Force From KE

[Agnaa]

I have found three calcs (One, Two, Three), two of which are accepted, that involve dividing the energy of KE by the length of a character's arm to get force.

I see no reason for this to be valid. The third of these provided no explanation for it when @Dark-Carioca asked, with @Ugarik accepting it without elaboration. In the second one, @Aguywhodoesthings asked what was up, but when the third one was posted, they seemingly assumed that it was okay. And the first one has me questioning it.

I have reason to suspect that this is an invalid method.

KE = 1/2 * m* v^2

That can be rearranged to KE = (m * d^2)/(2 * t^2), where d is distance and t is time.

F = ma

That can be rearranged to F = (m * d)/(t^2)

While dividing KE by distance gets you close to force, it doesn't quite get you there; the value would be half as large as it should be.

More glaringly the distance needs to be the same as the distance traveled, the length of the character's arm has absolutely no place being here.

When I took a feat derived like the three above and directly applied F = ma, I got a result 8.15x lower. When I took a feat derived like the three above, and instead of using the corresponding character's arm, used the distance traveled, I got a result half of the one found with F = ma. This seems to clearly be the more correct way to derive it; divide KE by distance traveled, and multiply by two.

However, I remember @DontTalkDT having issues in the past with people just rearranging equations to get the right units without properly accounting for what's happening, so this "more correct" method may not necessarily be something we should use.

I would appreciate input on all of this. I currently feel certain that the feats above should not be accepted as-is, but aren't sure whether they're fixable in this way or not. Getting LS from KE may be something we don't want to do. I don't strongly care either way tho.

 

[Armorchompy]

i don't care to get into yet another long-winded and exhausting standards discussion but i think this type of calculation is legitimate if the feat can be considered a LS one, recall it being agreed in some other thread. method can be made better though, i don't mind that

 

[Mr. Bambu]

While I haven't been tending to calcs lately, I actually have noticed a considerable uptick in weird takes on methods stemming from the whole LS from KE thing. I'd like to hear from other folks, as I'm no expert, particularly @KLOL506 and @DontTalkDT.

 

[KLOL506]

Not sure what the hell is going on in the first two calcs so I can't speak for those, but why is the second calc using arm distance when the actual distance to use for speed and thus acceleration would be the distance the rock was thrown? I'm confused here.

 

[Agnaa]

All of 'em are using arm length instead of distance traveled, which is my main contention. I'm as lost as you on why they are.

I've already told the creator of the first two about it, but I guess I should ping the creator of the third too @USklaverei

 

[KLOL506]

Yeah, in that case, arm length in these cases is... weird. The actual distance moved that should be used would be how far you sent the object flying/hurling back.

 

[Nullflowerblush]

Apparently, arm length is used instead of the distance traveled the movement of the arm is what gives a projectile its force.

 

[KLOL506]

Apparently, arm length is used instead of the distance traveled the movement of the arm is what gives a projectile its force.

That's not how F= ma works at all. You're supposed to calculate the displacement of the object you moved to get LS. Movement of the arm here is completely irrelevant.

 

[Agnaa]

Actually, I just thought of a potential reason; one could argue that the distance the object is accelerated to its speed over is the arm length. That wouldn't quite be true, and would vary from feat to feat, but is an argument.

EDIT: To clarify, I seriously doubt it would actually get you force. Point being that even if "distance moved while accelerating it" was correct, arm length would be a very rough approximation of that (characters could've swung their arms while extended, simply chucked from the shoulder, or a whole variety of things that would make that measurement bad).

 

[KLOL506]

Actually, I just thought of a potential reason; one could argue that the distance the object is accelerated to its speed over is the arm length. That wouldn't quite be true, and would vary from feat to feat, but is an argument.

Oh?

In any case, I personally haven't done feats like that at all, I always used the distance travelled by the object after yeeting, using their acceleration and then F=ma'ing them. Can't say much about the "arm length" calcs. Best to wait for DT then.

 

[DMUA]

They straight up can just apply acceleration to the thrown object directly so like, I dunno what's up with this

 

[DontTalkDT]

Well, as far as real-life physics is concerned you can calculate speed from KE. Then use the distance over which that speed was attained to calculate acceleration. Then use F=m*a to get force.
Now, we don't really calc speed from KE, but one could argue that this might be valid anyway, as one can also related force to energy directly, i.e. KE = Force * Distance (for a constant force. Otherwise integral is needed). In that case Force = KE/Distance.

