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A gun fires a 5 g bullet at v = 400ms1.
Fired at a plate (mass of 500 g), such a bullet penetrates 5mm into it, but not through.
i) Determine the speed of the plate after collision.
ii) Will such plate protect you from the speeding bullet?
iii) What if the mass of the plate was a) lighter; b) heavier ?
 2 years ago
 2 years ago
twitter Group Title
A gun fires a 5 g bullet at v = 400ms1. Fired at a plate (mass of 500 g), such a bullet penetrates 5mm into it, but not through. i) Determine the speed of the plate after collision. ii) Will such plate protect you from the speeding bullet? iii) What if the mass of the plate was a) lighter; b) heavier ?
 2 years ago
 2 years ago

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twitter Group TitleBest ResponseYou've already chosen the best response.0
Attempted Solution: i) Assumptions: Momentum is conserved \(m_1u_1 + m_2 u_2 = (m_1 +m_2) v\) Where: \(u_1\)=the initial speed of the bullet; \(v\) = speed of plate with the bullet inside \[v=\frac{m_1 u_1}{m_1 +m_2}=4ms^{1}\] So I will get hit by a 0.5 kg travelling at 4 ms^1 Part need help: ii) Will I be alright if I hit by such thing? Firstly I need to know the force of the plate exerted on me so I can get an idea on how equivalently heavy it would be. \[F=ma\] But I don't know how to find the acceleration of the block.
 2 years ago

imron07 Group TitleBest ResponseYou've already chosen the best response.0
To my knowledge, there's no way to find the force the plate exert on your body. Unless you know the contact time. If you do, we can find average force with: \[I=\int F dt\\ \Delta p=F\Delta t\] where F is average force and \(\Delta t\) is contact time of plate with your body. If you want to get an idea about the effect of moving plate with your body, I think you can find it's kinetic energy.
 2 years ago

rosemuricken Group TitleBest ResponseYou've already chosen the best response.1
1.v=m1u1/(m1+m2)=3.96m/s 2.will protect as it penetrated only 5 mm,not ''pierced'' 3. a.lighterwill not protect as bullet may pierce through more , 3.b.heaviermore possibility to protect,even 5mm may not go in
 2 years ago

twitter Group TitleBest ResponseYou've already chosen the best response.0
@imron07 well, if I assume the bullet decelerates constantly during collision, I could find the \(t \) of collision between the bullet and the plate. Is this \(t\) also the same duration when the plate collide with me?
 2 years ago

imron07 Group TitleBest ResponseYou've already chosen the best response.0
@twitter : The time is different, since the plate still can move even the bullet inside already stopped (relative to plate). I think @rosemuricken has good answer to this problem..
 2 years ago

twitter Group TitleBest ResponseYou've already chosen the best response.0
I don't like it. Unscientific. He said it will protect just because the bullet doesn't come through. Wrong. If the force generated big enough, you can have broken ribs. Talking about force, is the force generated by the bullet equal the force generated to me by the plate?
 2 years ago

imron07 Group TitleBest ResponseYou've already chosen the best response.0
You can think of it this way: If you push Earth with force F, would Earth push another person at it's other side with the same force?
 2 years ago

twitter Group TitleBest ResponseYou've already chosen the best response.0
Good point. Now about conservation of momentum. Do you think the mometum here is approximately conserved? Why? Is there a way of telling when assumption of momentum conservation is unreasonable?
 2 years ago

imron07 Group TitleBest ResponseYou've already chosen the best response.0
Yes, it IS conserved. The momentum is always conserved if there's no net external forces on the system.\[\Sigma F_{ext}=0\\ \frac{dp}{dt}=0\\p=constant \]
 2 years ago

twitter Group TitleBest ResponseYou've already chosen the best response.0
During the collision, the plate move about 0.1mm. If it move lesser or further than that is the momentum still conserved?
 2 years ago

twitter Group TitleBest ResponseYou've already chosen the best response.0
Is there any relation between the two?
 2 years ago

twitter Group TitleBest ResponseYou've already chosen the best response.0
Certainly I am the external force?
 2 years ago

imron07 Group TitleBest ResponseYou've already chosen the best response.0
I think you must specify the system first. If the system is bullet and plate only, and these two aren't in touch with another object. The momenntum is conserved. If it is in touch with your body, then an external normal force act on the bulletplate system. Momentum is NOT conserved.
 2 years ago

twitter Group TitleBest ResponseYou've already chosen the best response.0
It moves 0.1mm. Please address that
 2 years ago

imron07 Group TitleBest ResponseYou've already chosen the best response.0
It moves 0.1 mm, it means an external force made it stop. Momentum is not conserved.
 2 years ago

imron07 Group TitleBest ResponseYou've already chosen the best response.0
And yes, you're the external force. :)
 2 years ago

twitter Group TitleBest ResponseYou've already chosen the best response.0
I was asking is it approximately conserved.
 2 years ago

twitter Group TitleBest ResponseYou've already chosen the best response.0
Most real life problem have not PRECISE momentum conservation. As a physicist is it our job to think whether we can neglect this or that variable. Nothing is exact.
 2 years ago

imron07 Group TitleBest ResponseYou've already chosen the best response.0
Not even approximatey. It will be conserved if you include you and earth in the system.
 2 years ago

twitter Group TitleBest ResponseYou've already chosen the best response.0
So how much can it more so you can consider it would be acceptable to use that assumption?
 2 years ago

imron07 Group TitleBest ResponseYou've already chosen the best response.0
I don't know the answer to that question. But if you collide two billiard ball, say, the linear momentum is approximately conserved. Even if external forces act on the twoball system: table friction, air friction.
 2 years ago

twitter Group TitleBest ResponseYou've already chosen the best response.0
Now you're just taking a piss mate. If there is a collision no matter what, the time during collision is not zero. Maybe t will be of magnitude 10^6 but it is not zero. Hence the thing must have been moving during this time.
 2 years ago
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