Work and Energy Legacy Problem #8 Guided Solution
Problem*
The Taipei 101 in Taiwan is a 1667-foot tall, 101-story skyscraper. The skyscraper is the home of the world’s fastest elevator. The elevators transport visitors from the ground floor to the Observation Deck on the 89th floor at speeds up to 16.8 m/s. Determine the power delivered by the motor to lift the 10 passengers at this speed. The combined mass of the passengers and cabin is 1250 kg.
Audio Guided Solution
A good problem solver will read a problem carefully and identify the known and the unknown information and will take the time to plot out a strategy as to how to get from the known information to the unknown information. Here we have a story of the world's fastest elevator, at least at this moment, and we're told that this elevator is lifting passengers and the cabin itself at speeds of 16.8 meters per second and we're given the mass of the cabin and passengers, we're asked to calculate the power delivered by the motor to lift these 10 passengers at this speed. Now when you think power, you likely are thinking we need to calculate work and divide by time and certainly if you can calculate work and you have the time, that's certainly a great way to calculate the power. Now the work is usually calculated as a force times the displacement and here in this problem, we're not given a displacement. We can determine the force because we're told that the mass is 1250 kilograms. So we can find the downforce of gravity and presume that you need equal amount of upforce in order to raise these passengers at that speed. But what we don't have is we don't have a distance. So we can't actually calculate work directly, but that doesn't rule out the possibility of calculating power. So in the process of plotting my strategy, I'm going to have to find a way to get the power from the force and the speed. So you ought to get out a sheet of paper as always and you should be ready to write down the following. First we're going to start with the equation P equals W over T. Then we're going to take the numerator there and understand that to be the force multiplied by the displacement. So P equals F times D over T. Now you'll notice that in the numerator is a D and in the denominator is a T. You ought to recognize that a D over a T is actually a speed or an average speed. So we can rewrite the equation as P equals F times V, where the V represents the constant speed or the average speed at which the object moves. So now we're ready to solve the problem because we can calculate the force acting upon the cabin and passengers as M times G, which comes out to be 12,250 newtons. And we can multiply that force times the speed of 16.8 meters per second in order to get the power.
Solution
2.06 x 105 W
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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