# 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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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.

(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.

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.

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)

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.