The work done by the force of gravity is the same if the object falls straight down or if it makes a wide parabola and lands 100 m to the east. This is because the force of gravity does no work when an object is transported horizontally, because the force of gravity is perpendicular to the horizontal component of displacement.
Work Problems with Graphs
There’s a good chance SAT II Physics may test your understanding of work by asking you to interpret a graph. This graph will most likely be a force vs. position graph, though there’s a chance it may be a graph of
vs. position. Don’t let the appearance of trigonometry scare you: the principle of reading graphs is the same in both cases. In the latter case, you’ll be dealing with a graphic representation of a force that isn’t acting parallel to the displacement, but the graph will have already taken this into account. Bottom line: all graphs dealing with work will operate according to the same easy principles. The most important thing that you need to remember about these graphs is:
The work done in a force vs. displacement graph is equal to the area between the graph and the x-axis during the same interval.
If you recall your kinematics graphs, this is exactly what you would do to read velocity on an acceleration vs. time graph, or displacement on a velocity vs. time graph. In fact, whenever you want a quantity that is the product of the quantity measured by the y-axis and the quantity measured by the x-axis, you can simply calculate the area between the graph and the x-axis.
Example
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The graph above plots the force exerted on a box against the displacement of the box. What is the work done by the force in moving the box from x = 2 to x = 4? | |
The work done on the box is equal to the area of the shaded region in the figure above, or the area of a rectangle of width 2 and height 4 plus the area of a right triangle of base 2 and height 2. Determining the amount of work done is simply a matter of calculating the area of the rectangle and the area of the triangle, and adding these two areas together:
Curved Force vs. Position Graphs
If SAT II Physics throws you a curved force vs. position graph, don’t panic. You won’t be asked to calculate the work done, because you can’t do that without using calculus. Most likely, you’ll be asked to estimate the area beneath the curve for two intervals, and to select the interval in which the most, or least, work was done. In the figure below, more work was done between x = 6 and x = 8 than between x = 2 and x = 4, because the area between the graph and the x-axis is larger for the interval between x = 6 and x = 8.
