Given that Johnny’s mass and the pitch of the roof are known, all that is left to discover is the coefficient of kinetic friction. This simple experiment involves dragging one material across another, and measuring the minimum amount of force required to do this at a constant velocity. The materials we used were rubber, the same sort found in Johnny’s shoes, and a wet asphalt shingle, of the same variety found on Johnny’s roof. Our experiment gave us a value of 0.3 for the coefficient of kinetic friction between rubber and wet asphalt, one which was consistent with researched results.
Calculations
These calculations require vector analysis, all of which is based upon the diagram below.
Provided that the Johnny’s body does not bounce, and that wind resistance is assumed to be negligible, the force of impact will be calculated by first evaluating his potential energy while on the patio:
mg = (56.8)(9.8)
mg = 556.64 N
mg cos θ= N= 556.65(cos 30)
mg cos θ= N= 482.10 N
mg sin θ= 556.64(sin 30)
mg sin θ= 278.32 N
F = µk(N)
F =(0.3)(482.10)
F= 141.62 N
The calculations show that the friction force, F, was less than the force with which Johnny would have slid off the roof, meaning that it is very likely in his inebriated state Johnny fell by himself, without any foul play.
Conclusion
If the net force on the body is greater than zero, then the body will slide down the inclined plane with acceleration (g sin θ − fk/m), where fk is the force. Calculations performed to determine the force of impact on the body utilise an initial velocity of 0 Newtons, arrived at through this calculation.
References
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"Coefficient of Friction Reference Table - Engineer's Handbook." Mechanical Engineering Design Guide - Engineer's Handbook . Web. 20 Nov. 2011. <http://www.engineershandbook.com/Tables/frictioncoefficients.htm>.
