1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

  1. Sep 5, 2015 #1
    • Poster has been reminded to fill out the Template and show their Attempt at the Solution
    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:
     
    Last edited by a moderator: Oct 23, 2017
  2. jcsd
  3. Sep 5, 2015 #2
    Where is your attempt of the question?
     
  4. Sep 5, 2015 #3
    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?
     
  5. Sep 5, 2015 #4
    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.
     
  6. Sep 5, 2015 #5
    here is the complete attempt, you may verify it
    20150905_142358.jpg
     
  7. Sep 5, 2015 #6
  8. Sep 5, 2015 #7

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    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/.
     
  9. Sep 6, 2015 #8
    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 wont get the force also. Am i right?
    Thanks for the correction regarding average force. But please answer my above question.
     
  10. Sep 6, 2015 #9

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    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.
     
  11. Sep 7, 2015 #10
    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.
     
  12. Sep 7, 2015 #11

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    Yes.
     
  13. Oct 22, 2017 #12
    am new here so can you elaborate on your calculations
     
  14. Oct 23, 2017 #13

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    Please post your own attempt in a new thread.
     
  15. Oct 23, 2017 #14
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Newton's laws of motion problem -- Knife penetrating cardboard
Loading...