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!

Why x^2 for PE?

  1. Jul 29, 2013 #1
    Hi all,

    I notice the patterns such as v = 0.5at^2 and PE(spring)=0.5kx^2, etc...but, all examples I have seen show the slope (acceleration, or the spring constant, k) as being a 45 degree angle. Thus, the area of the triangle underneath the graph makes good sense (x^2 or t^2).

    But, let's say we have an example where the spring constant is much larger or much smaller. Why is x^2 still valid as the base x height, if the two are not equal values?
     
  2. jcsd
  3. Jul 29, 2013 #2
    Maybe I'm just tired, but I'm really confused about your question. So that people don't start answering every question except what you meant, would you mind clarifying? (also, x, not v in your first one)
    What do you mean a or k is a 45 degree angle?
    I'm guessing that the answer you are looking for is going involve integration. What level of math are you comfortable with?
     
  4. Jul 29, 2013 #3
    Sorry for the confusion. I'm evidently tired too.

    I have it answered. All it took was writing PE = 0.5 k(x) times x. I couldn't intuitively see the x^2 mentally.
     
  5. Jul 29, 2013 #4

    berkeman

    User Avatar

    Staff: Mentor

    Those terms come from calculus derivations. Are you familiar yet with differential and integral calculus?
     
  6. Jul 29, 2013 #5

    PhanthomJay

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    that is s = 1/2at^2
    when you plot v vs.t, and the acceleration is constant, then you have a linear equation v = at, and the slope of the line is the acceleration. Thus, the area of the triangle underneath the graph is 1/2 at^2. Or since F=kx, the slope of the line is k. and the PE is 1/2kx^2. But the slope is not always 45 degress, it could be much higher , say 60 degrees , but the area under the curve (straight line) is still the same, the area of the triangle.
    Tey don't have to be equal. The area of the triangle is still 1/2kx^2 for the spring PE case, whether k is 1 (straight line graph for f = kx, k=1, 45 degree slope, or k is greater than 1 (higher slope and thus greater angle) or less than 1, (less steep slope , angle less than 45 degrees).
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Why x^2 for PE?
  1. Why r^2? (Replies: 16)

Loading...