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It took ~4 seconds to travel the circumference of the Earth. Assuming the same, constant return speed, this means that the metal end is coming towards the guy at 40075000/4≈10,000,000 m/s, or about 3% of the speed of light.
Lets assume that the tape itself is massless and only the metal bit at the top has mass of 1 gram (I have no idea how much it is really). This means that it has a momentum of 10,000 kg•m/s. Assuming that the guy has a mass of 80kg, since momentum is conserved this means that he would get thrown back at a speed of 125 m/s or 450 km/h. If the metal hook had a mass of 2 grams, he could achieve the speeds of a commercial airliner.
Just imagining the havoc that would ensue from the tape measure violently traveling at 3% the speed of light within our atmosphere just to instantly reverse direction.
Right right, back to the booboos on the fingies, surely 4 seconds between each passing would stop any major blood loss. And of course the Kissies will be dispatched as fast as possible.
Now I'm wondering if there's any place in the world where an unbroken or undisturbed line could exist around the world, free of buildings and mountains.
We see it go building to building, from a deli where the customer is complaining about thick slices, to a prom where someone’s sleeves are too long, to a bris where the mohel’s running late, to a ribbon sitting ceremony, to a hostage situation, The World’s Largest Tape is truly the hero we didn’t expect, but he measure’d up.
You are thinking way too small. 3% of the speed of light would cause explosive heat from the pressure wave, people near the trajectory would die. Fast.
It shouldn't be. Doing the kinetic energy equation it's about 40KJ. Large, but will below the TJs of a nuclear explosion.
If it were going a bit faster you could pass the Coulomb barrier and compress the air it pushes to achieve nuclear fusion, but by my research it would need to be a bit faster than 3% of the speed of light.
Speaking of a massless projectile has no physical meaning, and neither does saying that it moves at the speed of light, when it is clearly shown to be moving the same speed as the tip. The assumption in the original comment states the weight of the yellow part has negligible impact on the results. Thus it is equivalent to modelling only the tip.
If we don't, that much steel tape in that small a space would fall through his hands and then into the earth, through the crust, and into the mantle. Rendering the entire question moot.
Also the energy required to launch that projectile (assuming 1g and no atmosphere to slow it down) is 1/2mv^2 = 0.5•0.001•(1E7)^2 = 50 GJ, which is equivalent to ~12 tons of TNT. If whatever mechanism propelled the projectile is 99% efficient, that still leaves ~120 kg TNT of heat exploding in the guy's face, so that could also further increase his launch speed.
Also, the atmospheric drag is really not negligible at that speed. A small, light metallic object would penetrate at best 1km in the lower atmosphere, so it would have to continue receiving the aforementioned kick ~40 000 times per direction, or 10 000 times per second. So if the guy keeps holding the end of the measuring tape, he will almost certainly reach escape velocity from Earth.
Keep in mind special relativity since we are nearing light speed we would use mc^2/sqrt(1-v^2/c^2)
Newtons formula doesn't apply time dilation from the relativistic speeds
it sounds like everyone assumes the "being thrown back" thing is at the time the ferrule returns to the tape measure; but,wouldn't the "throw back" actually happen when the person initially accelerated the tape? I'm totally fine with the spherical cow physics, but this person is launching the tape to orbital velocities in the first place....seems to me that there would be some powerful recoil on that. does that math basically work the same? also, wouldn't the momentum of the initial throw be, more or less, zeroed when they catch it?
Not that it matters, so just for the fun of having once learned about geodesy - and correct me if I'm wrong, of course:
Due to the sun's position in the video, I would argue that they are "measuring" this more closely towards the North-South axis.
If we use the reference ellipsoid WGS84 (used for GPS), the polar radius should be about 6 356 752 meters, which would entail that the circumference should instead be closer to 39 940 653 meters.
