Given that force equates to mass times acceleration, so how come massive objects travelling at a constant velocity (acceleration = zero) can cause damage when they hit something? After all, if I'm knocked over by a car doing a constant 70mph, I'm going to end up a mess, aren't I? I'm going to experience force! I'm a bit rusty on all this stuff. Can some clever-arse bastard disabuse me of my ignorance? Cheers.
The problem is that the car when it hits you accelerates (bits of) YOU.
Conservation of momentum (momentum = mass x velocity). Momentum before collision = momentum after, measuring yours and the object's together. So some gets transferred to you, meaning you end up with some velocity, and the object with less. Further, for the object to therefore have less velocity after, and you to have some, a force must be applied to each object. You supply the force to change the velocity of the object, and vice versa. Good luck if the object is a car, or planet.
It's that force which does the damage - oh, and any acceleration of the object at the moment of impact is not relevant. It's the velocity that counts. If you fall off a chair, the damage the Earth does to you and vice versa is minimal. Not so if you fall out of a plane, but (in principle and ignoring air resistance), your acceleration at the moment of impact is the same in both cases.
Also why a bullet does so much damage. Small mass but very large velocity.
Because when it hits you it decelerates (change in velocity) and that hurts.
Another Dave
If the car stops exactly as it hits you then nothing will happen to you. The force is what accelerates you to ~70mph when it does hit you.
Its conservation of momentum that you should read next.
Because:
1) The large object in it's constant speed state and you in your at-rest (standing around whistling) state both experience zero force (excepting gravity which is not relevant here)2) When the lump hits you at 70mpg either it stops or you go or something in between.
You going from 0-70mph (more or less) is going to require a force depending on how quickly you get to 70mph.
Lets assume you can be "squished" by 1cm before you hit bone - so between the object touching you and the object moving 1cm forward, you need to accelerate 0-70mph.
That's a lot of force!
In the most pathological case, if you are 30cm "thick" and we go for full splattage, your mass needs to accelerate 0-70mph as the original large object moves through 30cm. At 0cm it starts imparting force. At
30cm it has by definition contacted all of your material mass so that is now moving at nearly 70mph.In the real world, it would hit your legs, break them, you'd buckle and fold around the front of the object and things get more complicated. But it's still Bad (TM) :)
Does that help?
And the heads of small masonry nails (those in cable clips) if they break off when bashed with a big hammer. They will enter your eye and go through to your brain. Always wear eye protection.
Bill
Then the bit that REALLY hurts is when you hit the wall/tree/whatever and decelerate from 70mph to zero.
Newton?
Still missing something.
OK, but force = mass x acceleration; f=ma
So according to the equation, it doesn't matter what the mass of the object is, if it's traveling at constant velocity, then it's not accelerating, so that factor is zero and anything times zero (force in this case) is zero. Doesn't make sense.
It's not travelling at constant velocity WHEN it hits you. It's decelerating and you are accelerating (fast) - so lots of force.
if it doesn't hit anything it is travelling at constant velocity.
The moment it does, then that equation has non zero acceleration.
exactly. Speef doesn't kill. Acceleration does.
You are.
You have an object - you - at zero velocity and known mass. You have an object coming towards you, with velocity and mass.
What happens when those two objects meet? Energy is transferred from the moving object to the static object. Some of the energy is absorbed by the two objects deforming. Some of the energy causes the static object to accelerate. Those energies are determined by the relative masses, and by the deformability.
If you stand there and are hit with a 1kg pillow at 20m/s, the pillow deforms, and absorbs much of the energy, so little is transferred. It doesn't hurt.
If you stand there and are hit with a 1kg brick at 20m/s, the brick doesn't deform, and more energy is transferred. It hurts.
If you stand there and are hit with a 1000kg pallet of bricks at 20m/s, the bricks don't deform, a fuckload of energy is transferred. It _REALLY_ hurts. But not for long.
I've never quite 'got' conservation of momentum, either. Is that the one that says for every action there's an equal and opposite reaction? If so I have a problem with that too. Imagine a 9mm pistol mounted on model train being fired. The energy of the bullet leaving the gun's muzzle seems to me to be vastly greater than the resulting recoil which makes the model jump backwards on the tracks. :-/
Ah! Right. Got it now. Cheers.
That's because the engergies are NOT the same. The momentum is :)
OK - with semi realistic figures:
Train mass = 0.1kg Bullet mass = 0.01kg (it's a small bullet).
Bullet speed = 100m/s on exit
So the bullet's momentum is:
100x0.01 = 1 kg.m/sSo the train's momentum must be -1 kg.m/s (- means backwards) and thus it's speed is -1 / 0.1 = 10m/s
----
Bullet's kinetic energy = 1/2 m.v2 = 1/2 x 0.01 x 100x100 = 50 J (joules)
Train's kinetic energy = 1/2 x 0.1 x 10x10 = 5 J
So the bullet ends up with 10 times as much energy :)
Don't be put off :) I did my degree in physics and concepts like these often had WTF? moments trying to get my head around them!
In message , ARW writes
Consider.... a tennis ball bouncing off the front of a moving train. Did the train stop momentarily:-)
The classical speeder excuse!
Its actually energy that kills.
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