Final Blog

Home Alone or Murder Alone? (PGP-13)

   This film is about a young child using his creative mind to fend off obstinate burglars from ruining his holiday. This movie depicts Kevin McCallister constructing wild Rube Goldberg traps from everyday household items. The iconic 1990 film highlights overcoming adversity with comical perseverance and has brought joy to all ages in the winter seasons. Despite that some scenes were exaggerated to deride the physical torment endured by the home burglars, this scene stood out to me as the most realistic yet flawed.


Q: How much force is exerted by the paint bucket to Harry & Marv's face?

Physics concept: Conservation of Energy, Impulse, 2D Kinematics, Pendulum (Period Formula)

In this scene, we can see that potential energy (stored energy) exists when holding the paint bucket over his head. The instant Kevin threw the paint bucket the energy is then transferred to kinetic energy (motion energy). Assuming that the bucket has enough mass to knock over 2 adults, it then accumulates velocity thus increasing its net force.

We can calculate v by...            CONSERVATION OF MECHANICAL ENERGY

  • MEf = MEi                                  PEf + KEf = PEi + KEi                 PEf = 0            KEi = 0
  • 1/2mv(f)^2 = mgh                       v(f) = √2gh                                     v(f) = √(2(9.8m/s^2)(4m))
  • m= 5.44 kg                                  g= 9.8 m/s^2                                   h= 4 meters
  • v(f)= -8.9 m/s                              m= 5.44 kg

Period Formula: T = 2π * √(L/g)

Since the trap was built to swing the paint buckets towards the intruders like a pendulum, we can apply the period formula of a pendulum as a supplement to our research. By using the period formula we can gather the height or the maximum length of rope utilized by the device.
Pendulum Period (T)= (4.014 sec/2)= 2.007 sec
Length (L)/Height (h)= 4 m
Acceleration due to gravity (g)= 9.8m/s^2

Using this f(v) above as the initial velocity of the paint bucket, we can calculate the impulse (the change in an object's momentum over time) and can extract the net force that was emitted to both burglars' faces. 

*Impulse is derived from Newton's 2nd Law (F=ma). Sir Isaac Newton promotes that when a net external force acts on an object, the object experiences an acceleration in the direction of the resultant force with a magnitude proportional to the force and inversely proportional to its mass.*

Impulse

  • \Delta p = F\Delta t or
  •                                  F = mVf - mVi/🛆t                        F = (-5.44kg)(-8.9 m/s)/2s
  • F= 24.2 Newtons
  • m= 5.44 kg
  • Vi= -8.9 m/s
  • Vf= 0 m/s
  • 🛆t= 2 sec (estimate)
**Final Velocity is 0 m/s since the paint bucket came to a rest after impact**

Image result for home alone

In Conclusion...

Kevin indeed was having the time of his life torturing the antagonists of his film, maybe too much fun. Although his traps were not intended for killing, data provides that almost any one of Kevin's booby traps can incapacitate or finish his enemies for good. Unlike cartoon characters, the human skull was not made to engage with high amounts of force. 24.2 newtons of force or 5.44 lbs was shifted to Harry and Marv's skull. This can be compared to having 17 baseballs to the face. In reality, it takes 2,300 Newtons to crush a human skull. This is also enough to give a mild concussion or serious brain damage after a heavy impact with both the paint bucket and floor. Another incongruity that contravene the laws of physics is the immediate reaction of the transference of kinetic energy. Many Hollywood movies, including Home Alone, portray bad guys flying backwards after getting hit with a high velocity object. Newton's 3rd law states that whenever one object exerts a force on a second object the second object exerts an equal but opposite force on the first; or equal in magnitude, opposite in direction. We can clearly see that the paint bucket did not fly backwards at the same magnitude as both Harry and Marv.


Happy Holidays!!


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