Saturday, December 7, 2013

Home Alone Paint Cans

I saw a commercial for the classic holiday movie "Home Alone" and wondered about the physics that I saw.  The scene I'm referring to is the one where Macaulay Culkin throws paint cans tied to a rope off of the banister that swing and hit burglars in the head.

I was interested in the force with which the paint cans hit the robbers.

  • I estimated the length of the rope and the mass of the paint can
  • L=3m
  • mass of paint can=4.5kg
  • I found this equation online for the velocity of a pendulum at the bottom of it's swing (aka the point of contact with the robbers' heads)
  • v = √{2gL[1-cos(a)]}
  • I assumed that the rope didn't get taught until ~45degrees
  • v=(2)(9.8m/s^2)(3m)[1-cos(45)]=5.3m/s
  • a(radial)=v^2/r
  • a(radial)=5.3^2/3m=9.3m/s^2
  • F=ma
  • F=(4.5kg)(9.3m/s^2)=42N

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