Work: Force through a Distance (page 2)
The work done will depend on the force needed to pull the box and the distance it moves. In the example, the work done is 4.45 J.
Work is what is accomplished when a force causes an object to move. The amount of work done is equal to the product of the force applied to an object times the distance the object moves in the direction of the force. Another requirement for work to be done is that the distance the object is moved must be in the same direction that the force is applied. In this experiment, a horizontal force moves the box in a horizontal direction, so work is done.
Try New Approaches
- Does the speed at which an object moves affect the work needed to move it? Repeat the experiment twice, first at a higher but constant speed and then at a lower but constant speed.
- How does the weight of the object being moved affect the work done to move it? Repeat the original experiment twice, first using a lesser weight in the box and then using a greater weight. Note: Try to pull the box at the same speed for each testing.
Design Your Own Experiment
- A machine is a device that makes work easier. Machines make work easier by changing either the size or the direction of the input force. Simple machines are the most basic machines, such as an inclined plane (a flat, slanted surface). Inclined planes are used to transport an object to a specific height. Design an experiment to determine if using an inclined plane affects the overall work done on the object being moved. One way is to add weight, such as marbles, clay, or coins, to a small box with a lid. Close the box and secure the lid with tape. Tie a string around the box and attach the hook of a spring scale to the string. Use the scale to slowly raise the box a vertical distance of 1 meter. As you raise the box, ask a helper to note the reading on the scale in newtons, grams, or pounds. If the reading moves up and down slightly, record the average reading. Employ the previous method of determining force in newtons using pound or gram units. Then determine the work done in lifting the box using this equation: w = f × d. Then prepare an inclined plane by placing one end of a board at least 1 meter longer than the box on a stack of several books. Use the scale to move the box up the inclined plane for a distance of 1 meter. Repeat the procedure for determining the force needed to move the box and the work done. Use diagrams to display the results of the experiments.
- Sometimes a force on an object is at an angle to the direction of motion. An example would be pulling a wagon's handle at an angle, causing the wagon to move horizontally (see Figure 5.2). In this case, the relationship of the force acting on the wagon can be expressed by the equation da/dh = fh/fa, where da is the distance of the side adjacent to the angle of the applied force, dh is the distance of the hypotenuse (side opposite the right angle), fh is the force causing horizontal motion parallel to the direction in which an object is moved, and fa is the force applied at angle A°. The cosine (cos) of an angle is equal to the length of the adjacent side (da) divided by the hypotenuse (db). Since cos A° = da/dh and da/dh = fh/fa, then cos A° = fh/fa. Thus the horizontal force (fh) causing the wagon to move in a horizontal direction can be calculated using this equation: fh = fa × cos A°. (See Appendix 1 for the cosine value of different angles.)
- How does the angle affect the amount of work done in the previous experiment? Repeat the experiment three times, first at a smaller angle and second at a greater angle, but less than 90°. For the third trial, use an angle of 90°, thus slightly lifting the box above the table. Prove mathematically that while the box is moved horizontally while applying a force at 90°, no work is done. Science Fair Hint: Show vector diagrams for each angle. You do work in lifting an object, but once the object is lifted, you do no work in carrying it across a room. For an explanation of this seeming paradox, see work in a physics text and Larry Gonick and Art Hufamn, The Cartoon Guide to Physics (New York: HarperPerennial, 1990), p. 75.
Design an experiment to calculate the work done by a force that is at an angle to the direction in which an object is moved. One way is to attach a scale to a weighted box. Move the box across a table by pulling on the scale so that this force is at an angle to the movement of the box, as shown in Figure 5.3. Measure and record the distance (d) the box is moved. Use a protractor to measure the angle (A°) of the applied force. Determine the work using this equation:
For example, if the box is moved 0.6 m by a force of 10 N applied at an angle of 30°, the work done would be:
For more information about work done by a constant force that is applied at an angle relative to the direction of motion, see J. P. Den Martog, Mechanics (New York: Dover, 1961), pp. 133-135.
Get the Facts
Power is the rate of doing work. Since power is work divided by time, power is expressed as joules per second in SI units. The power unit of watt was named after James Watt (1736–1819), the inventor of the steam engine. How do the units of watt and horsepower compare to the SI unit of joules/ sec? See a physics text for a comparison of power units.
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