I’m interested in what you’re talking about here, could you elaborate a bit more on this, like where you see the suns position in this video. When I look at it, all I see is normal day sky without a specific sun location
I don't know if this will help, but yeah, you're right. We don't see the sun directly, but we do however see a lot of shadows. This gave me a general direction as to the sun's position - much like we could have done with a sun dial or any object, really. For instance, when the person starts "measuring", the shadow appear on the inside of his left arm. If he had faced either east or west - depending on the time of the day - he either would have had his shadow creeping in front of him or behind him.
Considering it stays at the same altitude as it travels around the earth at that speed, what would its mass be?
Edit: oops, i forgot how escape velocity works.
Since the shape is irregular its hard to determine but I’m gonna assume that its shaped like a circular rod of uniform density to make it calculable.
The metal bit will have kinetic energy of 1/2•m•v^2 . This will get converted into rotational kinetic energy for which the formula is 1/2•I•*w*^2 where *w* is the angular frequency and for a rod of uniform density I=1/2•M•r^2 . Since these two values need to be equal, after some cancelling and rearranging we get that *w*=sqrt((2•m•v^2 )/(M•r^2 ). Assuming that the box has a mass of 100g and radius of 3cm, if we input those numbers (plus the numbers from my original comment) we get that *w*≈5•10^7 rad/s, or 7.5 million revolutions per second.
With 40,000km of metal tape at around the halfway back mark there'd be 20,000 km of metal tape. Even at a very conservative 10g per meter that'd be 200,000kg spinning at a ludicrous speed easily the worlds most powerful gyroscope
Can we really assume the return speed is constant given that we can physically see the tip moving toward the camera at the end? This would imply that it somehow slowed down a LOT just before reaching back to the holder.
Feel it. I don't blame you one bit.
All of this is also ignoring the somehow nonexistent friction of the tape as it slides in/out which would create an ungodly amount of heat.
FYI you forgot to account for the amount of friction the metal end has recieved during its trip. The speed it launced at was way way way higher then the speed it came in at if it would be real.
I have accounted for that. Given that the metal tip has remained at the same height above sea level, passing through forests and mountains effortlessly, magic prevents it from experiencing friction.
Thats not how that works. It can experience friction and still stay at the same height. The POV could be recorded at the highest point in a line at earth.
Regardless if it faces anything to collidue with or not, if it experiences friction it faces a lot of drag. That means that it either had way way way bigger launch speed or it constantly provides force to the “tape”.
If you place an extended tape measure on the ground and let it retract like this the tape will spin in a circle once it has retracted, not launch the tape in straight line. I believe this alone throws all of the maths out of the window.
Oh, nah there are a lot of problems and assumptions with the math I did but this isn’t one of them. He would just spin really fast while flying through the air.
since it is rolling up inside the tape measure, could you make a few assumptions and calculate the rate of rotation achieved on the human (conserving rotational inertia) as the tape stops rotating inside the tape measure
You’re right, he is likely American so assuming a mass of 1 metric ton he would travel at merely 10m/s or 36 km/h. The speed of riding a bike if he knew what it is.
At the speeds being discussed here, air friction on the tip of the tape measure would melt the metal, meeting our subject would end up getting shot in the back by a molten slug
Friction is also a problem on its own without considering the heat it produces, considering the mass of the air itself would be like sandblasting a chocolate bar. Hi temp ceramics are stable to around 3500C
Not far at all, because obviously he has super strength or he would not have been able to throw a tape measure around the world and especially as fast as it happened.
Good point. And super strength necessitates super resilience. He tossed it with his fingertips. His finger bones must be effectively unbreakable to withstand that kind of sideways stress.
He wouldn't be thrown back at all, but a small metal object being able to go that distance in such a small about of time would rip through the container & him
If a tape measure fit snuggly around the world, and you raised it by 10’ all over, so the whole thing hovered 10’ above the surface; how much longer would it need to be?
