Energy methods for spring velocity

In summary, we are given information about a spring attached to a collar that is able to rotate around a fixed body. Its starting position is at the top of a circle with a radius of 180 mm and is given a slight push to start moving. At point A, which is located halfway down the circle, we are asked to find the collar's velocity using energy methods. Using the equations for potential spring energy and gravitational potential energy, we can calculate the potential energy at point A. However, we are unsure of how to use this information to determine the velocity.
  • #1
physicsnewb7
42
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Homework Statement


A spring is attatched to a single position with a 1.2 kg collar at the end. The collar is attatched to a circular fixed body so it can rotate around it. The radius of the circle is 180 mm and the position of where the spring is attatched is 75mm directrly above the center of circle. The springs constant is 300 n/m and its undeformed length is 105mm. It starts out at rest at the top of the circle and is given a slight push to get it moving. It passes through point A on the circle, which is located halfway down on the circle. Using energy methods, find the velocity of collar as it passes through point A.


Homework Equations


Vs=1/2kX^2=potential spring energy, Vg=(distance)x(weight)=gravitational potential energy
T1+V1=T2+V2

The Attempt at a Solution


the distance of point A to the attatched spring is sqrt(75^2+180^2)=195mm
The elongation of the spring is therefore 195-105=90mm then the potential energy would be 1/2kX^2=1/2(300N/m)(.09mm)^2=1.215 J
and the gravitational potential energy would be (.18mm)(1.2 kg)(9.8m/s^2)=2.1
This is where I don't know what to do after calculating the potential energy at point A. How am I supposed to get velocity out of all this mess?

I understand this is a lengthy problem so any help will be GREATLY appreciated.
 
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  • #2
The gravitational potential energy has decreased.
apart from the spring's energy, what is this converted into?
 
  • #3
So you're saying that the gravitational potential energy lossed was conserved by the increase in kinetic energy?
 
  • #4
physicsnewb7 said:
So you're saying that the gravitational potential energy lossed was conserved by the increase in kinetic energy?
+ the springs PE

I don't claim to be the first person to say that:smile:
 

FAQ: Energy methods for spring velocity

How do energy methods work for calculating spring velocity?

Energy methods involve using the principle of conservation of energy to determine the velocity of a spring. This means that the potential energy stored in the spring is equal to the kinetic energy of the mass attached to it at any given point in time.

What are the different types of energy methods used for spring velocity?

The two main types of energy methods used for calculating spring velocity are the elastic potential energy method and the work-energy method. The elastic potential energy method involves using the spring's stiffness and displacement to calculate the potential energy, while the work-energy method involves using the work done by the spring to calculate the kinetic energy.

How accurate are energy methods for determining spring velocity?

Energy methods are considered to be highly accurate for calculating spring velocity as they take into account all the factors that affect the spring, such as its stiffness, displacement, and the mass attached to it. However, the accuracy may vary depending on the complexity of the system being analyzed.

Can energy methods be used for non-linear springs?

Yes, energy methods can be used for non-linear springs as long as the principle of conservation of energy is still applicable. However, the calculations may be more complex and may require additional equations or numerical methods to solve.

What are the advantages of using energy methods for spring velocity over other methods?

Energy methods are advantageous as they provide a more comprehensive understanding of the spring's behavior by taking into account both potential and kinetic energy. They also allow for the analysis of complex systems and can be applied to non-linear springs. Additionally, energy methods are often quicker and easier to use compared to other methods such as differential equations or numerical simulations.

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