i tried to find it in books but i was unable to do so and i am not able to understand this and I couldn't think of a better example. i repeat. its just an example. if i punch someone's face with my arm having constant velocity, it will mean that the acceleration of my arm is zero. F=ma, therefore force exerted by my arm is zero. Now if the force applied is zero the why does the person whom i punched experiences pain. please help. thanks.
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3 Answers
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This is an example in which one needs to be careful to make the distinction between net force, which may vanish, and one of the individual, nonzero interaction forces that contributed to the net force
The fact that your knuckles are not accelerating does not mean that the contact force with the person's face is zero, it means that the net force on your knuckles is zero. The contact force with the person's face will balance the force exerted by your arm on the knuckles so that the acceleration of your knuckles is zero, but your knuckles and (by Newton's Third Law) the person's face will still feel the contact force itself.
Note. To maintain your knuckles at zero acceleration during the punch, your arm would have to provide extra force (relative to free knuckles) to balance the forces experienced by your knuckles.
answered Feb 4, 2014 at 18:47
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For simplicity's sake, let's start with punching a concrete wall. Let's assume you are not strong enough to actually damage the wall. So (again for simplicities sake) if your fist is traveling at 1 m/s, when it hits the wall it will be moving zero, so it DECELERATES as part of the process of colliding with the wall, and the force of that deceleration will be applied to your hands (possibly breaking your knuckles). The mass of the wall is not relevant; this is why your hand would take the same damage from a smooth rock as it would from punching a large lead weight, it's just about the deceleration of your hand.
If you start slowing down your hand slightly before you punch the wall, your hand will have to do less deceleration when it collides, that's why your knuckle bones would be less broken. The same would be true if you were moving slower to begin with.
Now let's say you're trying to punch Neo from the Matrix. He sees you coming and dodges backwards, and coincidentally he happens to quickly accelerates enough (which takes energy from his muscles) so that he is moving his face backwards at the same speed that your fist is moving. Your fist will never actually hit him, so there will be no force applied to your hand.
Now let's say you're trying to punch the guy that stole your girlfriend. The same deceleration will occur. Some of the force from the deceleration of your fist at collision will go into breaking his jaw. Some of the force from the deceleration will go into moving his head back (if his head moves, your fist and his face receive less damage, because the force of your punch went into moving his head backwards). And some of the deceleration force will still go into hurting your hand.
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Its not about your hand moving in a uniform velocity , the person's face was at rest before you punching him and when you did punch him , there was a change in velocity (it moves) , in other words these is acceleration . Hence force is acted upon.
In classical mechanics, the kinetic energy of a point object (an object so small that its mass can be assumed to exist at one point), or a non-rotating rigid body depends on the mass of the body as well as its speed. The kinetic energy is equal to the mass multiplied by the square of the speed, multiplied by the constant 1/2. In formula form: E=.5mv^2Since energy is conserved, it has to go somewhere. $\endgroup$