Solve Kinetics, Springs: Find Collar Velocity at s=1 ft

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Homework Help Overview

The problem involves a 2-lb collar on a smooth shaft and a spring, with the goal of determining the collar's velocity at a specific position when it is initially given a velocity. The subject area pertains to kinetics and spring dynamics.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the relationship between kinetic energy and the work done by the spring. There are attempts to express the spring force and its impact on the collar's velocity. Questions arise regarding how to incorporate kinetic energy calculations and the non-constant nature of the spring force into the analysis.

Discussion Status

The discussion is ongoing, with participants exploring the implications of the Work-Kinetic Energy Theorem and the need for integration to account for the variable spring force. Some guidance has been provided regarding the relationship between kinetic energy and work done by the spring, but no consensus has been reached on the specific calculations required.

Contextual Notes

Participants note the complexity of the problem and express surprise at the level of difficulty without prior explanation of kinetic energy calculations. There may be assumptions about the initial conditions and the behavior of the spring that are being questioned.

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Homework Statement



The 2-lb collar C fits loosely on the smooth shaft. If the spring is unstretched when s = 0 and the collar is given a velocity of 15 ft/s, determine the velocity of the collar when s = 1 ft.

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Homework Equations



F = kx

The Attempt at a Solution



x = l-l0 = (√[1 + s2] - 1) ft

Fsp = kx = [4√(1 + s2) - 4] lb

So, now I've found the spring force, how does velocity fit into this?
 
Last edited:
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Kinetic energy. Some has been given to the spring, whatever is left...
 
Kabbotta said:
Kinetic energy. Some has been given to the spring, whatever is left...

But how do I calculate the velocity?
 
I guess I am a little surprised they gave you a question this hard without even explaining how to calculate kinetic energy.

Work-Kinetic Energy Thm.
[tex]K = 1/2mv^2[/tex]
[tex]\sum W = K_{f} - K_{i} + W_{other forces}[/tex]

The spring force is your other force doing work, and it will be negative work that takes away some kinetic energy, the final kinetic energy contains the velocity you are looking for, but the spring force is not constant so you have to do an integral for the work.

[tex]W_{spring} = \int F \cdot dx[/tex]
 

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