Newton's laws of motion problem -- Knife penetrating cardboard

[Shivansh Mathur]

An open knife edge of mass 200 g is dropped from height 5 m on a cardboard. If the knife edge penetrates distance 2 m into the cardboard, the average resistance offered by the cardboard to the knife edge is:

 

[Hamza Abbasi]

Where is your attempt of the question?

 

[Shivansh Mathur]

For finding the initial speed
V(2)-u(2) = 2xgxh (g=10m/s(2)
V(2)= 2x10x5
V= 10m/s
So,speed of knife before it hits the cardboard is 10m/s. Now?

 

[Shivansh Mathur]

I know we just have to find the negative acceleration by the cardboard. If there was a mention about how much time it takes for the knife to stop, I would have done it.

 

[Shivansh Mathur]

here is the complete attempt, you may verify it

 

[Shivansh Mathur]

oops!

 

[haruspex]

Please do not post images of handwritten algebra. Images are fine for diagrams and textbook extracts, but take the trouble to type in your working.

Your calculation overlooks the fact that the blade continues to descend after hitting the top of the cardboard. Gravity doesn't suddenly switch off at that time. Also, it is unnecessary to find the impact velocity. There's no point in translating energy into velocity then back to energy again.

However, my main complaint is with the question itself. The method you use, dividing energy by distance, is clearly the one intended (since it is the only information you have) but it is not generally valid. It is OK if the force is constant during the deceleration, but it won't be. Average force is momentum divided by time, $\frac{\Delta mv}{\Delta t}$, which need not be equal to $\frac{\Delta E}{\Delta s}$.
See section 3 of https://www.physicsforums.com/insights/frequently-made-errors-mechanics-forces/.

 

[Shivansh Mathur]

i'm sorry, wasn't aware about the handwritten part.

However, you are suggesting that it is unnecessary to find the impact velocity. But if i don't do so, how am i going to find the negative acceleration produced on the knife because of the cardboard? And if i don't get the acceleration, i won't get the force also. Am i right?
Thanks for the correction regarding average force. But please answer my above question.

 

[haruspex]

However, you are suggesting that it is unnecessary to find the impact velocity. But if i don't do so, how am i going to find the negative acceleration produced on the knife because of the cardboard?
.

after finding the velocity, you used the SUVAT equation $v^2-u^2=2as$. If we multiply that equation through by m/2 we get $\frac 12 mv^2-\frac 12 mu^2=mas=Fs$. Clearly this is an energy equation, $\Delta KE =$ work done in accelerating the mass. Before that you used $\Delta KE=-\Delta PE$. By eliding the KE bit, we can go straight from PE to work done against the force.
However, there is one point I made to which you did not respond. The blade continues to lose PE after it strikes the cardboard.

 

[Shivansh Mathur]

Yes now I've understood what you were trying to say. So the only problem was that I didn't take gravity into account after hitting the cardboard. 'So gravity does not switch off :)'

Well, modifying the calculation gives me a different answer i.e 7N . Now I'm confident about it.
Thanks.

 

[haruspex]

Yes now I've understood what you were trying to say. So the only problem was that I didn't take gravity into account after hitting the cardboard. 'So gravity does not switch off :)'

Well, modifying the calculation gives me a different answer i.e 7N . Now I'm confident about it.
Thanks.

Yes.

 

[bell Cranel]

am new here so can you elaborate on your calculations

 

[haruspex]

am new here so can you elaborate on your calculations

Please post your own attempt in a new thread.

 

[bell Cranel]

Ok