How does mass and velocity affect the amount of damage?

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I’m not a science-y person, but I love sci-fi. In a novel I read near a decade ago (Larry Niven’s Known Space series), he mentions occasionally kinetic weapons. I’ve seen this online as well with tungsten-based projectiles being discussed. So my question is how does mass and velocity affect the amount of damage? If I had a nickel-sized object, how fast would it need to go to cause city-wide devastation (would it be possible or would the damage output be capped based on either size or velocity)? Conversely, If I launched something at the speed of sound, would the damage output be the same if it were different-sized objects?

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12 Answers

Anonymous 0 Comments

The amount of *energy carried by a moving object* is equal to (mv^2)/2. (m is mass, v is velocity) 2x mass is 2x energy, 2x velocity is 4x energy.

The *force created on impact* is mv/t. (t is time during which the impact occurs and velocity is being changed) 2x mass is 2x force, 2x velocity is 2x force, 2x time is 0.5x force.

There was a video made by Veritasium on youtube, and he explains the kinetic projectile idea quite well.

Anonymous 0 Comments

(Placeholder until a better answer arrives)
Some things to consider: there’s resistance in the air, so the object has to be hard enough to not be immediately destroyed on drag. A heavier object requires more energy to travel at the same speed as a smaller object, so higher mass at same speed = higher energy = higher force on impact. (A car vs a marble at 300,000 mph for example, or why a bus at 50 mph wins vs a car 50 mph in collision). As for force required to cause damage, a satellite can get entirely destroyed by a screw from another satellite. So, I’d imagine anything hard enough to withstand air resistance + large enough to not pass directly through the planet + high enough speed, will = force required to = (devastating asteroid). There is no ‘cap’ on nature’s destruction, or creation.

Anonymous 0 Comments

The amount of damage varies if I apply less or more force, the Force in physics is calculated with F=ma, Force=mass times acceleration, acceleration is not technically the speed of the object but in real life the two things are usually connected so yeah, speed is usually how hard you threw the object, the more force you use to kick a ball the faster it goes, so when it impacts on something all the force goes from the movement of the ball to the thing that it hit. Mass is a little bit more complex: you know that two objects, even if they have different weights, will fall at the same speed ? That’s because the gravity generated by earth “manifests” as an acceleration on your body that is equal for everyone, but when you touch the ground that’s when all of that acceleration becomes a Force and the more you weight the more you’re going to damage the ground.

Anonymous 0 Comments

Kinetic energy is mass times velocity squared.

Since energy is conserved the more energy your projectile has the more it takes to stop it. The thing you hit has to absorb all that damage by deforming or getting kinetic energy as well and flying in multiple direction, or by heating up (wich ones of these happen depend on a bunch of complicated phyiscs, but in general the more energy is involved the more severe the results will be)

>If I had a nickel-sized object, how fast would it need to go to cause city-wide devastation (would it be possible or would the damage output be capped based on either size or velocity)?

There is no cap. There is a maximum speed (speed of light) but approaching it your mass will increase so the total energy has no limit. So a penny at relativistic speeds can have the same effect as a nuclear bomb. For example at 99% lightspeed is about 100 kilotons of TNT equivalent (so a very small nuke). But then if you go to 99.9% lightspeed it gets exponentially bigger

>Conversely, If I launched something at the speed of sound, would the damage output be the same if it were different-sized objects?

No heavier means more damage. Throwing a baseball at someone hurts less then a bowling ball hurled at the same speed (wich takes more energy to get that fast, and also to stop it again)

Anonymous 0 Comments

The more mass and the greater the velocity the more energy it has and that energy can be released in a collision. So you can increase the velocity of a standard candle so it will pass completely through a solid wooden door.

Anonymous 0 Comments

Think about putting a weight on a scale. The 10lb weight will read 10lbs if it is just sitting there. But lift it a few inches and drop it, and an analog scale will have a spike above 10lbs. This is because when you accelerate the mass of the object, you are putting energy into it. When the weight is stopped by the scale, it “dumps” that energy into the scale, and the scale reads it as a spike above 10lbs. In this case you lift the weight, creating potential energy and dropping it releases that energy via gravity. But that’s another topic all together.

The higher your lift and drop the weight, the more energy is in it, and the higher that needle will move. Of course it won’t be long until that 10lb weight will have enough energy to destroy/break the scale. The same is true for cars, planes, bullets, people. To make a mass move, you have to give it energy. The equations the other posters wrote down define that for you, but the high level idea is, if you double the speed of a given object, you quadruple the energy. THat’s why a car crash at 60mph can be catastrophic, and one at 5mph may do nearly 0 damage. It’s also why getting hit with a baseball bat will break you, but getting hit with a cardboard tube at the same speed might not leave a mark. The faster and/or more massive something is, the more energy it has. When you make that stop you have to use up that energy, and that’s why bends, breaks, and blows things up.

Anonymous 0 Comments

Look no further than the crater made by a meteorite. The rock that impacted is many times smaller than the diameter of the impact crater. But it was moving fast, on average rocks hit planets and moons and one another at around 18km/s. Some have been known to hit at even higher speeds, 30, 40, even maybe 50 km/s given the right conditions.

When you catch a ball, does it just lightly land in your hand, or can you feel it “smack” your hand as you catch it? It had velocity, and it has mass. When you caught the ball, it transfered that potential energy into your hand. What happens if I throw the ball faster? Bigger smack. What happens if I throw a heavier ball?

Let’s say I lob a tennis ball at you, you’ll be able to catch it with one or two hands, no sweat. If I throw a bowling ball along the same trajectory, you will need two hands, and you will probably need to take a step back as you catch it to stop it knocking you over – because you need to send that momentum somewhere.

