# Are spring forces really non-impulsive? Why or why not?

I've heard that spring forces are generally non-impulsive as they don't really contribute to a change in momentum(of any body attached to it). How can we actually say that spring forces are non-impulsive? Is this because of the fact that springs are slow to adapt to any change made to it? Can someone provide me a more intuitive answer?(I'm just a 12th-grader!)

• The source where you heard that seems to be rather inaccurate. Here is a video of a spring force contributing to a change in momentum youtu.be/YtgfoynHeiw – Dale Apr 30 at 13:13

To me, that definition seems too specific and non-intuitive compared to the general concept of an "impulse" in physics.

An impulse in physics is typically defined as the integral of force over time. Determining the impulse will tell you how much the momentum of the object changed over that time period.

It's fairly trivial to show that over time, springs absolutely can change the momentum of an object they interact with. A trivial example is a object suspended by a spring which is first extended, and left alone to oscillate up and down. The velocity of the object connected to the spring is constantly changing, and it's mass remains the same. This means that the spring is changing the momentum of the object, and thus would be an impulsive force, as per the definitions I'm aware of.

Their version of "impulsive force" seems to be a specific definition, not the general physics definition. Wikipedia seems to shed some light on this:

The term "impulse" is also used to refer to a fast-acting force or impact. This type of impulse is often idealized so that the change in momentum produced by the force happens with no change in time. This sort of change is a step change, and is not physically possible. However, this is a useful model for computing the effects of ideal collisions (such as in game physics engines).

They seem to be using this specific definition of impulse. They are referencing specifically a fast acting force/impact. I personally find that overly restrictive, since the concept of impulse can be applied well beyond that range (as the wikipedia page for impulse shows). A related concept is the Dirac delta function; which is useful for measuring change in momentum of objects which interact over very short periods of time.

On another note, determining what is "fast-acting" is entirely relative and quite subjective. Depending on the mechanics of what is happening, an object interacting with a spring could be considered a "fast-acting" force, and thus an impulse. To really show how abstract it is, you could consider the forces of two billiard balls interacting to be a type of "spring force", as the interaction between them would approximately follow Hooke's law; just like springs.

A sufficiently stiff spring would behave much the same as billiard balls colliding, so I can't see how you could completely rule out springs having impulse forces, even when you define impulse forces as forces that act over a short timeframe. Given the wide range of spring properties, I don't think that statement is overly justified, though in context it might have made more sense.

I apologize for how wordy this got, I apparently had a lot to say.

• This is is an interesting answer! Just to clarify a thing- If I do have a situation where a spring is attached to a body B(and the system is at rest initially) and another body A(of mass << that of B) comes and hits the body B, then supposedly a little part of A's velocity is transferred to B and B moves too after the collision(thus compressing the spring). Is it valid then to say that the spring force generated on the body B is non impulsive(implying that momentum is conserved)? (Sorry, but this was actually the context in which I had asked this question!) – Abhinav Tahlani Apr 30 at 15:04
• @AbhinavTahlani I don't really follow that. Momentum is always conserved in total, whether it's "impulsive" or "non-impulsive" forces. A transfers some momentum to B. Depending on the velocities, masses, and spring stiffness, the momentum transfer could be very quick, or very slow, so that's why I find it strange to say outright that springs would be non-impulsive. A very stiff spring could be impulsive even with the strict definition of transferring momentum near instantly. – JMac Apr 30 at 15:12
• Yeah, I know that momentum is going to be conserved! Just wanted to know if we could definitely say that the spring had a non-impulsive force.Thanks a lot for clarifying it! – Abhinav Tahlani Apr 30 at 15:58

An impulse by definition acts instantaneously (almost zero elapsed time). As a result a system under an impulse will have its momentum changed during this very short period of time. The forces acting during the impulse are in essence unknowable.

A spring is a force member that according to Newton's law changes momentum in a system gradually over time.

In summary, an impulse is a specified applied momentum, and a spring is a specified applied force.

• I don't really agree with this. Impulse has much broader definition that doesn't require it to be instantaneous. I know that some do include that, but the term is used in a much broader sense. Also, a stiff enough spring would functionally be the same as billiard balls hitting together, so could you not say springs could be impulsive too, even if fast acting is a requirement? – JMac Apr 30 at 14:06
• No, the definition of impulse is $\int_{t_1}^{t_2} \vec{F} dt$ and there are no restrictions on the time interval. You are thinking of impulsive interactions (an unfortunate use of the adjective), which are short time interval interactions. And the forces are not "unknowable." I can do a collision of a cart with a fixed spring that happens in milliseconds, and I can measure that force vs time curve. It's a nice quadratic hump. – Bill N Apr 30 at 14:18
• @BillN - Contact forces are only knowable for idealized situations during impacts. In real life the complex interactions between the stress waves propagating through different materials and geometries and bouncing all around make accurate modeling and prediction daunting. Only <average> force over some time increment could be established reliably. If I drop a marble on the floor, the contact forces are unknowable. What is knowable is the change in momentum. – John Alexiou Apr 30 at 17:23

I think you have read something that is, as Dale say, highly inaccurate. For the simplest case, take a block moving on a friction less floor and a spring attached to a vertical wall, some metres ahead. After hitting the spring, the mass will rebound in the opposite direction.

Or you can also consider a spring pendulum, (horizontal,not vertical (you can say gravity acts in vertical direction)). Very obviously, its momentum is changing continually.

And, as Jmac says, almost everything in this universe can be considered as a spring. You can compromise a tiny degree of rigidity to generalise it like that, but since there are no absolutely rigid bodies, I don't think that would matter.