D&D 5E Mage Hand and Trap Avoidance

[KYRON45]

Just use a better trap.

 

[el-remmen]

Something that can lift 10lbs can apply more than 10lbs of force. Why? 10lbs is the force of gravity on a 4.5kg object (0.3 slugs, iirc non-metric unit of mass) So 10lbs of force neutralizes gravity....but that's it. It can't lift it higher. Want to go up? Add more force.

I will point out that a Gnome or Halfling under the effect of the Reduce spell weighs around 5lbs.

By the same token, Unseen Servant can push around a character sitting on Floating Disk.

Maaaaagic!

I am having a hard time parsing this response.

So you are saying it not fair to say if a mage hand is limited to lifting 10bs, it can only apply 10 lbs of force - ok, so how many lbs of force can it apply? I was literally asking that.

 

[MarkB]

My issue with traps is they are usually out if proportion to the treasure. The dinkiest d4 poison costs 100gp/dose. Yes, yes, not an economic simulator, blah, blah, but as a player I am more likely to make more money stealing the trap than whatever it protects.

For the love of sanity people, have your trap be no more than 50% the value of the treasure! Why protect 100gp with a 4,000gp trap?

You want an ogre to protect 100gp from thieving goblins? Have a ceiling beam slam down when one end becomes unpinned. A crude crossbow fires a bolt. A bear trap built into the treasure chest.

Also, they're almost always some form of damaging effect. To me, by far the most effective trap to put on something in a populated area would be an alarm.

 

[CleverNickName]

I haven't read through this whole thread, so forgive me if this has already been mentioned.

I hate it. It is so boring.

My feelings on traps have evolved over the years and ultimately they boil down to this: if the trap can be easily bypassed with mage hand, it is a bad trap. Full stop.

I've never had a problem with Mage Hand. But if it were, and it had gotten to the point where it was making my game boring, I have ways to work around it. For example, I would set the weight limit of a pressure plate to 11 pounds, and/or make its blast radius 35 feet.

I wouldn't do this on every trap, just one or two at the very most. The purpose of boobytraps is to make my players paranoid, after all, and I only need one good boobytrap to make that happen.

EDIT: Yep, this has been mentioned. Many times.

So many times.

 

[Reynard]

I haven't read through this whole thread, so forgive me if this has already been mentioned.



I've never had a problem with Mage Hand. But if it were, and it had gotten to the point where it was making my game boring, I have ways to work around it. For example, I would set the weight limit of a pressure plate to 11 pounds, and/or make its blast radius 35 feet.

I wouldn't do this on every trap, just one or two at the very most. The purpose of boobytraps is to make my players paranoid, after all, and I only need one good boobytrap to make that happen.

Just as a reminder: I was running the adventure pretty much as written (for ease). I wouldn't have written the trap if it was my adventure, or kept it lie that if I had been doing any real prep besides a quick read.

 

[kigmatzomat]

ok, so how many lbs of force can it apply? I was literally asking that.

You are not going to like the answer. It's why simulationists get headaches. You see the answer is greater than 11.6lbs but less than infinity.

I won't make everyone look at math.

Spoiler

So why 11.6 - infinity? Force is mass x acceleration. So the amount of Force It depends on how much acceleration it can impart. And how fast that thing was moving when it started, as it will need to accelerate/decelerate it appropriately.

Pounds are actually a unit of force, not mass. An object that, at rest, exerts 10lbs of force on a scale masses 0.31 slugs (imperial unit of mass) or 4.5kg (metric unit of mass)

For simplicity we'll assume continuous acceleration of an object that started at rest. The spherical cow of basic physics. May Newton guide my hand.

from d = 0.5(a)t^2 we get 30ft=0.5a(6s^2) => 1.67ft/s^2
::: 0.31 slug x (32.2ft/s^2 / + 1.67ft/s^2 ) = 11.6lbs

But wait! This is a floor! The actual force can be more! What if you catch a 0.31slug/4.5kg object that is falling? What if it got dropped last round and this round you are going to catch it with Mage Hand and then lift it 30ft?

the initial velocity will be v = at where a is gravity so 32.2ft/s^2 x 6s => -193ft/s
d=0.5at^2 ‐vt
30ft =a18s^2 -1158ft
66ft/s^2 = a
:::0.31slug x a=21lbs

Repeat up to v= terminal velocity.

but...this assumes a bit of "bounce" as the hand goes down on impact, then rises up. what if the hand is already at 30ft and can't move away? There's nothing saying anything can "push" a mage hand. More massive things just pass through. Less massive things...??

In that case you can convert the kinetic falling energy to force, that is e=F d, where f is the force and d is the distance the force is applied.