In both cases, the distance component has to be the distance over which the force is applied. That distance of course varies based on the circumstances. If we for example had someone throw a baseball, it would the distance the hand traveled while it held the ball (roughly). How that is calculated depends on which throwing motion the person makes. It could be something a little longer than arm-length for a straight motion or something lie a semicircle with arm-length radius for a wide over-head swinging motion.
The details essentially have to be adjusted based on the scenario. In throwing it will usually be the distance the hands travels in some way.

 

[Agnaa]

@DT Sure, but I think even then just dividing the KE result by the distance the arm traveled is the wrong way to derive this.

Taking the first example in the OP; arm distance = 1.166m, distance projectile traveled = 19m, time projectile took to travel that distance = 2s, mass of projectile = 64kg.

Velocity = 9.5 m/s.

Timeframe accelerating = 0.27435 seconds (assuming it accelerated at a linear rate).

Acceleration = 34.627 m/s^2

Force = 2,216.1 kgf

KE = 2888 J

KE divided by arm length = 2,476,8 =/= 2,216.1

From this practical example, the method used in these calcs is flawed.

 

[KLOL506]

Well, as far as real-life physics is concerned you can calculate speed from KE. Then use the distance over which that speed was attained to calculate acceleration. Then use F=m*a to get force.
Now, we don't really calc speed from KE, but one could argue that this might be valid anyway, as one can also related force to energy directly, i.e. KE = Force * Distance (for a constant force. Otherwise integral is needed). In that case Force = KE/Distance.

In both cases, the distance component has to be the distance over which the force is applied. That distance of course varies based on the circumstances. If we for example had someone throw a baseball, it would the distance the hand traveled while it held the ball (roughly). How that is calculated depends on which throwing motion the person makes. It could be something a little longer than arm-length for a straight motion or something lie a semicircle with arm-length radius for a wide over-head swinging motion.

I get the arm movement like converting the angle moved to rad then multiplying the rad value with the arm length, but uh... don't we usually calculate the distance the object was thrown upto right before it starts decelerating?

 

[DontTalkDT]

I get the arm movement like converting the angle moved to rad then multiplying the rad value with the arm length, but uh... don't we usually calculate the distance the object was thrown upto right before it starts decelerating?

For this method of calculation the distance should be until it stops being accelerated. (which typically is once there's no touching anymore)
For other calcing methods other distances might be relevant, of course.

@DT Sure, but I think even then just dividing the KE result by the distance the arm traveled is the wrong way to derive this.

Taking the first example in the OP; arm distance = 1.166m, distance projectile traveled = 19m, time projectile took to travel that distance = 2s, mass of projectile = 64kg.

Velocity = 9.5 m/s.

Timeframe accelerating = 0.27435 seconds (assuming it accelerated at a linear rate).

Acceleration = 34.627 m/s^2

Force = 2,216.1 kgf

KE = 2888 J

KE divided by arm length = 2,476,8 =/= 2,216.1

From this practical example, the method used in these calcs is flawed.

I get an acceleration of 38.7006861063464837 m/s^2 from the given parameters. (Calculated as described here)
Correspondingly a force of 38.7006861063464837 m/s^2 * 64kg = 2476.8439108061749568 N
0.5*64*9.5^2 / 1.166 = 2476.8439108061749571N
That matches within rounding error.

How did you calculate the timeframe for acceleration? That might be where the problem lies.

 

[Agnaa]

How did you calculate the timeframe for acceleration? That might be where the problem lies.

I got it from...

Timeframe accelerating = distance accelerated over / (0.5 * final velocity), as with linear acceleration from 0 to a velocity, the average speed is half of the final velocity.

Acceleration = final velocity / timeframe.

 

[DontTalkDT]

How did you calculate the timeframe for acceleration? That might be where the problem lies.

I got it from...

Timeframe accelerating = distance accelerated over / (0.5 * final velocity), as with linear acceleration from 0 to a velocity, the average speed is half of the final velocity.

Acceleration = final velocity / timeframe.

Timeframe accelerating = distance accelerated over / (0.5 * final velocity) = 1.166m / (0.5 *9.5 m/s^2) = 0.2454736842105263s
9.5 m/s / 0.2454736842105263 s = 38.7006861063464861943 m/s^2.
38.7006861063464861943 m/s^2 * 64kg = 2476.8439108061751164352 N

Which is the desired result within rounding error.

I guess you just had a typo somewhere.

 

[Agnaa]

Ah yeah, it was just a typo. I eyeballed 9.5 * 0.5 as 4.25. mb

So huh, I guess this strangely enough does work.