLoWhAt]

Have you tried adding another sig fig? use .22 for k and .0005 for m and take it out 2 places.

 

[toothpaste666]

without rounding the answer is 32.94930172. I am not sure if that's what you mean

 

[BiGyElLoWhAt]

Yea that's about what I got, but it wants 2 sig figs and 33 isn't working, so maybe they mis stated and want 2 after the decimal? I'm honestly not sure, toothpaste. Your algebra looks good, we got the same answer, and assuming it did in fact say that .22N/m was the correct k value (I didn't double check that), I'd probably just punch it in the face and call it a day, honestly.

Btw, I've been meaning to say something for a while, but I think your name is effing hilarious XD

 

[toothpaste666]

yeah its telling me .22 N/m is correct on the first part. =[ so frustrating.

and thank you! :D i love this username!

anyways thanks for your help i guess ill email my professor, maybe there is a problem with mastering physics.

 

[BvU]

Listen up, you two: if a.29 g fly swings with 4.5 Hz a HEAVIER fly swings at a LOWER freq. So anything above 4.4 Hz is plain wrong.

 

[nasu]

By increasing the mass the frequency must decrease. You should be aware that 30 something does not make sense if the original frequency was 4.4 Hz.

Check your units and calculations.

 

[AlephZero]

(1/2Pi)(.22N/m/.0005kg)^.5 is correct.

You must be doing something wrong with your calculator. You are getting the decimal point in the wrong place.

 

[BiGyElLoWhAt]

Yea I see what you guys are saying, I kind of feel like a noob for not seeing that. That's my bad everyone =[

I just think it's weird we both got the same (wrong) thing.

 

[toothpaste666]

I forgot parenthesis on my calculator. I entered 20.976/2Pi instead of 20.976/(2Pi)... sorry guys. I got 3.3 this time and mastering physics accepted it

 

[BvU]

My point is that at all times you should make a reasonable guess about the outcome:
1. The square root can't be far from 20,
2. The freq has to be lower than 4.4 by a factor of around 1.5

 

[toothpaste666]

Yea i should have noticed that. Sometimes the intuition aspect of it doesn't come very easily to me