# Velocity of Spring: Solved 2m/s

• Batman4t
In summary: The spring force is variable, so you should use kx instead of 40N. Then the equation becomes F(x)=kx.
Batman4t
[SOLVED] velocity of a spring

## Homework Statement

https://wug-s.physics.uiuc.edu/cgi/courses/shell/common/showme.pl?cc/IAState/phys221/spring/homework/05/block_spring_nofriction/4.gif
A spring is stretched a distance of Dx = 40.0 cm beyond its relaxed length. Attached to the end of the spring is an block of mass m = 8.00 kg, which rests on a horizontal frictionless surface. A force of magnitude 40.0 N is required to hold the block at this position. The force is then removed.

When the spring again returns to its unstretched length, what is the speed of the attached object?

## Homework Equations

http://wug.physics.uiuc.edu/cc/IAState/Phys221/spring08/course%20info/FS.pdf

## The Attempt at a Solution

change in X=.4m
mass=8kg
F=k*dx
calculated k=100N/m
w=f*dl
work=.5mv^2
v=?
projected v=2m/s

How come 2m/s is not working for my speed did I make an error?

Last edited by a moderator:
Your problem statement is incomplete. What's the question? At what point are you looking for the speed (if that's the question)? Also, calculating work as the given force of 40N times its displacement is not correct. We can assist further once you clarify the problem and note all givens, and have made another attempt at a solution.

Sorry, When the spring again returns to its unstretched length, what is the speed of the attached object?

I solved it:

Using the spring constant that I found:
F(x) = kx

I found the new Work (W) done for the new distance using:

W = (1/2)k(x2)^2 - (1/2)k(x1)^2

Then with the new amount of work done used the equation Wtotal = (delta)K. So...

W(new) = (1/2)m(v2)^2 - (1/2)m(v1)^2

Starting form it's stretched point the velocity is zero so you're just left with

W(new) = (1/2)m(v2)^2

$$\sqrt{2}$$

Batman4t said:
Sorry, When the spring again returns to its unstretched length, what is the speed of the attached object?
OK, I see what you may have done, you set the work done by the spring equal to the KE, which is good, but you incorrectly calculated the work. The spring force is variable (it is 0 at the unstretched length), so you can't use a constant 40N as the force...what shouldyou use? Or it is better to use conservation of energy, since only conservative forces are involved..

Edit: OK, you got it.

Last edited:

## 1. What is the definition of velocity of spring?

The velocity of spring is the speed at which a spring moves or oscillates back and forth when it is stretched or compressed from its resting position.

## 2. How is the velocity of spring calculated?

The velocity of spring is calculated by dividing the distance covered by the spring by the time it takes to cover that distance. This can be represented by the formula v = d/t, where v is the velocity, d is the distance, and t is the time.

## 3. What are the factors that affect the velocity of spring?

The velocity of spring is affected by factors such as the mass of the spring, the spring constant, and the amplitude of the spring's oscillation. Other factors like air resistance and friction can also affect the velocity of spring.

## 4. Can the velocity of spring be negative?

Yes, the velocity of spring can be negative. This means that the spring is moving in the opposite direction of its initial motion, which could happen when the direction of the force acting on the spring changes.

## 5. How does the velocity of spring relate to its potential and kinetic energy?

The velocity of spring is directly related to its potential and kinetic energy. As the spring stretches or compresses, it stores potential energy. When it is released, this potential energy is converted into kinetic energy, resulting in the motion of the spring. The velocity of the spring is highest at the point where the potential energy is completely converted into kinetic energy.

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