Rubber cord oscillation help

In summary, the problem involves a 2kg block hanging from a rubber cord with an unstretched length of 0.500 meters and a mass of 5.3 grams. The spring constant for the cord is 105 N/m. The task is to find the tension when the block is at its lowest point. To do this, one needs to find the distance the cord has stretched and use the spring constant to calculate the tension. This can be done using energy principles, specifically the equation mgh = 0.5kx^2, where h is equal to x.
  • #1
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Homework Statement


So a 2kg block hangs from a rubber cord and it's being supported so that the cord is not stretched. The unstretch length of the cord is .500 meters and its mass is 5.3 grams. The spring constant for the cord is 105 N/m. The block is released and stops at the lowest point. a)Find the tension b),c) I know how to solve, I only need tension...


Homework Equations


I set up Newton's second law equation when it's at the bottom but I have two variables T and x. I also looked at the osciallation way of approaching this problem but could not think of how I can relate everything together. I know there's only like one equation I'm missing and that's all I need but I don't know what.
Thanks
 
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  • #2
I assume they only want the tension when the block is at the lowest point. The tension will not be exactly uniform, since the cord has mass, but the cord's mass is so small compared to that of the block I am assuming you can ignore that. What you need to find is how far the cord has stretched when the block comes to rest and use the spring constant to find the force the cord is providing at that time. That will be the tension. You should be able to use energy principles to find it.
 
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  • #3
hm...part b asks how far it stretches so I thought there would be some other way to approach this. I'm having some troubles trying to visualize the energy equation since at the beginning it has potential energy, but no kinetic right? Then at the lowest point, it is another potential energy. So would it be just mgh=.5kx^2? then h is basically the x correct? so we get 2mg/k=x?

EDIT: Yay I got the answer correct! Thank you soooo much!
 

1. What causes a rubber cord to oscillate?

The oscillation of a rubber cord is caused by the transfer of energy from a source, such as a hand pulling on the cord, to the cord itself. This energy causes the cord to stretch and then recoil, creating the oscillating motion.

2. How can I control the oscillation of a rubber cord?

The oscillation of a rubber cord can be controlled by adjusting the force and direction of the initial pull, as well as the length and thickness of the cord. Additionally, the surrounding environment, such as air resistance, can also affect the oscillation.

3. What factors affect the frequency of a rubber cord's oscillation?

The frequency of a rubber cord's oscillation is affected by the length, thickness, and tension of the cord, as well as the surrounding environment. A longer, thinner, and more tensioned cord will have a higher frequency, while a shorter, thicker, and less tensioned cord will have a lower frequency.

4. How does the material of the rubber cord impact its oscillation?

The material of the rubber cord can impact its oscillation in several ways. A stiffer material will result in a faster and more rigid oscillation, while a more elastic material will result in a slower and more flexible oscillation. The density and weight of the material can also affect the oscillation.

5. Can the oscillation of a rubber cord be used for practical purposes?

Yes, the oscillation of a rubber cord can be harnessed for practical purposes such as in shock absorbers, musical instruments, and even energy harvesting devices. It can also be used to study the properties of materials and to demonstrate principles of physics.

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