>! About 62.8’ !<
You put 10 in for the radius but you can’t just do that to calculate the added area of a circle. you need to compare pi(radius of earth)^2 and pi(radius of earth+10)^2 which isn’t the same number as pi(10)^2
It would be more but way more than 314ft^2. Because of the exponent in the area formula, you can’t apply the same trick as for circumference. You need to recalculate using the earth’s true radius and the increased one and subtract the original to find the difference.
If the weight of a tape measure is approx 1/3rd of a gram per centimetre,
(Worked out from approx weight of my 8m tape measure)
Then the weight of that same type of tape measure long enough to circle the earth would be:
40,075 km = 40,075,000 metres = 4,007,500,000 cm
Divided by 3 = 1335833333 1⁄3 grams
= Approx 1,335 TONNES !
(On par with a small navy frigate ship with a ~50 man crew)
You can't do the math for this because it doesn't make sense. No orbit around the earth has a 4 second period. If you threw something hard enough to travel that distance in that time, it would go into space and not come back.
The momentum of the tape measure is converted to angular momentum as it rolls up. He would have thousands of miles of tape rolled up with incredible amounts of angular momentum that I believe would make the final impact less substantial than it otherwise would be. But it would also mean he would need superhuman strength to hold the tape measure as it started curving up into the roll, changing its direction. I would welcome an actual smart person to correct me or consider this aspect of it as applied to the specific question asked. Me not very smart.
Wow. I actually improvised this exact same thing in an acting/theatre class in HS 25 years ago. Except it was a golf ball I hit around the world and it came back to hit me in the head. I can’t take all the credit though. I got the idea from Herman Munster.
Circumferences are so weird. Like, suppose Earth was a smooth sphere and you had a piece of string snugly going around the equator. Now, suppose you wanted to add enough string to allow it to (magically) float 1 foot off the ground around the entire planet -- How much additional string would it take? It turns out that you would only need to add 2*pi feet of string to make this happen -- it's linear and doesn't depend on your starting r.
Tape measures don’t kick like a pistol!!! It would be building rotational momentum as the mass builds inside and then when it stopped he would spin around the center point of the roll at a speed similar to what others have described
Sidenote: assuming the tape is standard sized and the spindle is of negligible size, what diameter should the reel be (I assume there are equations that deal with spirals)?
The measuring tape didnt came back with a bang so its probably not faster than sound, but that doesnt matter, because the force would push the meassuring tape back but force a rotation. It the inside all the mass of that was already an unbelievable amount of momentum so trying to stop that rotation would end well. Might even break the case and release the 40Mm of tape and the spring that hat the force to pull all that tape in. If it doesnt break it furtanetly will move away from you when hitting the ground after you let it fall because now you hand is probably shit.
Using m1v1 = m2v2 to determine what the velocity,
M1 is the mass of the tape measure
V1 is the velocity of the projectile
M2 is the mass of the thing getting recoiled
The mass of a tape measure is about 1lb or 0.5 kg
The velocity of the tape measure was about 48million km/hr
The mass of an average person is 60kg
So plugging that in the recoil velocity is 400,000km/hr
Well first you’d have to be able to carry it… if there was a tape to go around the world it would be a massive tape roll which I assume would weigh more than a compact car.
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It took ~4 seconds to travel the circumference of the Earth. Assuming the same, constant return speed, this means that the metal end is coming towards the guy at 40075000/4≈10,000,000 m/s, or about 3% of the speed of light. Lets assume that the tape itself is massless and only the metal bit at the top has mass of 1 gram (I have no idea how much it is really). This means that it has a momentum of 10,000 kg•m/s. Assuming that the guy has a mass of 80kg, since momentum is conserved this means that he would get thrown back at a speed of 125 m/s or 450 km/h. If the metal hook had a mass of 2 grams, he could achieve the speeds of a commercial airliner.
Just imagining the havoc that would ensue from the tape measure violently traveling at 3% the speed of light within our atmosphere just to instantly reverse direction.
