1. Not finding help here? Sign up for a free 30min 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!

Confused about E = mv²/2

  1. May 5, 2017 #1
    1. The problem statement, all variables and given/known data
    Calculate the energy needed for 1 kg mass at the velocity of 2 m/s go up to the velocity of 6 m/s.

    2. Relevant equations
    Ek = mv2/2

    3. The attempt at a solution
    From the mass point of view, it is stationary and goes up to a velocity of delta (6-2) m/s = 4 m/s
    so the energy needed must be Ek = 1*42/2 J = 16/2 J = 8 Joules

    But the answer is 16 Joules.
    Ebefore = 1*22/2 = 4/2 Joule = 2 Joule
    Eafter = 1*62/2 = 36/2 Joule = 18 Joule
    Edelta= Eafter-Ebefore = (18-2) Joules = 16 Joules

    How can the answer not be 8 Joules? From the mass perspective, it is stationary and just goes up 4 m/s.
     
  2. jcsd
  3. May 5, 2017 #2

    BvU

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Hello penutbutr, :welcome:

    With your reasoning a succession of accelerations with only 1 m/s would be energetically cheaper still, so there must be something wrong. Can you fathom what ?
     
  4. May 5, 2017 #3
    So in order to get correct calculations. "v" in the formula mv2/2 can only be measured by someone in rest relative to the mass?
     
  5. May 5, 2017 #4
    How can it be harder to accelerate an extra 1 m/s, in high speed like 50 m/s ? than it would be in low speed like 2 m/s. That is what the latter method implies, right?
     
  6. May 5, 2017 #5

    BvU

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    The speed and the kinetic energy should be in the same frame of reference. In your first post
    the second part isn't correct: from the mass point of view it is stationary and stays stationary...
     
  7. May 5, 2017 #6
    Oh, That makes sense!
    So kinetic energy is always relative to something, the more speed an object has the more destruction it can cause at the object in rest. Meanwhile an object travelling close to the speed of the other object will perceive it as having less kinetic energy.
     
  8. May 5, 2017 #7

    BvU

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    If you are familiar with the SUVAT equations for uniform acceleration:

    If you push with a force of 1N on a mass of 1 kg for 2 seconds, it speed is 2 m/s ##\ \ ## (##at##), ##\ \ ## and you have pushed over 2 m ##\ \ ## (##{1\over 2}at^2##). ##\ \ ## The work is 2 J and the kinetic energy is 2 J as well.

    Now push with the same force for another 2 seconds. The speed increases to 4 m/s and you have pushed over ##\ \ 2*2 + {1\over 2}*1*2^2 = 6## m. ##\ \ ## The work is 6 J and the kinetic energy has increased by 6 J from 2 J to 8 J, which is equal to ##{1\over 2}mv^2##​
     
  9. May 5, 2017 #8

    CWatters

    User Avatar
    Science Advisor
    Homework Helper

    I wouldn't use SUVAT to solve the OP. Just stick with calculating the change in energy.
     
  10. May 5, 2017 #9

    BvU

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    I don't think solving is the subject. Thread starter did that. Understanding the reference frame for kinetic energy and speed is the issue.
     
  11. May 5, 2017 #10
    Did this method now, and got the answer 18 joule which verifies it :thumbup:
     
  12. May 5, 2017 #11

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    Yes. KE is not the same in different inertial frames. Consider a reference frame moving up at 4m/s. In this frame there is no change in KE.
    You mean 16J, right?
     
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: Confused about E = mv²/2
  1. Help with F=mv^2/r (Replies: 6)

  2. E=hf Confusion (Replies: 10)

Loading...