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!

Homework Help: Newton's 2nd Law Problem

  1. Sep 16, 2016 #1
    1. The problem statement, all variables and given/known data
    A 0.25 kg particle moves in an xy plane according to x(t) = -15 + 2t - 4t3 and y(t) = 25 + 7t - 9t2, with x and y in meters and t in seconds. Find formulas at time t<35 sec for the (a) the magnitude and (b) the angle (relative to the positive direction of the x axis) of the net force on the particle (in radians), as well as (c) the angle of the particle's direction of travel (in radians)

    2. Relevant equations
    Pythagorean thereom

    3. The attempt at a solution
    With the x(t) and y(t) being the decoupled position vector, I thought I would use Pythagorean Thereom to come up with the vector r
    approximating the square roots for the coeffecients:
    I have a strong suspicion that I went about this in a very wrong way
  2. jcsd
  3. Sep 16, 2016 #2
    As Force=mass*acceleration and the acceleration in each direction is the second derivative of the decoupled position function the acceleration functions would be ax(t)=-24t ay(t)=-18
  4. Sep 16, 2016 #3
    Making the force function=((576t^2+324)^.5)/4 ???
  5. Sep 16, 2016 #4


    User Avatar
    Homework Helper

  6. Sep 16, 2016 #5
    Okay so the angle of the force would then be .25 arctan(-18/-24t) ??
  7. Sep 16, 2016 #6
    or .25 arctan(3/4t) simplified and the angle of the velocity being arctan(-18t/.12t^2)=arctan(3/2t)
  8. Sep 16, 2016 #7
    Those last two were incorrect.
  9. Sep 16, 2016 #8


    User Avatar

    Staff: Mentor

    Pay attention to the quadrant that the acceleration vector lies in. The arctan function can be a trap when the signs of the x and y components are not both positive. You need to sort out the correct quadrant yourself and adjust the result accordingly.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted