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How do you quantify the additional force exerted by an object due to its motion? An object at rest on a surface exerts a downward force equal to it's weight: F=ma, where "a" is gravity. Now drop that same object from a height, and there would appear to a force greater than the object's weight exerted. In fact, the object may now cause damage (dent, crack, etc.) to the surface whereas when it was at rest no damage was caused. The object's momentum (mass x velocity) at impact can easily be calculated, but what relation does the momentum have to the additional force exerted by the object due to its motion. To illustrate this more graphically, envision holding a sheet of paper horizontally, with a 50 gm object resting on top of it. To start with, the object is supported by the sheet of paper. Gradually increase the weight of the object (while maintaining the same surface contact area with the paper), and you will eventually reach a weight at which the object breaks through, let's say that weight is 200 gm. Now, start again with the 50 gm object and a new (identical) piece of paper, and drop the object onto the paper at small increments of height, and eventually you will reach the minimum height at which the 50 gm object will break through the paper. Now, how do I relate the two scenarios??
One way of calculating this force is via the impulse.
QuoteOne way of calculating this force is via the impulse.Yes; A good way of approaching a lot of problems.You can also consider the problem in terms of the energy needed to rip the paper. Whilst the breaking process is happening, there is a force acting in a direction and the work done is the force times the distance. (Again, this may not be uniform - but you can / could sum the effect over many small intervals). If there is enough KE at the start, the object can do the work needed to get through - else it stays there. The static weigh force would also be relevant, but would be a small proportion of the force, once the drop height was large. (The weight of the hammer, doesn't contribute much to driving a nail in! )There have been many experiments, using high speed photography, to examine the speeds of bullets hitting armour (etc.) in which the progress of an object has been analysed as it goes through a substance.I wouldn't be bothered enough, personally, to do the actual sums but you could make some reasonable estimates after some simple experiments in which you measured the depth of 'dimple' formed when the object doesn't quite get through, for a range of drop heights and weights.A complex structure, like paper, would be very non-linear, though; metal is a bit better behaved.. You might be better to use thin sheets of foil and ball bearings. I could see an 'interesting' evening in the kitchen with some simple equipment, like a ruler and kitchen scales. You could have a few cans of beer to take the pain away.
It depends on how dedicated he is and how much measuring he's prepared to do. The minimum drop height for puncturing the paper and the amount of distortion would give you a very reasonable idea of the actual average force. You don't need to use the time of the event.The principle is there but, personally, I'd rather not.You don't have an objection to the basics? Possibly the accuracy would be poor but so is cosmology and people get very excited about those statistics.
If the hole through the paper is, say, 5mm deep (0.005m) (the paper has been pushed that far, leaving burrs of 5mm)
Very naff diagram but do you see what I mean?the distance over which the ball was exerting a force would be 5mm. It would be much easier if the ball fell through a soft, thick medium for which the distance would be better defined, of course, and the force would not be constant, at all.[diagram=296_0]An incredibly impracticable thing to do but, if you were investigating a crime, for instance, it could yield some ball-park figures about the mass of a falling object or where it fell from, for instance.
Elementary my dear Watson?In any case - it's easier than bloody photons!
"ball park figures"Getting a figure near enough "within the ball park".