# Calculating impact force of a block accelerated by a spring

1. Apr 11, 2012

### superman22x

I'm working on a small design project and need some help remember what equations to use here. Basically, we are creating a hammering device. A compression spring will be loaded, and a block on the end is accelerated into another block. I need to have it hit with a certain impact force so I am designing the spring to match this.
I know the force of the spring:
F=k(dx)

And total energy equation:

TE=.5*k(dx)^2

But I'm not really sure where to go from there since the spring will be accelerating the mass as it uncompresses.

2. Apr 11, 2012

### haruspex

With hammering, pile-driving etc., you're not expecting energy to be conserved. Neither are you much concerned with forces, as such. What you want is impulse (momentum).
It's usually a reasonable approximation to assume negligible recoil. The block, mass M1, strikes the target, mass M2, at speed U. They then continue together at speed V (at first).
By conservation of momentum, M1.U = (M1+M2).V.
The two masses together then have to overcome some resistive force as they travel on. The distance they travel now depends on their combined kinetic energy, (M1+M2).V^2/2 = (M1.U)^2/(2(M1+M2)).
I assume you want to optimise the distance the block travels before impact for the maximum travel after. The further it goes towards the point at which the spring is fully relaxed, the harder it will strike. On the other hand, if it goes to completely relaxed then the spring will start to act the other way and reduce the distance the target is driven. (Conversely, to the extent that impact is earlier, the spring will assist the travel after impact.)
If you can't figure out the calculus I can help, but I suspect the best answer is to have a slack tie in series with the spring. This would allow the spring to expand fully before impact but not inhibit the subsequent travel. Its sole function would be to allow the block to be drawn back into loading position.

3. Apr 12, 2012

### superman22x

We aren't really looking for the maximum impact, we just need to hit with at least 100N. And we are assuming block 2 is stationary, even when impacted.

4. Apr 12, 2012

### haruspex

A Newton is a unit of force. Impact (momentum) is usually expressed in kg m/s or, equivalently, N.s (Newton seconds).
To ask that it strike with a given force is meaningless.
If you want the impact to be, say, 100 kg m/s and the mass is 1 kg then you need the spring to accelerate it to 100 m/s, giving it a kinetic energy of 5000 J.

5. Apr 13, 2012

### sookw

The project may look simple but actually it is quite impossible to determine the impact force. Even if you have two bodies that collide in space, thus neglecting all the friction and drag forces, it is still difficult to predict the impact force.
I guessed you may have to experiment with your project and fine tune to have the required impact force, and I suspect that the impact force may still vary with each test.

6. Apr 13, 2012

### haruspex

As I said, impact and force are two different things. You can't determine the force, but you can determine the impact (change in momentum). That's fortunate, because in a hammer it's the impact that matters.

7. Apr 13, 2012

### Staff: Mentor

Who decided on that constraint? The point people are trying to convey is that it is a poor constraint.

8. Apr 13, 2012

### haruspex

Quite so. Perhaps I can make it even clearer.

The force will follow some function over a short period of time, rising from 0 to a peak and falling away again. For the purpose of hammering a nail or driving a pile you hardly care about the shape of the function: what matters is the momentum change (impulse), the area under the curve, $\int$F.dt. This is simply the mass of the hammer multiplied by its velocity on impact.
The shape will depend on what is struck. Hit an egg and the function will be very tall and narrow; hit a rolled up blanket and it will be much broader and lower. Hence it is meaningless to ask what force the hammer will deliver; it will deliver a range of forces over the duration of the impact, the details depending on the materials of the hammer and the target. It does become interesting if what you care about is whether the target will survive the impact. In that case you'd like to know the peak force.

The shape of the curve may also be of some interest in unusual cases for hammer and nail. The hammer blow achieves nothing until the force rises above the resistance of the nail's substrate. So, strictly speaking, it's integral starting at the point in time where this threshold force is achieved; the little bit of lead-in to that point is wasted. Normally this is negligible, but it explains why a light tap might get you nowhere.

Wherever you got the 100N requirement from, go back and ask for a requirement that means something.

9. Apr 14, 2012

### superman22x

It's a constraint used to build buildings. It's called the Michigan Soil Test.

We are building a mechanism to perform it, rather than a person hitting a can of soil on a board like is currently performed. Our project says the force of impact should be between 40-140N, so we aimed at 100N.

10. Apr 14, 2012

### haruspex

The Michigan Soil Test specifies that, or is this an interpretation by the person who designed the project? Can't find any more details online. Do you have a link for this?