Unstretched Spring and Angular Velocity Problem

In summary, the problem involves a disk of mass 73 kg held by a spring with an unstretched length of 88 cm and stiffness constant of 430 N/cm, resting on a frictionless table. The disk is then orbited in a circle at an angular velocity of 0.675 rad/s. After some derivation, the solution is found to be x = r/((k/mw^2)-1), where r is the length of the spring in meters, k is the stiffness constant in N/m, m is the mass of the disk in kg, and w is the angular velocity in rad/s. After converting the units correctly, the spring is found to be stretched by 0.121 cm.
  • #1
BitterSuites
38
0
[SOLVED] Unstretched Spring and Angular Velocity Problem

Homework Statement



A disk of mass 73 kg is held by a spring of unstretched length 88 cm and stiffness constant 430 N/cm, and rests on a frictionless table. It is then orbited in a circle at angular velocity .675 rad/s.

By how much is the spring stretched? Answer in units of cm.

Homework Equations



After a bit of derivation, I came up with x = r/((k/mw^2)-1).

The Attempt at a Solution



r = 88
k = 430
m= 73
w = .675

It does not seem to work out. Am I being to complicated about it? Any help/hand-holding is greatly appreciated.
 
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  • #2
Force acting on the disc in circular motion== mv^2/r

Now use hook's law to calculate extension..
 
  • #3
BitterSuites said:
After a bit of derivation, I came up with x = r/((k/mw^2)-1).
Looks good to me.

The Attempt at a Solution



r = 88
k = 430
m= 73
w = .675
Make sure you are using standard units. Express lengths (and k) in terms of meters, not cm.
 
  • #4
Thanks for the catch on conversion. I changed length to .88 and K to 4.3, getting an answer in m. I then converted it to cm but the online system still says I am incorrect.

I can't use mv^2/r because I don't have v. That is why I did that insane derivation.

Or am I wrong?

I think I'm a few baby steps away from having this.
 
  • #5
BitterSuites said:
I changed length to .88 and K to 4.3...
Redo that last one. :wink:
 
  • #6
Uh oh. Did I go the wrong way with it? 43000N/m?
 
  • #7
That's better.
 
  • #8
Oh, thank you so much *sighs in relief*

Converting correctly makes the problem work. Who knew? :D
 

What is an unstretched spring?

An unstretched spring is a type of elastic material that is typically made of metal or plastic and is used in many scientific and industrial applications. It is a flexible material that can stretch and return to its original shape when a force is applied and then removed.

How does an unstretched spring behave in terms of force and displacement?

When an unstretched spring is stretched, it exerts a restoring force that is proportional to the displacement from its original length. This relationship is known as Hooke's Law and can be written as F = -kx, where F is the force, k is the spring constant, and x is the displacement.

What is the relationship between angular velocity and the length of an unstretched spring?

The angular velocity of an unstretched spring is not directly related to its length. However, it can affect the spring's behavior when it is stretched. The longer the unstretched spring, the more potential energy it can store, and the larger the angular displacement it can undergo before reaching its elastic limit.

How does the angular velocity of a rotating object affect the tension in an unstretched spring?

The angular velocity of a rotating object can affect the tension in an unstretched spring if the spring is attached to the object and is rotating with it. In this case, the angular velocity will affect the magnitude of the force exerted on the spring, which can impact the spring's behavior and potentially cause it to stretch or compress more.

What factors can affect the angular velocity of an object attached to an unstretched spring?

The angular velocity of an object attached to an unstretched spring can be affected by several factors, such as the mass of the object, the length and stiffness of the spring, and any external forces acting on the object. Additionally, the initial conditions, such as the initial angular displacement and velocity, can also impact the angular velocity of the object.

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