Force & Physics of Lifting/Moving Objects in Pathfinder

[Julix]

Alright, so in Pathfinder (like Dungeons and Dragons) there's a spell that allows you to lift/move stuff within 25 ft with 5 pounds of force.

A dagger weighs 1 pound [a rapier 2 pounds, a star dagger weighs 3 pounds]. I assume the remaining [2-]4 pounds of force wouldn't be enough to stab for significant damage. However, if the object is lifted and then released above the enemy that might work.

1. Damage
a. How much force does a 1 pound object falling 25 feet deliver assuming normal gravity? (would be nice if you show the math so I can repeat it with different weights)
b. I haven't yet found out the surface area of a dagger tip, but if it was known, and I combined it with the result from a. to get X (force/square inch for dagger falling), and then compared it to Y (the force/quare inch necessary to penetrate bone/skull), how much would X have to be larger than Y to penetrate? If the two were exactly the same would it just penetrate or just not?

2. Speed
if the object weighs 1 pound, and it's pulled upwards with 5 pounds of force, how fast is it being lifted? - My first idea was that it would be the same question as 1.a. except with 4 pounds and in the opposite direction, but heavier doesn't fall faster, only stronger, right?

I just imagined a powerful crane slowly lifting a feather, as it's designed for moving heavier things... Then I imagined me being in the gym trying to lift 80 pounds quickly (almost throwing) instead of steadily/with proper technique. For some things that makes it easier (cheating yourself), for other's (say straight up) it's a bad idea because at the tip of the lift movement for a moment it'll feel like it's falling, as in weighs even more than it's full weight. I assume because of heavy things that aren't in motion wanting to stay not in motion, trying to "convince" them faster would take stronger force... - Is there a maximum speed that 1 pound object can be lifted at using 5 pounds of force?

I'm excited to hear your thoughts, and thanks a lot
Julian


P.S. if you don't like the idea of trying to kill mean orks in a game, then replace dagger with metal ball, and assume I'm trying to trigger a pressure plate trap (so my people don't run in) that requires a certain amount of force/square inch to be activated. ;-)

 

[thegreenlaser]

1a) This is unfortunately more difficult to answer than you'd think. A 1 lb object at 25 ft will have 25 ft-lb of gravitational potential energy, and that energy will be converted to force, but how much force depends on how long the impact takes. A 1 lb metal ball will hurt a lot more than a 1 lb pillow because the metal ball delivers its energy very quickly (high force) while the pillow delivers its energy very slowly (low force). There's no way to calculate the force exerted without knowing more about the impact (e.g., what is the time interval between when the knife makes contact and when the knife stops moving)
1b) I'm not really qualified to answer this question, but my gut tells me that pressure (force/in^2) isn't going to be the value you need in this case, since it's more of a piercing than a cracking action. But I don't know the answer.

2) If I'm not mistaken (I'm not overly familiar with imperial units) a W = 1 lb object with a F = 5lb upward force on Earth (acceleration due to gravity = g) will undergo an acceleration of a = ((W-F)/W)*g = (5-1)*32 ft/s^2 = 128 ft/s^2. So, assuming it starts on the ground at a rest, its velocity will be (128*t) ft/s, and its position will be (64*t^2) ft where "t" is the time in seconds. If your target is x feet off the ground, the knife hits the target when t = sqrt(x/64) = sqrt(x)/8, at which point the speed is v = 128*t = 128*sqrt(x)/8 = 16*sqrt(x). So if your target is x feet off the ground, then the knife hits the target at a speed of v = 16*sqrt(x). As you can see there's no real limit to how fast the knife moves, because it starts off not moving at all and then will move faster and faster as long as you apply a force (assuming no air resistance). Though again, assessing how much damage a knife does from below does may be somewhat difficult to assess even if you know the speed it's traveling.

 

[Julix]

Thanks for your input. I agree that I'm oversimplifying, but remember the scope of the question. It's not to calculate what exactly would happen in the real world, only if it's significantly/qualitatively bad. I did think about the time it would take for the object to decelerate, and how if I ignored friction the knife would just go straight through the body. Thought about how the tip might have a ridiculously low size, increasing the force per area by a lot, but the blade would get wider and how all that would matter... The real world does seem overly complicated... :-D

I wasn't too worried exactly about the amount of damage, just whether or not it does make some... However I just realized that the spell also allows me to throw the object 15 ft. in *any* direction. So if I lift it 20 ft and then throw it downwards, that should add quite a bit of force to the impact... enough that I think I can make a case for sneak attack damage (which is a special form of damage gained when attacking someone who doesn't expect it, in a way that hits a critical area (say armpit to heart, or such) - brain is pretty critical if you can get there... ;-) If it doesn't kill it, it would certainly be painful, confusing, or nauseating... certainly surprising.

Again, thanks for the input.

