Calculating Change in Length of Rubber Tube

In summary, the conversation discusses the calculation of delta L, the change in length of a rubber tube attached to a spinning ball. Using the equations for centripetal force and elastic force, the value of k is found to be 50 N/m. However, when plugging in values for mass, angular velocity, and k, the resulting calculation for delta L is approximately 0.09m, with the hint that angular velocity should be measured in radians. After discovering this error, the correct answer is determined to be 0.0857m.
  • #1
huskydc
78
0
A 100 g ball is attached to a rubber tube and is spun around in a circle at a rate of one revolution every second. A force of 0.5 N is required to stretch the tube 1.0 cm.

If the original length is L = 1.0 m, what will be the change in length of the rubber tube when the ball is revolving?

It was given as a hint that centripetal force is equal to elastic force:

F_c=mass *length*omega^2,

where length is now the stretched length, that is,
length= L+delta L.

The elastic force is equal to
F_el=k*delta L.

first, I found k to be 50. but I plugged in k to the above equation and tried to find delta L. as .002 , but it's incorrect, hints?
 
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  • #2
I get delta L = about 0.09m.

I see nothing wrong with your approach. You must have a calculation error.
 
  • #3
0.09 is also incorrect...
 
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  • #4
I found delta L to be .002 m as well.
Here's what I did.

Fc=m*(dL+1)*w^2
Fs=k*dL

.5 N=k*.01 m
k=50 N/m

Fc=Fs
m*(dL+1)*w^2=k*dL
m*w^2=k*dL - m*w^2*dL
m*w^2=dL*(k-m*w^2)
dL=(m*w^2)/(k-m*w^2)

When you plug in the values (m=.1 kg; w=1 rps; k=50 N/m) the answer is dL=.1/49.9
So dL = .020 m
 
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  • #5
I also get 0.09 (0.086) m...

[tex]\Delta L = \frac{mL \omega^2}{k-m\omega^2}\approx 0.09 m[/tex]
 
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  • #6
=( , i tried them all, none of them works...
 
  • #7
I agree with Gokul; the answer is about 0.09m. What makes you think that this answer is wrong?

zwtipp05 said:
I found delta L to be .002 m as well.
Here's what I did.
...
dL=(m*w^2)/(k-m*w^2)

When you plug in the values (m=.1 kg; w=1 rps; k=50 N/m) the answer is dL=.1/49.9
So dL = .020 m
[itex]\omega = 2 \pi[/itex], not 1. (It's measured in radians.)
 
  • #8
the answer turns out to be .0857m, I guess we'er all too caught up in the big picture and totally forgot about the omega being 2pi, thanks
 

1. How do you calculate the change in length of a rubber tube?

To calculate the change in length of a rubber tube, you need to measure the original length of the tube and the final length after it has been stretched. Then, subtract the original length from the final length to get the change in length.

2. What is the formula for calculating change in length of a rubber tube?

The formula for calculating change in length is: change in length = final length - original length.

3. What unit of measurement is used for change in length of a rubber tube?

The change in length of a rubber tube is typically measured in millimeters (mm) or centimeters (cm), depending on the size of the tube.

4. Can other factors affect the change in length of a rubber tube?

Yes, there are other factors that can affect the change in length of a rubber tube, such as the type of material the tube is made of and the amount of force applied to stretch it.

5. Why is it important to calculate the change in length of a rubber tube?

Calculating the change in length of a rubber tube is important in understanding the properties of the material. It can also be used to determine the elasticity of the tube and its ability to return to its original shape after being stretched.

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