[thebrain13 (OP)]

I'm not sure I get why this makes sense. Okay, it takes 4 times as much energy to accelerate an object twice as much cause it is a squared function e=(1/2)mv^2 however when objects collide, objects moving twice as fast don't affect the other objects 4 times as much so what gives?

for example if you accelerated a 4 pound bowling ball to 2mph and then threw a 16 pound bowling ball at 1mph the opposite direction the sixteen pound bowling ball would over power the 4 pound because it has more momentum p=mv and momentum is conserved, but the amount of energy it took accelerating the two would be the same, so why doesn't this violate conservation of energy?

[Pmb]

I'm not sure I get why this makes sense. Okay, it takes 4 times as much energy to accelerate an object twice as much cause it is a squared function e=(1/2)mv^2 however when objects collide, objects moving twice as fast don't affect the other objects 4 times as much so what gives?

What do you mean by “effect”? If you mean “causes damage” then you’re wrong.  The amount of damage caused to one body by another is determined by the other body’s kinetic energy, not its momentum. It’s change in motion is determined by its momentum.

Does that help?

[syhprum]

Colliding moving bodies seem to need a lot of complex mathematics to work out their resulting energy and momentum especialy when energy is dissipated in the collision, the trivial case where two elastic bodies collide head on in a straight line is fairly easy to calculate but when they collide at an angle and are not perfectly elastic vectors must be used and calculations become difficult.
A recent case in point was the elastic collision of the Earth and a rogue asteroid where the massive Earth was little affected but the asteroid suffered a considerable change in velocity.
(I refer to a gravitational interaction as an elastic collision as there is little or no dissipation of energy).   

[lightarrow]

I'm not sure I get why this makes sense. Okay, it takes 4 times as much energy to accelerate an object twice as much cause it is a squared function e=(1/2)mv^2 however when objects collide, objects moving twice as fast don't affect the other objects 4 times as much so what gives?

for example if you accelerated a 4 pound bowling ball to 2mph and then threw a 16 pound bowling ball at 1mph the opposite direction the sixteen pound bowling ball would over power the 4 pound because it has more momentum p=mv and momentum is conserved, but the amount of energy it took accelerating the two would be the same, so why doesn't this violate conservation of energy?

i tried to understand what you intended, but I'm not sure.
However, the fact the bigger ball over powers the smaller depends, indeed, on the momentum, not on the energy so the fact they have the same kinetic energy is irrelevant, for that effect (it's an effect which depends on momentum and not on energy).

[lightarrow]

What do you mean by “effect”? If you mean “causes damage” then you’re wrong.  The amount of damage caused to one body by another is determined by the other body’s kinetic energy, not its momentum. It’s change in motion is determined by its momentum.

Infact the key concept here is which is the effect considered.
About causing damage, it depends on the kind of damage. For example, if you shoot a bullet of kinetic energy E_k against someone, you could make him more damage than heating his body sending him 10E_k joules of thermal energy through IR radiation []