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

In summary, the given problem asks for the velocity of a collar with a 2-lb spring on a smooth shaft, given a velocity of 15 ft/s at s = 0. Using the equations for spring force and kinetic energy, the final velocity can be determined by taking into account the work done by the spring force. This can be calculated through an integral.
  • #1
red123
22
0

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?
 
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  • #2
Kinetic energy. Some has been given to the spring, whatever is left...
 
  • #3
Kabbotta said:
Kinetic energy. Some has been given to the spring, whatever is left...

But how do I calculate the velocity?
 
  • #4
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]
 

1. What is kinetics and how does it relate to springs?

Kinetics is the branch of mechanics that deals with the motion of objects and the forces that cause that motion. Springs are objects that store potential energy and release it as kinetic energy when they are stretched or compressed. Kinetics is important in understanding the behavior of springs and how they move.

2. What does "s=1 ft" mean in the context of solving for collar velocity?

In this context, "s=1 ft" refers to the displacement or distance of the collar from its equilibrium position. It is a specific point in the spring's motion at which we are trying to find the velocity of the collar.

3. How is collar velocity at s=1 ft calculated?

The velocity of the collar at s=1 ft can be calculated using the equation v = √(k/m) * √(A^2 - s^2), where k is the spring constant, m is the mass attached to the spring, and A is the amplitude or maximum displacement of the spring.

4. What factors affect the collar velocity at s=1 ft?

The collar velocity at s=1 ft is affected by the spring constant, mass of the object attached to the spring, and the amplitude of the spring's motion. Additionally, external forces such as friction can also affect the velocity.

5. Why is it important to solve for collar velocity at s=1 ft in springs?

Knowing the velocity of the collar at s=1 ft can help us understand the behavior and performance of a spring in various applications. It can also help us design and optimize springs for specific purposes, such as in shock absorbers or suspension systems.

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