Julian

P.S. I dislike imperial units a lot... but a lot of stuff that comes from the U.S. uses that, so I'll just have to cope :D
Edit: The reason I asked question 2 was to see if it was worth keeping the dagger light so the lifting wouldn't take forever, but I still don't understand how that works... So 2 objects one 1 and one 4.5 pounds, both being lifted by a 5 pound force. Is there a difference in speed?

 

[berkeman]

Thread closed for Moderation...

 

[berkeman]

Thread is re-opened. Sorry for the delay.

 

[Julix]

Let's try 1a again with a metal ball? gravitation is 9.81 somethings... kg/s^2? it's been years. I thought classic physics was all about overly simplifying stuff, that's all we ever did in high school, and it was fun! :D

I just remembered that a 1 kg ball will fall at the same speed as a 2 kg ball of the exact same size... forgot about that. So shape matters... unless I deliberately decide it doesn't... it's a 100 % aerodynamic arrow... basically a thin needle that's 1 kg in weight. (changed the weight because I can't think straight in pounds, and for the final math I can just plug the right numbers if I can get the formula right).

So a tiny 1 kg object is dropped from 7 m hight. How fast is it at the time of impact?

 

[I like Serena]

The relevant formula is:
$$v^2 = 2 g h$$

In your case:
$$v = \sqrt{2 \cdot 9.81 \cdot 7} = 11.7 \frac m s$$

 

[mfb]

For daggers and similar objects, and reasonable heights, you can neglect air resistance.
The mass is important for the force needed to lift it and the force on impact, but it does not influence the velocity if you let it drop down.

 

[Julix]

Since the spell allows me to throw the object ~5 m in any direction, I could throw it up ~5 m, and then it would fall all the way from up there (12 m) instead. However, it would take more time to fall, and thus be more likely to be noticed by someone underneath, allowing more time to doge. Since it's exactly the same amount of force used to throw it up or down, could I calculate the speed as though it was 12 m?

If so using the formula I got 15.34 m/s. which multiplied by a pound gives me either momentum or impulse and ~7 Newton seconds (m kg / s) ... which doesn't tell me much, since I don't know what that means... :D

However, yours was already 42 km/h, now that it's thrown it's 55.2 km/h... metal is denser than bone, with a sharp edge I'm pretty sure that should penetrate... let him custom make an arrow with a 2 kg weight near the tip... thanks for the math!

ahaha, just realized you did provide velocity first. If I multiply that by 5 pounds (and let google do the converting) I get 533.968938 m kg /s^2 which I multiply to get pound-force by 0.22481 = 120 lb_F -- I used to weigh 120 lb not too long ago... now if that weight was on a dagger's tip... that would be quite awful...

Yay I'm satisfied. Wish there was a way to give you all digital cookies! thanks for helping out!

 

[mfb]

Where do those 7m come from?

Since it's exactly the same amount of force used to throw it up or down

If you have the same "magic" force in both directions, the acceleration upwards will be lower (slowed by gravity) as the acceleration downwards (accelerated by gravity).

ahaha, just realized you did provide velocity first. If I multiply that by 5 pounds (and let google do the converting) I get 533.968938 m kg /s^2 which I multiply to get pound-force by 0.22481 = 120 lb_F -- I used to weigh 120 lb not too long ago

I don't understand what you are doing here. To convert momentum to force, you have to find some timescale for the deceleration of the object.

 

[technician]

Was it a wise decision to re-open this thread? Is it meaningful physics?

 

[mfb]

It does not matter if we have a force due to a string, or due to magic - the latter is not possible, but the physics of the massive object stays the same. You can reduce the question to "how does a massive object react if we apply some force on it".

 

[Julix]

7 meters is 22 ft which is less than 25 ft which is the spell range, or the maximum distance that the object can be lifted without losing control. 5 m is slightly more (16 ft) than the distance that it can be thrown (15 ft).

Since the spell specifies the throwing distance but not direction, you're right that it's not really "exactly the same force". I just meant if you can throw it up 5 more meters to get extra speed on the way down, throwing it downwards with that same force should be at least as powerful.

Velocity is already m/s² so I figured if I multiply that by the weight of the falling object it should become Newton, or kg·m/s², right?
I found here ( http://en.wikipedia.org/wiki/Newton_(unit) ) that 1 N ≡ 1 kg·m/s² ≈ 0.22481 lb_F. So I figured if I multiply something in N by 0.225 it becomes lb_F, right?

 

[mfb]

Velocity is m/s, you cannot convert it in a force like that.

I don't see any mention of a "throwing distance". And it is unclear whether those 25 feet range are the geometric distance in 3D, or the horizontal distance.

 

[Julix]

dammit! where do I remember m/s^2 from? hm... Thanks for trying to help, I'll see if I can come up with a more clear representation. :-)