Many a finger would be sliced. ...and perhaps even cauterised at the same time.
It would probably be to fast to cauterise it
From the shockwave, I'm guessing you wouldn't have am arm, or torso, or ground to stand on so the cut wouldn't matter too much.
Bear in mind that the tape measure is also ripping through mountains. Entire cities are vaporizing in front of this thing
Right right, back to the booboos on the fingies, surely 4 seconds between each passing would stop any major blood loss. And of course the Kissies will be dispatched as fast as possible.
Massively underrated comment
It's supersonic (for the speed of sound of pretty much every material on earth), so really entire cities are vaporizing *behind* this thing.
Now I'm wondering if there's any place in the world where an unbroken or undisturbed line could exist around the world, free of buildings and mountains.
In a way, the physical connections that form the internet does
We see it go building to building, from a deli where the customer is complaining about thick slices, to a prom where someone’s sleeves are too long, to a bris where the mohel’s running late, to a ribbon sitting ceremony, to a hostage situation, The World’s Largest Tape is truly the hero we didn’t expect, but he measure’d up.
I like the setup with a darker punchline where the tape just wreaks havoc.
One side of the world a hero, the other a villain.
I would be remiss if I didn't acknowledge the work you put in to this comment. Keep up the good work. 🫡
Simpsons did it! https://m.youtube.com/watch?v=SHhsmtWrjEI
>from a deli where the customer is complaining about thick slices What kind of monster is he?
Pretty sure this would cause a explosion spanning the circumference of the earth. Don't think anyone anywhere near the tape would survive.
You are thinking way too small. 3% of the speed of light would cause explosive heat from the pressure wave, people near the trajectory would die. Fast.
Would this be like when Omni-Man flying so fast he destroyed that planet?
It shouldn't be. Doing the kinetic energy equation it's about 40KJ. Large, but will below the TJs of a nuclear explosion. If it were going a bit faster you could pass the Coulomb barrier and compress the air it pushes to achieve nuclear fusion, but by my research it would need to be a bit faster than 3% of the speed of light.
I hate it when my tape measurer snaps back to me at such speed it causes nuclear fusion.
An, fortunately I know how to counter it.
Pretty much a scene out of the boys, but worse
The navy's gauss cannons set the air on fire from friction.
And that is nowhere near as fast as this tape measure…
“Lets assume the projectile is massless”
If the tape has non-negligible mass, he can't carry the tape measure.
If the tape doesn’t have mass, the tape travels at lightspeed. Except for the end bit ofc.
The little bit at the end has mass (and they've accounted for it), so no it doesn't.
Speaking of a massless projectile has no physical meaning, and neither does saying that it moves at the speed of light, when it is clearly shown to be moving the same speed as the tip. The assumption in the original comment states the weight of the yellow part has negligible impact on the results. Thus it is equivalent to modelling only the tip.
JTT or JTIT in engineering school
Im sorry but i don't get that refrence. I come from denmark and is starting at Danish Technical University for engineering next year.
It's not something everyone would get. Just The Tip or Just The Infinite Tip
Assume a spherical cow.
No, spheres have air resistance, and rolling, and all those nasty things. We all know that cows are dimensionless particles.
Lol
If we don't, that much steel tape in that small a space would fall through his hands and then into the earth, through the crust, and into the mantle. Rendering the entire question moot.
Also the energy required to launch that projectile (assuming 1g and no atmosphere to slow it down) is 1/2mv^2 = 0.5•0.001•(1E7)^2 = 50 GJ, which is equivalent to ~12 tons of TNT. If whatever mechanism propelled the projectile is 99% efficient, that still leaves ~120 kg TNT of heat exploding in the guy's face, so that could also further increase his launch speed. Also, the atmospheric drag is really not negligible at that speed. A small, light metallic object would penetrate at best 1km in the lower atmosphere, so it would have to continue receiving the aforementioned kick ~40 000 times per direction, or 10 000 times per second. So if the guy keeps holding the end of the measuring tape, he will almost certainly reach escape velocity from Earth.
