Work and Energy Legacy Problem #5 Guided Solution
Problem*
While training for breeding season, a 380-gram male squirrel does 32 pushups in a minute, displacing its center of mass by a distance of 8.5 cm for each pushup. Determine the total work done on the squirrel while moving upward (32 times).
Audio Guided Solution
No, I know it's hard to believe, but a squirrel can do a push-up and during breeding season it's not too uncommon to look into your backyard and see a squirrel doing push-ups. Here we have a male squirrel whose average mass is about 380 grams doing some push-ups. During that push-up the squirrel lifts himself up about 8.5 centimeters and what we wish to do is determine the amount of work done for 32 of these push-ups just considering the up movement. So to do that what we need to do is use the equation that the work is equal to the force times the displacement times the cosine of the angle between force and displacement. Here the force can be determined if we presume that the amount of force needed to lift the 380 gram squirrel up is equal to the force of gravity on that squirrel. So we would take the 380 grams and change it to kilograms such that it becomes 0.380 kilograms. Then we would multiply by 9.8. That would give us the force of gravity. The applied force is equivalent to that, 3.724 newtons. Now the displacement of the squirrel during a single push-up would be 8.5 centimeters or 0.085 meters. So if we take the force in newtons and multiply by the displacement in meters we would get a quantity of work in joules. That would be for one push-up and the value would be 0.3165 joules. If we multiply by 32 we would get the total amount of work done for a good workout for a squirrel doing 32 push-ups and that would be about 10.129 joules. We can round that to two significant digits such that it becomes 10 decimal place joules.
Solution
10.0 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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