Work and Energy Legacy Problem #4 Guided Solution
Problem*
Sheila has just arrived at the airport and is dragging her suitcase to the luggage check-in desk. She pulls on the strap with a force of 190 N at an angle of 35° to the horizontal to displace it 45 m to the desk. Determine the work done by Sheila on the suitcase.
Audio Guided Solution
When a force is exerted upon an object to cause that object to move, we say that work is being done upon the object. We can calculate the amount of work done if we know the force value, the displacement of the object, and the angle between the force and the displacement vector. Here Sheila is dragging her suitcase along the floor. She's exerting a force of 190 Newtons on it. This is at an angle of 35 degrees to the horizontal. To displace it 45 meters, we presume along the floor. And so if we wish to calculate the work done by Sheila upon the suitcase, we need to multiply F times D times the cosine of the angle between F and D. That would be 190 Newtons times 45 meters times the cosine of 35 degrees. When we do all that, we get 7,003.75 joules, and we can round that to two significant digits such that the answer becomes 7.0 times 10 to the third joules.
Solution
7.0 x 103 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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