Work and Energy Legacy Problem #23 Guided Solution
Problem*
According to ABC's Wide World of Sports show, there is the thrill of victory and the agony of defeat. On March 21 of 1970, Vinko Bogataj was the Yugoslavian entrant into the World Championships held in former West Germany. By his third and final jump of the day, heavy and persistent snow produced dangerous conditions along the slope. Midway through the run, Bogataj recognized the danger and attempted to make adjustments in order to terminate his jump. Instead, he lost his balanced and tumbled and flipped off the slope into the dense crowd. For nearly 30 years thereafter, footage of the event was included in the introduction of ABC's infamous sports show and Vinco has become known as the agony of defeat icon.
- Determine the speed of 72-kg Vinco after skiing down the hill to a height which is 49 m below the starting location.
- After descending the 49 m, Vinko tumbled off the track and descended another 15 m down the ski hill before finally stopping. Determine the change in potential energy of Vinko from the top of the hill to the point at which he stops.
- Determine the amount of cumulative work done upon Vinko's body as he crashes to a halt.
Audio Guided Solution
A classic sports show from the 1970s and 1980s was called ABC's Wide World of Sports. In the trailer to the show, it showed a skier skiing down a hill, losing his balance and sliding off the hill, tumbling through a crowd to a final stop. The Wide World of Sports show featured events and athletics that involved the thrill of victory and the agony of defeat. And this particular scene of the skier became the icon for the agony and defeat. The name of the skier is Vinko Bogotaj, and in this problem, we're asked to determine a number of things about the motion of Vinko as he goes down the hill and ultimately loses his balance and tumbles to a stop. Vinko's mass is 72 kilograms, and in the first question, we're asked to determine the speed of Vinko after he has descended 49 meters below the initial starting location. That 49 meters is a change in height, and so we would presume of Vinko that he has changed his original potential energy from some original value to some final value. We can calculate the potential energy change of Vinko, and say all of this potential energy changes into kinetic energy. Doing so demands that we use the equation that the change in potential energy is equal to mg, the change times the change in height. The m is 72 kilograms, the g is 9.8 newtons per kilogram, and the change in height is 49 meters. Plugging this information into our equation and calculating the change in potential energy gives us 34,574.4 joules. Now all of this potential energy changes to kinetic, so the kinetic energy achieved by Vinko when he gets to this point would be 34,574.4 joules, and that would be equal to one half mv squared, where the m is 72. Plugging this number into the equation gives us a V value of 30.9903 meters per second. We can round that to the two significant figures. It's after 49 meters of descent that Vinko loses his balance and begins to spin out of control. He slides another 15 meters vertically down the hill, giving him a total change in height of 64 meters. This would mean that his potential energy change from the top of the hill to the point where he finally stops is found by mg delta h, where the delta h now is 64 meters. This is a total potential energy change of 45,158 joules. Now all of this potential energy change would have resulted in a change of kinetic energy of an equal amount, were he not to tumble and spin out of control. But instead, he does tumble, he spins out of control, and work is done on his body in order to change his energy to zero joules. So the amount of work done has got to equal this change in energy. So the amount of work done is negative 45,158 joules of work. We can again round this to two significant digits.
Solution
- 31 m/s
- -4.5 x 104 J
- -4.5 x 104 J
Habbits of an Effective Problem Solver
- Read the problem carefully and develop a mental picture of the physical situation. If necessary, sketch a simple diagram of the physical situation to help you visualize it.
- Identify the known and unknown quantities in an organized manner. Equate given values to the symbols used to represent the corresponding quantity - e.g., \(\descriptive{v}{v,velocity}_\descriptive{o}{o,original} = 0 \unit{\meter\per\second}\); \(\descriptive{a}{a,acceleration} = 4.2\unit{\meter\per\square\second}\); \(\descriptive{v}{v,velocity}_\descriptive{f}{f,final} = 22.9 \unit{\meter\per\second}\); \(\descriptive{d}{d,distance} = \colorbox{gray}{Unknown}\).
- Use physics formulas and conceptual reasoning to plot a strategy for solving for the unknown quantity.
- Identify the appropriate formula(s) to use.
- Perform substitutions and algebraic manipulations in order to solve for the unknown quantity.
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