The physics of Ironpulls and Steelpushes

[Narglet]

Given someone does a "regular" push on an object, what determines how much force it exerts? For a long time I assumed that (discounting metal content, allomantic strength, ect) the force a push exerts is solely based on the inverse square law; that is to say it gets weaker as the separation increases exactly like gravity or the electrostatic forces.

However, there are a few lines in the series that suggest it's also based on the relative velocity of the Pushee and Pusher. When Vin Pushes on a coin horizontally, the recoil is barely strong enough to make her change her stance. However, the moment the coin hits a wall, it sends her flying. This suggests that objects moving away from an Allomacer are pushed on with less force than a stationary object.

In Shadows of Self, Wax has to use quite a few pushes in order to get to the top of ZoBell tower, leading him to use the grappling hook. However, on his exit, he is able to jump out and land by pushing on a single object on the ground. Physics tells us that the energy needed to lift an object to a certain distance is the same amount of energy needed to completely stop that object after falling that same distance. If the force was the same going up and going down, that single push would have only nullified a few stories of falling. My theory is that because he was falling, and therefore going towards the coin(or was it a bullet?) his push was much stronger than when rising.

This has interesting implications for weaponized coins. Bullets, slings, and bows are dangerous because of the kinetic energy that was imparted onto them before contact. Shot coins however would be more like a stabbing spear; the initial speed is good and all, but what really matters is how hard you're pushing while going through the target.

[Quantus he/him]

It's...complicated

Check this thread out, there's a lot of ground to cover:

 

[+Oltux72 he/him]

1 hour ago, Narglet said:

Given someone does a "regular" push on an object, what determines how much force it exerts? For a long time I assumed that (discounting metal content, allomantic strength, ect) the force a push exerts is solely based on the inverse square law; that is to say it gets weaker as the separation increases exactly like gravity or the electrostatic forces.

It is complicated. The only thing we are reasonably sure of is that it is not subject to the inverse square law.

1 hour ago, Narglet said:

In Shadows of Self, Wax has to use quite a few pushes in order to get to the top of ZoBell tower, leading him to use the grappling hook. However, on his exit, he is able to jump out and land by pushing on a single object on the ground. Physics tells us that the energy needed to lift an object to a certain distance is the same amount of energy needed to completely stop that object after falling that same distance.

Well, in a vacuum and with 100% efficiency. Both conditions are not met.Looking at allomancy in terms of energy does not make sense. Energy is added from outside. Wax does not rise in a ballistic arc. It is a powered ascent. In terms of physics he is a helicopter not a bullet.

 

[Narglet]

8 minutes ago, Oltux72 said:

Well, in a vacuum and with 100% efficiency. Both conditions are not met.Looking at allomancy in terms of energy does not make sense. Energy is added from outside. Wax does not rise in a ballistic arc. It is a powered ascent. In terms of physics he is a helicopter not a bullet.

It doesn't matter if the trajectory is ballistic or not. If he's being pushed with a conservative force(as opposed to being variant with respect to velocity), it's going to do the same amount of mechanical work regardless of which path he takes. He wasn't making himself lighter so I don't think air resistance is enough of a factor to explain the discrepancy.

Edited January 7, 2020 by Narglet

[Pagerunner he/him]

We do know that force is inversely proportional to distance, and there are some other interactions that suggest the force is also related to relative velocity (like steelpushing contests between two Allomancers, as shown in the linked Impossible Physics thread). So the ZoBell tower could be another scenario explained by a relative velocity factor on steelpushes.

But there are a couple of other factors to consider beforehand, which all require a closer reading of the text.

• You can push harder on larger anchors; what was Wax pushing on as he was going up the side of the tower, vs coming down?
• When you're calculating the work done, you're essentially integrating force times distance. If you're not directly adjacent to what you're pushing off of, you're not going to be able to get as much work out of a push (since the force will start off smaller, and you'll be able to accomplish work over less of a total distance). How far was Wax from what he was pushing off of on his way up?
• I'm not certain air resistance is negligible. According to Google, it takes a human 12 seconds/1500 feet to reach terminal velocity, about the height of the Empire State Building. ZoBell tower is about a fifth of that (20 stories, Empire State Building is 102), so I'd estimate that there's enough time for air resistance to accomplish some effect on the free fall. Air resistance operates against Wax's pushes going up (he has to put in more energy to reach the same height), and with Wax's push coming down (has to put in less energy to slow down).

So, there are a lot of other factors that could potentially be responsible for Wax needing one object on the way down, and more on the way up. When exactly did this scene occur?

 

As to the gun vs spear comparisons, remember that once a coin enters someone's body, the Allomancer can't push on it any more. (Which is why people hide coins in their mouths.) By the time the coin begins to slow down, it will already have broken the skin and be inside the body, so you won't be able to sustain that push anymore.

[Elsecaller_17.5 he/him]

The thing to remember with all of the magic systems is that though the make sense, they sometimes don't in the real world. The key is that they are internally consistent. 

Edited January 7, 2020 by Truthwatcher_17.5

[Narglet]

59 minutes ago, Pagerunner said:

We do know that force is inversely proportional to distance, and there are some other interactions that suggest the force is also related to relative velocity (like steelpushing contests between two Allomancers, as shown in the linked Impossible Physics thread). So the ZoBell tower could be another scenario explained by a relative velocity factor on steelpushes.

But there are a couple of other factors to consider beforehand, which all require a closer reading of the text.

• You can push harder on larger anchors; what was Wax pushing on as he was going up the side of the tower, vs coming down?
• When you're calculating the work done, you're essentially integrating force times distance. If you're not directly adjacent to what you're pushing off of, you're not going to be able to get as much work out of a push (since the force will start off smaller, and you'll be able to accomplish work over less of a total distance). How far was Wax from what he was pushing off of on his way up?
• I'm not certain air resistance is negligible. According to Google, it takes a human 12 seconds/1500 feet to reach terminal velocity, about the height of the Empire State Building. ZoBell tower is about a fifth of that (20 stories, Empire State Building is 102), so I'd estimate that there's enough time for air resistance to accomplish some effect on the free fall. Air resistance operates against Wax's pushes going up (he has to put in more energy to reach the same height), and with Wax's push coming down (has to put in less energy to slow down).

So, there are a lot of other factors that could potentially be responsible for Wax needing one object on the way down, and more on the way up. When exactly did this scene occur?

As to the gun vs spear comparisons, remember that once a coin enters someone's body, the Allomancer can't push on it any more. (Which is why people hide coins in their mouths.) By the time the coin begins to slow down, it will already have broken the skin and be inside the body, so you won't be able to sustain that push anymore.

The scenes were right before and after the party where we first meet Governor Innate, chapter 8 and chapter 11. The anchors were steel girders on the way up, and a single bullet on the way down. Going up the tower was very nearly vertical, in AoL he was able to compensate by becoming light and firing his shotgun sideways. It took him about six pushes to get all the way to the top, but he was carrying Steris that direction, which I'll assume give him about double weight. Ignoring the massive difference between the anchor sizes, with a conservative-force style steelpush, he would still have two thirds of his original kinetic energy when hitting the ground.