Simple physics question

[jms]

It's been too long since I've been doing these kind of calculations;

I want to make a comparison between the force different free falling objects will hit the ground with. Lets take a wrench (0.5 kg) falling from 50 meters. What mass will that equal when another object is dropped from a lower height? Is it possible to compare with a car collision at a certain speed?

Don't need to take air resistance into the calculation I think.

TIA. Hope some of you guys can help.

[Umfriend]

IIRC, you're looking for "impuls" which, I think, equals VxM (Velocity times Mass).

V from 50 mtrs with g=1 is, uhm let's see.
V = V(0) + g0.5t^2 (?)
OK, I'm out.

[Umfriend]

p=mv
v(t) = v(0) + gt
x=x(0)+v(0)t+0.5gt^2

So:
m = 0.5, g = 1, x(0) = -50 and x must be 0 to find t
0 = -50 + 0 + 5t^2
10 = t^2
t = SQRT(10) = 3.16s

v(t) = 0 + gt = 31.6 m/s
m = 15.8

Suppose other object is from 20m then
0 = -20 +5t^2
t=SQRT(4) = 2 secs
v = 20 m/s
15.8 = 20m, mass must be 0.754

Could be totally wrong though.

[jms]

TY, and I found this:

http://www.livephysics.com/tools/cla...ng-object.html

[Umfriend]

OK, so I did make a mistake somewhere but the idea seems correct.

[jms]

Using that calculator is it then reasonable to say that a wrench with mass 0.5 kg dropped from 30 meters equals the impact force of a car (1500kg) dropped from 1 cm ?

I used 0.01 m as "distance travelled after impact".


0.5 kg dropped from:

5 meters ~ 2450 N equals 250 kg dropped from 0.01 m (1cm)
10 meters ~ 4900 N equals 500 kg dropped from 0.01 m (1cm)
30 meters ~14700 N equals 1500 kg dropped from 0.01 m (1cm)


Could this be correct when you don't take air resistance into account?

[az]

You can't really compare car collision impact forces to anything without crashing cars into objects and measuring the forces (which is why crash tests are done and not just calculated), because cars are not solid lumps of steel but very very complex bodies formed out of very different materials of different mass, thickness, hardness (is that a word?), form, etc. And of course, where do you want to measure? Where the car hits an object, or how much of that force reaches the passengers? There might be rules of thumb, but I wouldn't know.

[jms]

You can't really compare car collision impact forces to anything without crashing cars into objects and measuring the forces (which is why crash tests are done and not just calculated), because cars are not solid lumps of steel but very very complex bodies formed out of very different materials of different mass, thickness, hardness (is that a word?), form, etc. And of course, where do you want to measure? Where the car hits an object, or how much of that force reaches the passengers? There might be rules of thumb, but I wouldn't know.

OK, I see that.

But are the above calculation plausible? Thought the numbers were a bit high. That an object with mass 0.5 kg dropped from 30 meters equals an object with mass 1500kg dropped from 1 cm?

[Umfriend]

I do not think they are correct in the sense that the comparison is influenced by the distance travelled after impact and that may not be what you are after. Think of this: if that distance is infinity, neither mass nor velocity matter....

I'd say you're looking for kinetic energy (the 2nd result) or moment and I am not sure right now whether that would yield different results.

[TransformX]

Another thing you should very much keep in mind is the spread.
60kg are 60kg, nothing would change that, but putting 60kg of lead on your foot (say over an area of 60cm square ) vs putting these whole 60kg of lead on your toe (say an area of 6cm square) would yield very different results.
In the first example, you'll be having 1kg/cm. In the second, it's 10kg/cm.

A 1kg spear falling down from a shelf on your foot is meaningless if you only count weight, but if you take into account that all this weight is concentrated on a single square milimeter...

edit: it's a bit like this question about which is heavier, a pound of lead or a pound of feathers?
Once you claim they're the same, the person asking the question proceeds with offering to drop both on your foot to test this theory

[az]

In a vacuum, lead and feathers fall at the same speed and accelleration and thus exert the same force on your foot - not per area, of course, as the feathers take up much mre space than the lead. But put a kg of lead into a container and put a kg of feathers in a container exactly alike, and they'll fall and hurt the same, whether you're in a vacuum or not.

[jms]

OK, lets not overengineer this

What I want to show in my Safety Health and Work environment-presentation is what a wrench or hammer (~0.5kg) dropped from three different heights of a building (5m, 10m and 30m) will compare to if it was some other object dropped directly above your head (1cm).

As I initially thought I could use a car (~1500kg) as a comparison to a hammer dropped from 30 meters. Very wrong?


TIA

[az]

Only slightly. The hammer' force will be concentrated over a few cm^2, while the car's force will be more evenly spread (although in the case of a head, the area shouldn't be much larger). Keep in mind that when a car rolls over your feet, only a quarter of its weight rests on any one wheel.

Of course, 30 m is very high, most domestically used hammers weigh less than 500 g (except sledgehammers etc.), and a live presentation involving letting a hammer fall onto a watermelon would probably impress your listeners even more

[TransformX]

[jms]

Only slightly. The hammer' force will be concentrated over a few cm^2, while the car's force will be more evenly spread (although in the case of a head, the area shouldn't be much larger). Keep in mind that when a car rolls over your feet, only a quarter of its weight rests on any one wheel.

Of course, 30 m is very high, most domestically used hammers weigh less than 500 g (except sledgehammers etc.), and a live presentation involving letting a hammer fall onto a watermelon would probably impress your listeners even more

Hehe, that would be cool. But I think most of the carpenters will see the severity of dropping your hammer from that high when comparing with the 1500kg car I'll compare both with hitting on top of the head so the hit area will be very similar.