Opposing Forces on an Ideal Spring

In summary, the conversation discusses the limitations of exerting unequal forces on a massless spring in opposite directions. It is not possible to do so in a steady state. The conversation also delves into the dynamics of a massless spring and how its stored energy is converted into kinetic energy during motion. It is also mentioned that in the limit of small mass, the spring will overshoot its uncompressed length and the stored energy goes into kinetic energy.
  • #1
peeyush_ali
86
0
can we exert 2 unequal forces in opposite directions on the two sides of an ideal<mass less> spring?
 
Physics news on Phys.org
  • #2
Not in a steady state, no.
 
  • #3
can u tell me some more facts abt springs..how to solve problems involving springs with mass and without mass..??
 
  • #4
A massless spring is compressed then suddenly released. Does it overshoot its uncompressed length? Where does the stored energy go?
 
  • #5
YorkLarry said:
A massless spring is compressed then suddenly released. Does it overshoot its uncompressed length? Where does the stored energy go?

It can not overshoot its uncompressed length,because it's not accord with conversation of energy. when you release the massless spring,the stored energy switch the spring's kinetic energy,or else why the spring can kinetic without energy
 
  • #6
I did some calculations after the last post. I've never seen an actual massless spring, and I don't know how to make one or where to buy one, so I added some mass m by gluing a mass m/2 to each end of the spring. I worked out the dynamics and then took the limit as m approaches zero.

If the spring with relaxed length Lo is compressed to length L1 and then released, it will oscillate with amplitude (Lo - L1) independent of m. It has angular frequency sqrt(k/m). The potential and kinetic energy exchange during the motion so as to keep the total energy constant. The maximum kinetic energy equals the maximum potential energy.

As the limit of small m is approached, the angular frequency increases, and the ends of the spring move faster and faster. So the spring will overshoot its uncompressed length regardless of how small m is. The stored energy goes into kinetic energy during the motion, except at the extremes of spring length.

If the mass m is distributed along the length of the spring instead of being concentrated at the ends, the argument is the same. Slices of mass other than at the ends move more slowly than the ends so the kinetic energy formulas are slightly different. The amplitude is still Lo - L1. The angular frequency is still proportional to sqrt(k/m) with the proportionality constant dependent on details of the mass distribution. Behavior in the massless limit is the same.

I can provide details if anyone is interested.
 
  • #7
Apologies re the previous post - the angular frequency should be 2 sqrt(k/m). I dropped the factor of two.
 

1. What is an ideal spring?

An ideal spring is a hypothetical model used in physics to understand the behavior of real springs. It is an idealized version of a spring that has no mass, perfect elasticity, and follows Hooke's law, which states that the force exerted by a spring is directly proportional to the amount it is stretched or compressed.

2. What are opposing forces on an ideal spring?

The opposing forces on an ideal spring are the restoring force and the external force. The restoring force is the force exerted by the spring to return to its equilibrium position, while the external force is any force applied to the spring that causes it to stretch or compress.

3. How do opposing forces affect the motion of an ideal spring?

The opposing forces on an ideal spring affect its motion by creating a state of equilibrium. When the external force is applied, it stretches or compresses the spring, creating a restoring force that opposes the external force. This results in the spring oscillating back and forth around its equilibrium position.

4. What factors can affect the opposing forces on an ideal spring?

The opposing forces on an ideal spring can be affected by the stiffness of the spring, the amount it is stretched or compressed, and the mass of the object attached to the spring. These factors can alter the magnitude of the restoring force and the external force, thus affecting the motion of the spring.

5. How can the concept of opposing forces on an ideal spring be applied in real-life situations?

The concept of opposing forces on an ideal spring can be applied in various real-life situations, such as in the design of shock absorbers for vehicles, in the construction of buildings and bridges, and in the design of suspension systems for machinery. Understanding the behavior of opposing forces on an ideal spring is crucial in creating structures and systems that can withstand and dampen external forces.

Similar threads

Replies
4
Views
906
Replies
6
Views
871
  • Mechanics
Replies
19
Views
1K
Replies
9
Views
1K
  • Mechanics
Replies
10
Views
921
Replies
76
Views
4K
  • Mechanics
Replies
7
Views
880
Replies
9
Views
2K
Replies
75
Views
2K
Replies
2
Views
1K
Back
Top