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I have made Image which is self explanatory. It has the question

enter image description here

Suppose I have a metal plate that is travelling at V m/s.
A stationary body acts as a shearing body. When the metal plate contacts the still body, it starts to shear off. The plane in which it will be sheared is shown in diagram (red line). So I want to ask how much force will get applied for the shearing.

This is just an idea that I'm working through. I haven't seen this in any book that I have read (I haven't yet seen various books yet). This problem came in my mind yesterday while I was dreaming.

Also I am assuming that the acceleration of the moving plate will be equal to change in velocity (after shearing the plate stops), so a = (0 - V) / 1 (unit time)

So question is

how much mass should be considered for the equation F = ma ?

basically I want to calculate force required.

If am wrong in some calculation then correct me.

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Fennekin
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  • Please type out your question. Don't include it all in a picture. Is this a homework problem? Are the options at the bottom your ideas or are they answers? – hazzey Feb 18 '16 at 16:29
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    The part "thus a=v" makes no sense; one is acceleration and the other is velocity, they are two different things. – Carlton Feb 18 '16 at 16:31
  • Yes I forget to mention that the plate's velocity becomes 0 after the shear. I was thinking that the acceleration would be = (finalV-initV) / time – Fennekin Feb 18 '16 at 17:45
  • thus acceleration = (0 - V) / s which is equal to -V m/s^2. – Fennekin Feb 18 '16 at 17:46
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    That still makes no sense. What units are you using in your acceleration? you're dividing the velocity by time, but what unit is that $1$ in? Are you saying the velocity will go from $V$ to $0$ in 1 second? 1 hour? 1 year? 1 "instant" (not a unit of time)? – Wasabi Feb 19 '16 at 00:55
  • I meant unit time. and also the answer required was symbolic rather than substituted numbers. – Fennekin Feb 19 '16 at 01:34
  • "unit time" is a meaningless term. If you're saying $a=(v-0)/1$, then you are dividing by a number. That number must have an associated, defined unit (seconds, minutes, hours, etc). – Wasabi Feb 19 '16 at 11:55
  • lets say that the shearing is done by hydraulic means and time taken is 20 minutes – Fennekin Feb 19 '16 at 12:59

1 Answers1

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It seems like what you're really after is the force, not the mass. Now, if you're assuming that the plate will shear off, then the easiest way of calculating the force isn't through Newton's laws, but by calculating the force necessary to shear off the plate.

Simplistically, that can be found by

$$ F = A\tau $$ where $A$ is the transversal cross-section of the plate along the shearing plane (assuming thin-walled theory applies here) and $\tau$ is the shear strength of the chosen material.

This doesn't consider dynamic effects (buckling, warping, possibility of the plate simply bouncing off instead of shearing), but that's impossible to do with the information presented.

Wasabi
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  • So this is the only way to calculate the force applied ? – Fennekin Feb 19 '16 at 01:31
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    It is the only way to calculate the force required to shear the object the way you've described. The answer says nothing about the dynamics of the situation, such as momentum and energy transfer, angular momentum, speed before and after, etc. However, neither does the question. – do-the-thing-please Feb 19 '16 at 04:21