Except....if the hand isn't directed to move.....is the distance ~0?
Because if so, for e>0, F would approach infinity.
so...between 11.6lbs and infinity.

Wheee!

 

[CleverNickName]

What about impact force? Like, how hard could a Mage Hand slap a pressure plate? What if you have the Mage Hand ball itself up into a fist and pound on a trap's pressure plate at full speed? Surely that would generate the most force, right? After all, jumping up and down on a bathroom scale makes the needle go much higher than your own body weight...

Well, let's calculate it!

Spoiler: Science!

What you're looking for here is the impact force, which is calculated by the following formula:
F = Δp / Δt
where F is the impact force, Δp is the change in momentum, and Δt is the change in time.

So first, we calculate the change in momentum:
p = mv
where p is the momentum, m is the mass, and v is the velocity.

Velocity is easy to calculate: a mage hand can move up to 30 feet in 6 seconds, so that 5 feet per second (or 0.0015 m/s). The mass of a Mage Hand is not given, but from the description, I would assume the mass to be zero ("spectral") or lighter than air ("floating"). Let's be generous, and go with the mass of air. According to Google, a hand has a volume of about 410cc (or 0.00041 m³), and air has a density of 1.225kg/m³ at STP, so let's assume the mass of a Mage Hand is 5.02x10^-4 kg.

p = mv
p = (5.02x10^-4 kg)(0.0015 m/sec)
p = 7.65x10^-7 kg-m/s

Now to calculate the change in things (momentum and time), we need to define the initial and the final conditions. Initially, the mage hand is going to be at rest, 30 feet away from the pressure plate. Final condition will be the mage hand traveling at full speed and striking the plate.

Initial Condition: p = 0 because v = 0.
Final Condition: p = 7.65x10^-7 kg-m/s

Δp = p_final - p_initial
Δp = (7.65x10^-7 kg-m/s) - 0
Δp = 7.65x10^-7 kg-m/s

Now we need the impact time (or as it is sometimes called, the impact duration), which is the amount of time that the mage hand is in contact with that pressure plate. Assuming a perfectly inelastic collision (the mage hand doesn't stick to the plate), this would only be a fraction of a second. We calculate this with the following formula:
t₀ = sv_avg = 2sv_init,
where t₀ is the impact time, s is the distance over which the force is acting (the thickness of the pressure plate), and v_init is the velocity the mage hand is moving before it impacts the pressure plate.

So let's be generous, and say the pressure plate is only one millimeter thick (0.001 meters). Smaller impact time means larger force, so we are being conservative. If we use something thicker (like the lid of a chest, or a door), the impact time would be larger and the force would be less concentrated (and therefore lower). Anyway...

t₀ = 2(s)/v_init
t₀ = 2(0.001 m)/(1.524 m/sec)
t₀ = 0.0013 sec

Find the change in time from initial to final condition:

Δt = t₀ - t₁
Δt = 0.0013sec - 0 sec
Δt = 0.0013sec

And now we have Δp and Δt, so we can finally calculate F (the impact force).

F = Δp / Δt
F = (7.65x10^-7 kg-m/s) / (0.0013 sec)
F = 0.0000005022 kg-m/s²
F = 0.000588 Newtons
F = 0.000132 pounds(force)

That's about the amount of force a single grain of table salt would exert on a table.

So, not a lot.

 

[MarkB]

What about impact force? Like, how hard could a Mage Hand slap a pressure plate? What if you have the Mage Hand ball itself up into a fist and pound on a trap's pressure plate at full speed? Surely that would generate the most force, right?

Nah, I'd go with hauling a 10 lb weight up to the ceiling and then dropping it.

 

[CleverNickName]

Nah, I'd go with hauling a 10 lb weight up to the ceiling and then dropping it.

Too fast; the hand can only move 5 ft/sec.

But what if the hand weighed 10 lbs?

Spoiler: More Science!

First, convert weight to mass: 10 lbs(w) = 4.5359kg.
Then, solve for the new momentum: p = mv = (4.5359 kg)(0.0015m/sec) = 0.0068 kg-m/s
Finally, use the updated momentum to solve for force: F = Δp / Δt = (0.0068 kg-m/s)/0.0013 m/s) = 5.234 N = 1.17 lbs(force)

A little more than a pound of force. Way more then before (when the mage hand had the same mass as the air around it), but still not nearly as much as you would think. The velocity just isn't high enough.

 

[MarkB]

Too fast; the hand can only move 5 ft/sec.

I don't understand. How does its speed affect being able to drop a rock on a pressure plate? It's not exactly a moving target.