# shear force calculation with velocity and mass

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

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.

• 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
• 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
• 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 0:55

$$F = A\tau$$ 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.