Work and Energy Legacy Problem #2 Guided Solution
Problem*
Hans Full is pulling on a rope to drag his backpack to school across the ice. He pulls upwards and rightwards with a force of 22.9 Newtons at an angle of 35 degrees above the horizontal to drag his backpack a horizontal distance of 129 meters to the right. Determine the work (in Joules) done upon the backpack.
Audio Guided Solution
When 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 on the object if we know the force value, if we know the distance the object moves, and if we know the angle between the force and the directional motion. Here we are told that Hans Pohl is pulling his backpack across the ice, and he exerts a force of 22.9 Newtons at an angle of 35 degrees to the horizontal in order to drag the backpack 129 meters to the right. Now the backpack moves across the ice horizontally, and the angle of 35 degrees is between the force and the directional motion. So we'll take the force and multiply it by the displacement, and multiply it by the cosine of the angle between the force and the displacement vectors. That's 22.9 Newtons times 129 meters times the cosine of 35 degrees. And when we do that, we get 2419 point blah blah blah joules. And we can round that to 2.42 times 10 to the third joules.
Solution
2.42 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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