The more mass something has, the harder it can hit – it takes more force to stop it. The faster something is going, the more energy was used to get it going that fast, the more energy it will take to stop it. So naturally something with more mass and more velocity will just hit harder.

Tungsten has a pretty high density – its fairly massive (heavy) and conversely pretty rigid. Get a 0.5m chunk of it moving, say with a rail gun in a vacuum at 100km/s, and there you have it, a kinetic weapon.

Anonymous 0 Comments

This is also a pretty major plot point in The Moon is a Harsh Mistress (Heinlein) if you’re interested in sci-fi.

Anonymous 0 Comments

Ok, I’ll explain like you’re five:

An object with mass and speed has energy (kinetic energy, to be specific). On impact, the moving object stops. All that energy doesn’t just evaporate, it has to go somewhere, so it’s transformed into “damage”. The greater the energy, the greater the damage.

As someone else pointed out, the energy grows the same as the mass grows (double the mass, double the energy). However, it also grows as the SQUARE of the velocity (double the speed, QUADRUPLE the energy).

Let’s say you have two objects: a lightweight, slow one and a heavy, fast one. The second object has DOUBLE THE MASS and DOUBLE THE SPEED of the first. Considering what I wrote above, the energy of the second object is DOUBLE^((because of mass)) x QUADRUPLE^((because of speed)) = EIGHT TIMES that of the first object – so the damage would be eightfold!

>Conversely, If I launched something at the speed of sound, would thedamage output be the same if it were different-sized objects?

Size doesn’t matter, only mass and speed. If two objects have the same speed, the ratio of their energies (and, therefore, “damage”) will be the ratio of their masses. Conversely, if two objects have the same mass but move at different speeds, the ratio of their energies will be the ratio of the SQUARES of their speeds.

Anonymous 0 Comments

Howdy! Others have pointed out the equations for this, but here’s the application.

Take and object (piano, bowling ball, grain of sand) and throw it. The energy it carries to hit something depends on the mass (lets say How Heavy and leave it at that) of the object and how fast it’s moving. But — Double the speed, quadruple the energy. Double it again and now it’s Sixteen times the energy. So that tiny grain of sand moving way way fast can do enormous damage when it hits something.

First Problem – After getting your piano up to speed on your Acme Co Catapult Mark II, it’s likely in the atmosphere, so it has to push air out of the way on it’s trip to that horrible bird. BTW, launching it at double or quadruple the speed to get more energy means more energy in to do it!. Meanwhile, Air. The faster it goes, the more drag (air friction) holding it back. The bowling ball has a better shape to let the air slip by, so less drag. Grain of sand? Much less friction, but because it weighs nearly nothing, any drag will get in the way in a hurry.

Second Problem – If you’re going fast enough, the friction from drag will heat up the air, and the thing (lets go with bowling ball) it’s touching. Supersonic aircraft have to deal with this. And the rules change some once you hit the Sound Barrier. Think of a tugboat in the water chugging off to do tugboat things. It’s usually pushing a big hump of water ahead of it as it goes. This is called a Bow Wave, and it’s the water equivalent of a air Shock Wave. You actually use shock waves all the time! It’s called Hearing. Drop the bowling ball, not on your foot, please, and it goes Thump on the ground. Or drum your fingers on the desk. Whatever.

The air pushed away (suddenly!) makes an itty bitty shock wave, and so do the vibrations from whatever got hit by the ball (or fingers). Your ears detect this and…. Hearing! This waves, with their small energy, wiggle the eardrum, then magic pixies do their stuff and you can suddenly speak Swahili. Or something. The point it a wave moved through the air and your heard it.

Once at or past the Speed of Sound, the bow/shock wave can’t move away from the front of the object — they touch — because the object is moving faster than the sound can get out of the way. So, lots of friction, lots of drag, and lots of heating. This is where them 1 2 4 8 16 etc (increasing powers of two) progression really, really gets in the way.

The piano is probably a lost cause at this point, but the bowling ball has the best chance to really get some speed (and therefore energy) behind it. The grain of sand could do as well if you remove the air, and BTW the piano would still be a player in that environment.

Now I can finally get around to your ELI5 about how much devastation can you pack into a nickel? A lot but limited in the atmosphere, and insane amounts in the vacuum of space. Throw a piano at the Space Station at Mach 25, and the Blue Danube will never be the same.

A side point is the damage caused by gunfire. Just about all modern pellet projectors have enough oomph to get that 1/4 to 1/2 (hey — I’m winging it here) ounce bullet up past Mach 1 (about 1000 Feet Per Second) into the 2000 Fps range. The shape and density of the bullet get around much of the drag issue with decent aerodynamics. And here the mass plays directly into the speed part of the equation. When it hits, you have not just punched a hole into something, that supersonic shock wave (bullets passing near you can be heard as a Snap, not so much a whizz) is now inside your body, stretching and tearing things. It’s not the .45 you’ve been shot with — that’s an itty bitty hole (painful, yes) that not even 1/2 inch across. It’s the orange to grapefruit sized shock following the bullet as it moved through, ah, umm …. you. Well, somebody deserving, anyway.

So you can’t toss a penny off the Empire State Building and crush skulls. Air drag stops that (called terminal velocity), but in a vacuum it would be dangerous, because all the pedestrians below would be dead. Don’t bother throwing pennies at them you sick freak!

And as for your opening thoughts, a very heavy and dense tungsten telephone pole screaming (in space, no one can hear you….) down from 200 miles above only has a few miles of air to puncture before it arrives in Central Park. The front end would be very hot, even partially melted maybe. When it hit the dirt at Mach 25, the shock wave would do a lot of urban renewal in the nearest mile or two circle, and you’ll have to get your frappuccino from some other coffee shop. The Tic Tok videos would be spectacular, though!

Hope that helps!