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# Terminal Velocity: Free Falling (page 2)

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Author: Janice VanCleave

### Try New Approaches

How does weight affect the acceleration of falling objects? Repeat the experiment using a single coffee filter and a double coffee filter, made by placing two coffee filters together, one within the other. The shapes of the coffee filters should be as similar as possible, so that weight is the only factor being tested. A difference in acceleration can be determined by the time of fall. The greater the time of fall, the lower the acceleration. Likewise, the slower the time of fall, the greater the acceleration.

1. Design an experiment to determine the average falling time of an object at different heights. One way is to use a stopwatch to measure the time of descent of a coffee filter dropped from different heights. Tape a strip of paper to a wall, and starting at the floor, mark these heights on the paper strip: 0.5 m, 1.0 m, 1.5 m, and 2.0 m. Holding the coffee filter in line with but not touching the mark for 0.5 m, drop the filter and simultaneously start the stopwatch. Stop the watch when the filter hits the floor. Record the falling time in an Average Falling Time Data table like the one in Table 7.1. Repeat the experiment at the 0.5 m height three or more times and average the times. Repeat the experiment at the remaining heights.
2.
1. Free-falling objects accelerate toward Earth at a rate of 9.8 m/sec2. This means that if one neglects air friction, the velocity of a falling object increases in the direction of Earth 9.8 m/sec for every second it falls. The formula for calculating the time of a free-falling object is: , which is read as time equals the square root of 2 times distance (height) divided by gravitational acceleration (9.8 m/sec2).
2. Use the formula to calculate the time of descent in the coffee filter free-falls from heights of 0.5 m, 1.0 m, 1.5 m, and 2.0 m. Record this time in a Calculated Falling Time Data table like the one in Table 7.2.

3. When drag on a falling object due to air resistance equals the force weight of the falling object, the resultant force on the object equals zero, and the object stops accelerating. But the object does not stop moving—in fact, it continues to fall at a constant or final velocity, called terminal velocity. For each height, compare the average measured times of descent of the coffee filter in Table 7.1 with the calculated time of descent if the filter free falls. Determine the height at which the filter reaches terminal velocity. This can be expressed in reference to the height marks, such as before 0.5 m or between 0.5 m and 1.0 m. Note that once the filter reaches its terminal velocity, its falling time will increase because it is no longer accelerating. For more information about terminal velocity, see P. Erik Gundersen, The Handy Physics Answer Book (Detroit: Visible Ink, 1999), pp.36-37.
3.
1. Design an experiment to determine how weight affects the terminal velocity of a falling object. One way is to use objects that are of different weights, but light enough to reach their terminal velocity quickly, such as a single coffee filter and a double or triple coffee filter. Keep the shape of the single and double coffee filters the same so their surface areas are the same. Tape a sheet of paper to a wall and make a mark on it at 200 cm and 175 cm above the floor. Hold the single and double filters so they are in line with the 200-cm mark, then drop them. Ask a helper to note which reaches the floor first. Label this filter A, label the other filter B. Then hold filter A at a height of 200 cm and filter B at 175 cm. Release the filters to see if the lower height for filter B is enough to allow both filters to hit the floor at the same time. If not, continue lowering or raising filter B until both filters hit the floor simultaneously. Record the height of both filters.
2. The ratio of the heights at which filters A and B were released that resulted in their hitting the ground at the same time should be approximately equal to the ratio of their average velocities when dropped from this distance. This can be expressed as hA/hB = vA/vB.
3. Confirm this relationship by measuring the time it takes filter A to fall from 200 cm and for filter B to fall from the height determined in part 2a. Use the equation v = d/t, where d is the distance a filter falls (its height) and t is the time, to determine the average velocity of each. Compare this to the height ratios for the filters.

### Get the Facts

1. Newton was the first to recognize that an unbalanced or net force causes something to accelerate. The relationship between force and acceleration is called Newton's second law of motion. What is the mathematical expression of Newton's second law? How can this expression be written if the force is the weight of an object and the acceleration is due to gravity? For information, see a physics textbook.
2. Because of the air around Earth, what is the maximum or terminal velocity of a sky diver? What is the terminal velocity once the parachute is open? For information see P. Erik Gundersen, The Handy Physics Answer Book (Detroit: Visible Ink, 1999), p. 38.
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