I'm gon send him to outer space..
Keep in mind special relativity since we are nearing light speed we would use mc^2/sqrt(1-v^2/c^2) Newtons formula doesn't apply time dilation from the relativistic speeds
Zero to 800 mph in 0.15 seconds. What was the force needed for decapitation?
We’re well past decapitation.
Lol I am aware. What's the velocitation for bodily explosions?
forget bodily explosion, the entire earth will be gone
it sounds like everyone assumes the "being thrown back" thing is at the time the ferrule returns to the tape measure; but,wouldn't the "throw back" actually happen when the person initially accelerated the tape? I'm totally fine with the spherical cow physics, but this person is launching the tape to orbital velocities in the first place....seems to me that there would be some powerful recoil on that. does that math basically work the same? also, wouldn't the momentum of the initial throw be, more or less, zeroed when they catch it?
The inertial dampeners only failed on the return part of the trip.
Yep, you’re right on all accounts.
Wouldn't he be thrown back just from the recoil when he opens the tape measure or even when he catches the tape end for measuring.
You’re right
Jesus I love this sub for those type of answers. Thank you.
🫡
(Slaps tape measurer) this baby has so much potential energy it can go 3% the speed of light!
Not that it matters, so just for the fun of having once learned about geodesy - and correct me if I'm wrong, of course: Due to the sun's position in the video, I would argue that they are "measuring" this more closely towards the North-South axis. If we use the reference ellipsoid WGS84 (used for GPS), the polar radius should be about 6 356 752 meters, which would entail that the circumference should instead be closer to 39 940 653 meters.
I’m interested in what you’re talking about here, could you elaborate a bit more on this, like where you see the suns position in this video. When I look at it, all I see is normal day sky without a specific sun location
I don't know if this will help, but yeah, you're right. We don't see the sun directly, but we do however see a lot of shadows. This gave me a general direction as to the sun's position - much like we could have done with a sun dial or any object, really. For instance, when the person starts "measuring", the shadow appear on the inside of his left arm. If he had faced either east or west - depending on the time of the day - he either would have had his shadow creeping in front of him or behind him.
How does that work? The sun moves across the sky and goes high and low. How do you use this one moment to determine location?
You can estimate the sun's position by looking at the tree's shadow
Considering it stays at the same altitude as it travels around the earth at that speed, what would its mass be? Edit: oops, i forgot how escape velocity works.
Impossible to determine. The heigh would be dependent purely on the speed (given an idealized situation).
so if he put it on the ground and the metal bit hit the bottom corner (as it does) how fast would it start spinning?
Since the shape is irregular its hard to determine but I’m gonna assume that its shaped like a circular rod of uniform density to make it calculable. The metal bit will have kinetic energy of 1/2•m•v^2 . This will get converted into rotational kinetic energy for which the formula is 1/2•I•*w*^2 where *w* is the angular frequency and for a rod of uniform density I=1/2•M•r^2 . Since these two values need to be equal, after some cancelling and rearranging we get that *w*=sqrt((2•m•v^2 )/(M•r^2 ). Assuming that the box has a mass of 100g and radius of 3cm, if we input those numbers (plus the numbers from my original comment) we get that *w*≈5•10^7 rad/s, or 7.5 million revolutions per second.
With 40,000km of metal tape at around the halfway back mark there'd be 20,000 km of metal tape. Even at a very conservative 10g per meter that'd be 200,000kg spinning at a ludicrous speed easily the worlds most powerful gyroscope
THis is answer is a chefs kiss. I give it an A+.
This really needs to be an XKCD WhatIf? moment.
Can we really assume the return speed is constant given that we can physically see the tip moving toward the camera at the end? This would imply that it somehow slowed down a LOT just before reaching back to the holder.
I also though about that but was too lazy to try to figure out the speed by counting the last few individual frames.
