Reply to thread

Message: <blockquote data-quote="CleverNickName" data-source="post: 9605463" data-attributes="member: 50987">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 / Δtwhere 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 = mvwhere 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 m[sup]3[/sup]), and air has a density of 1.225kg/m[sup]3[/sup] at STP, so let's assume the mass of a Mage Hand is 5.02x10[SUP]-4[/SUP] kg.p = mvp = (5.02x10[SUP]-4[/SUP] kg)(0.0015 m/sec)p = 7.65x10[SUP]-7[/SUP] kg-m/sNow 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[SUP]-7[/SUP] kg-m/sΔp = p[sub]final[/sub] - p[sub]initial[/sub]Δp = (7.65x10[SUP]-7[/SUP] kg-m/s) - 0Δp = 7.65x10[SUP]-7[/SUP] kg-m/sNow 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:t[SUB]0[/SUB] = sv[SUB]avg[/SUB] = 2sv[SUB]init[/SUB],where t[SUB]0[/SUB] is the impact time, s is the distance over which the force is acting (the thickness of the pressure plate), and v[SUB]init[/SUB] 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...t[SUB]0[/SUB] = 2(s)/v[SUB]init[/SUB]t[SUB]0[/SUB] = 2(0.001 <s>m</s>)/(1.524 <s>m</s>/sec)t[SUB]0[/SUB] = 0.0013 secFind the change in time from initial to final condition:Δt = t[SUB]0[/SUB] - t[SUB]1[/SUB]Δt = 0.0013sec - 0 secΔt = 0.0013secAnd now we have Δp and Δt, so we can finally calculate F (the impact force).F = Δp / ΔtF = (7.65x10[SUP]-7[/SUP] kg-m/s) / (0.0013 sec)F = 0.0000005022 kg-m/s[sup]2[/sup]F = 0.000588 NewtonsF = 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.[/SPOILER]</blockquote>

Verification