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Work from normal force on a pendulum in non homogeneous field

  • 29-12-2013 3:39pm
    #1
    neufneufneuf
    Registered Users, Registered Users 2 Posts: 321 ✭✭


    I would like to study the work from the force from wall. For this, I study a simple 2d shape: a circle attract by a point mass M. Mass M is fixed. First image show the diagram and second image show the code (python language). I don't find 0 for the sum but it could. I don't compute all the movement of the circle, only a delta angle (very small angle). I compute all position of point to study in red circle, the length (distance) between this point and mass M. And the force.

    For compute the sum (I'm not sure the method is good), I look for angle and I multiply by the mean force. I try to sum only cos but it's the same I don't have 0.

    Second image showing a circle attract by a fixed mass. The normal force N from wall must not be like that for the red point. The red point would have the force like Nr not N I think. In a uniform field it's ok, back forces compensate front forces, but here I don't know where all these works from N can be compensated.

    Maybe a problem with atan ? or I need to take in account the angle between force and N force.
    # -*- coding: utf-8 -*-


from math import *

R = 10.0 
d = 1.0
r = 2.0
ys = 0.3 ## y at start
dys = 0.00000001 ## delta angle to move
k = 1.0 ## the force of attraction, can be mMG
nb = 900000 ## number if steps
PI = 3.1415927 
xc = [] ## all positions x of point to study around the circle
yc = [] ## all positions y of point to study around the circle
xc2 = [] ## idem but after moved
yc2 = []
f = [] ## all forces at start
f2 = [] ## all forces after moved


####################################################### 

x = 0.0
for i in range(0,nb):
    x = x + 2.0 * PI / nb
    xc.append((R-r)*sin(ys) - cos(x))
    yc.append(d + R - (R-r)*cos(ys) + sin(x))
    lg = sqrt( yc[i]*yc[i] + xc[i]*xc[i] )
    f.append(k / lg)
 
####################################################### 
 
ys = ys - dys
x = 0.0
for i in range(0,nb):
    x = x + 2.0 * PI / nb
    xc2.append((R-r)*sin(ys) - cos(x))
    yc2.append(d + R - (R-r)*cos(ys) + sin(x))
    lg = sqrt( pow(yc[i],2.0) + pow(xc[i],2.0) )
    f2.append(k / lg)
  
####################################################### 
  
sum = 0.0
for i in range(0,nb):
    if yc2[i]-yc[i] != 0 :
        angle = PI - ys - atan( (xc2[i]-xc[i]) / (yc2[i]-yc[i]) )
    else:
        angle = PI/2.0

    ##sum = sum + (f[i]+f2[i])/2.0 * cos(angle) ## sum of works from N
    sum = sum + cos(angle) ## sum of works from N
 

print(sum)


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