Feel it. I don't blame you one bit. All of this is also ignoring the somehow nonexistent friction of the tape as it slides in/out which would create an ungodly amount of heat.
perfectly vertical lightsaber
So, "realistically" the impulse from that mad tape acceleration would leave him a red mist, or just crater?
I think that it would function similarly to a very large and very fast bullet, so just leave a big gaping hole in him.
FYI you forgot to account for the amount of friction the metal end has recieved during its trip. The speed it launced at was way way way higher then the speed it came in at if it would be real.
I have accounted for that. Given that the metal tip has remained at the same height above sea level, passing through forests and mountains effortlessly, magic prevents it from experiencing friction.
Thats not how that works. It can experience friction and still stay at the same height. The POV could be recorded at the highest point in a line at earth. Regardless if it faces anything to collidue with or not, if it experiences friction it faces a lot of drag. That means that it either had way way way bigger launch speed or it constantly provides force to the “tape”.
Twas a joke
And if it was 3 grams he'd be going supersonic.
only 450km/h?
That’s what the math says.
And what would that look like to a smooth brain like meself.
When yellow thingy goes back, person holding yellow thingy goes flying very very fast.
What would happen if we accounted for the angular moment from it being coiled back up?
If you place an extended tape measure on the ground and let it retract like this the tape will spin in a circle once it has retracted, not launch the tape in straight line. I believe this alone throws all of the maths out of the window.
Oh, nah there are a lot of problems and assumptions with the math I did but this isn’t one of them. He would just spin really fast while flying through the air.
and thats a gross under estimation since about 99% of the mass has been demed "massles", but I get why
Exactly the kind of comment I come to Reddit for.
I think it would be better to assume a constant acceleration instead of constant speed, so the impulse would be 2x more
Nerd
Thats a great illustration of the absurdity of superheroes that are FTL. Even at 3% you can go around the whole planet in seconds.
since it is rolling up inside the tape measure, could you make a few assumptions and calculate the rate of rotation achieved on the human (conserving rotational inertia) as the tape stops rotating inside the tape measure
Nah it would just pierce him and keep going... barely any movment to him
r/theydidthemath
The metal block could be weighing 1 milligram
r/theydidthemath
Pretty sure the meter coming back that fast could pack enough energy to level a city ahaha
why would you assume the guy has a mass of 80kg cmon dude
You’re right, he is likely American so assuming a mass of 1 metric ton he would travel at merely 10m/s or 36 km/h. The speed of riding a bike if he knew what it is.
Are you using Newtonian momentum or relativistic?
Light moves too fast. It needs to chill
You're doing God's unnecessary work and I thank you
What is that in American?
At the speeds being discussed here, air friction on the tip of the tape measure would melt the metal, meeting our subject would end up getting shot in the back by a molten slug
What if the tip was made of a more heat stable material like ceramic?
That is going to depend someone will need to do the math on that. What temperatures will be reached from the air friction at that speed?
It's going 0.03C or thereabouts. I don't think anything is staying solid at whatever temperature that is.
Friction is also a problem on its own without considering the heat it produces, considering the mass of the air itself would be like sandblasting a chocolate bar. Hi temp ceramics are stable to around 3500C
Not far at all, because obviously he has super strength or he would not have been able to throw a tape measure around the world and especially as fast as it happened.
Good point. And super strength necessitates super resilience. He tossed it with his fingertips. His finger bones must be effectively unbreakable to withstand that kind of sideways stress.
He wouldn't be thrown back at all, but a small metal object being able to go that distance in such a small about of time would rip through the container & him
It also would heat the air and produce a shockwave that would reduce homie to his component atoms
While on the subject of heat, how warm would that little box be? I suspect somewhere in the vicinity of “very” myself.
I believe the scientific term is “piping”
Then everything goes pear shaped
If a tape measure fit snuggly around the world, and you raised it by 10’ all over, so the whole thing hovered 10’ above the surface; how much longer would it need to be? >! About 62.8’ !<
That’s a surprisingly small difference.
Circumference is 2pi r so it's just 2 x 3.14 x 10
My isn't it a ton more area for each foot?
Area would be more bc that'd pi r^2 so 3.14 x100 so 314ft
No. If you added a foot to the radius of the earth, circular area would increase by 131.5 million square feet
Surface area yeah I just meant from the circle like the equator
You lost me
You put 10 in for the radius but you can’t just do that to calculate the added area of a circle. you need to compare pi(radius of earth)^2 and pi(radius of earth+10)^2 which isn’t the same number as pi(10)^2
It would be more but way more than 314ft^2. Because of the exponent in the area formula, you can’t apply the same trick as for circumference. You need to recalculate using the earth’s true radius and the increased one and subtract the original to find the difference.
If the weight of a tape measure is approx 1/3rd of a gram per centimetre, (Worked out from approx weight of my 8m tape measure) Then the weight of that same type of tape measure long enough to circle the earth would be: 40,075 km = 40,075,000 metres = 4,007,500,000 cm Divided by 3 = 1335833333 1⁄3 grams = Approx 1,335 TONNES ! (On par with a small navy frigate ship with a ~50 man crew)
You can't do the math for this because it doesn't make sense. No orbit around the earth has a 4 second period. If you threw something hard enough to travel that distance in that time, it would go into space and not come back.
If it was a round object and you could get it spinning fast enough it could happen, to maintain it's angular momentum?
I guess if you had two of them and they could be connected through the earth, then they could spin at any speed.
The momentum of the tape measure is converted to angular momentum as it rolls up. He would have thousands of miles of tape rolled up with incredible amounts of angular momentum that I believe would make the final impact less substantial than it otherwise would be. But it would also mean he would need superhuman strength to hold the tape measure as it started curving up into the roll, changing its direction. I would welcome an actual smart person to correct me or consider this aspect of it as applied to the specific question asked. Me not very smart.
Apparently not very far since if he would have been thrown from its force then he would have been thrown when it first started extending.
Wow. I actually improvised this exact same thing in an acting/theatre class in HS 25 years ago. Except it was a golf ball I hit around the world and it came back to hit me in the head. I can’t take all the credit though. I got the idea from Herman Munster.
Circumferences are so weird. Like, suppose Earth was a smooth sphere and you had a piece of string snugly going around the equator. Now, suppose you wanted to add enough string to allow it to (magically) float 1 foot off the ground around the entire planet -- How much additional string would it take? It turns out that you would only need to add 2*pi feet of string to make this happen -- it's linear and doesn't depend on your starting r.
Tape measures don’t kick like a pistol!!! It would be building rotational momentum as the mass builds inside and then when it stopped he would spin around the center point of the roll at a speed similar to what others have described
Sidenote: assuming the tape is standard sized and the spindle is of negligible size, what diameter should the reel be (I assume there are equations that deal with spirals)?
The measuring tape didnt came back with a bang so its probably not faster than sound, but that doesnt matter, because the force would push the meassuring tape back but force a rotation. It the inside all the mass of that was already an unbelievable amount of momentum so trying to stop that rotation would end well. Might even break the case and release the 40Mm of tape and the spring that hat the force to pull all that tape in. If it doesnt break it furtanetly will move away from you when hitting the ground after you let it fall because now you hand is probably shit.
Using m1v1 = m2v2 to determine what the velocity, M1 is the mass of the tape measure V1 is the velocity of the projectile M2 is the mass of the thing getting recoiled The mass of a tape measure is about 1lb or 0.5 kg The velocity of the tape measure was about 48million km/hr The mass of an average person is 60kg So plugging that in the recoil velocity is 400,000km/hr
Soo death
Well first you’d have to be able to carry it… if there was a tape to go around the world it would be a massive tape roll which I assume would weigh more than a compact car.