1000 - 01 (1)

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1 Name ________________________ Lab Partner __________________ Date _________________________ Lab day & time ________________ PHYS 100 Lab 1 FALLING OBJECTS PURPOSE: To investigate the velocity and acceleration of falling objects, and the effects of air resistance. APPARATUS: Two-meter stick, golf ball, flat-bottom coffee filters, and stop watch. DISCUSSION: Objects falling freely under the influence of gravity near the surface of the earth experience a velocity and an acceleration. Both the velocity and the acceleration can be influenced by air resistance. If the air resistance is negligible, then the velocity increases as the object falls while the acceleration remains constant. In this case, the average velocity v avg that an object attains when falling through a distance d in time t is given by v avg = distance/time = d/t (1) while the acceleration a is given by (2) If air resistance is important, then both the velocity and the acceleration can be altered significantly, and the acceleration cannot be calculated from Eq. (1). In this experiment we will investigate the velocity and acceleration of falling objects under the conditions (1) where air resistance is negligible, and (2) where air resistance has a strong effect. 2 2 t d a =

2 PROCEDURE: Part I - Negligible air resistance Using the meter stick, the golf ball, and the stopwatch, drop the ball from heights of 0.5, 1.0, 1.5, and 2.0 meters, and use the stopwatch to determine the time of fall in each case. Because it will be more difficult to measure the time for the smaller heights, you might want to start with 2.0 m and work your way down. For 0.5 m the measurement will be quite difficult but do the best you can. Repeat the measurement 10 times for each height and fill in the following table: Trial Height Time Height Time Height Time Height Time 1 0.5 m 0.18 1.0 m 0.45 1.5 m 0.70 2.0 m 0.61 2 0.5 m 0.20 1.0 m 0.46 1.5 m 0.79 2.0 m 0.64 3 0.5 m 0.19 1.0 m 0.455 1.5 m 0.82 2.0 m 0.67 4 0.5 m 0.21 1.0 m 0.452 1.5 m 0.73 2.0 m 0.65 5 0.5 m 0.22 1.0 m 0.458 1.5 m 0.88 2.0 m 0.68 6 0.5 m 0.23 1.0 m 0.457 1.5 m 0.84 2.0 m 0.61 7 0.5 m 0.22 1.0 m 0.459 1.5 m 0.84 2.0 m 0.63 8 0.5 m 0.21 1.0 m 0.456 1.5 m 0.91 2.0 m 0.64 9 0.5 m 0.23 1.0 m 0.454 1.5 m 0.95 2.0 m 0.64 10 0.5 m 0.22 1.0 m 0.451 1.5 m 0.91 2.0 m 0.66 Now, calculate the average time for each height and use equation (1) to calculate the average velocity v avg and use equation (2) to calculate the acceleration, filling in the table below: Height 0.5 m 1.0 m 1.5 m 2.0 m Avg. time 0.215 0.459 0.767 0.646 v avg 2.325 2.179 2.604 3.086 a (acceleration) 5.523 9.753 16.372 8.566 Does the velocity change with increasing height? If yes, how does it change, i.e., does it increase or decrease? Yes, the velocity changes with increasing height. Generally, as the height increases, the average velocity also increases. You can observe this trend by comparing the values for different heights.

3 What does it mean when the velocity changes with time? Explain. When velocity changes with time, it indicates acceleration. In this experiment, the change in velocity with time is due to the acceleration of the golf ball under the influence of gravity. Does the acceleration change with increasing height? Yes, the acceleration changes with increasing height. You can observe this by comparing the a value for different heights. The acceleration is influenced by gravity and is not constant throughout the experiment. Now calculate the average value of the acceleration for the four heights and compare your value with that found by two other groups in your lab section: Your value: _____________ Other value 1: _____________ Other value 2: _____________ How do these average values compare with the acceleration of gravity near the earth (9.8 m/second/second)? Should they agree? Explain. Part II - Effect of air resistance Using the meter stick, a single coffee filter, and the stopwatch, drop the coffee filter flat side down from heights of 0.5, 1.0, 1.5, and 2.0 meters, using the stopwatch to determine the time of fall in each case. Repeat the measurement 5 times for each height and fill in the following table: Trial Height Time Height Time Height Time Height Time 1 0.5 m 83 1.0 m 1.11 1.5 m 1.34 2.0 m 1.72 2 0.5 m 0.80 1.0 m 1.22 1.5 m 1.44 2.0 m 1.82 3 0.5 m 0.68 1.0 m 1.13 1.5 m 1.32 2.0 m 1.88 4 0.5 m 0.64 1.0 m 1.12 1.5 m 1.29 2.0 m 1.73 5 0.5 m 0.66 1.0 m 1.10 1.5 m 1.38 2.0 m 1.75

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4 Now, calculate the average time for each height and use equation (1) to calculate the average velocity v avg , filling in the table below: Height 0.5 m 1.0 m 1.5 m 2.0 m Avg. time 0.72 1.14 1.35 1.78 v avg 0.69 0.88 1.11 1.12 Does the velocity change with increasing height? If yes, how does it change, i.e., does it increase or decrease? Yes, the velocity changes with increasing height. The velocity increases with higher heights. Assume that the acceleration is 9.8 m/s/s at the instant you release the filter (it has to be!). Then, what does your answer to the previous question tell you about the acceleration? What is the final acceleration? The observed increase in velocity with height is consistent with the constant acceleration due to gravity 9.8 m/s/s It means that the filter is experiencing acceleration throughout its fall. The final acceleration 9.8 m/s/s is which is the acceleration due to gravity. Now calculate the average value of the velocity for the four heights and compare your value with that found by two other groups in your lab section: Your value: _____________ Other value 1: _____________ Other value 2: _____________ Do your results agree with those found by the other two groups?

5 Finally, put two coffee filters together and three coffee filters together and drop each of these "systems" flat side down from a height of 2 meters, using the stopwatch to determine the time of fall in each case. Repeat the measurement 5 times for each case and fill in the following table: 2 filters 3 filters Trial Height Time Height Time 1 2.0 m 2.22 2.0 m 1.88 2 2.0 m 2.11 2.0 m 1.85 3 2.0 m 2.15 2.0 m 1.74 4 2.0 m 2.06 2.0 m 1.85 5 2.0 m 2.02 2.0 m 1.82 Now, calculate the average time for each height and use equation (1) to calculate the average velocity v avg , filling in the table below. For 1 filter use the data you took earlier for a height of 2.0 meters. 1 filter 2 filters 3 filters Height 2.0 m 2.0 m 2.0 m Avg. time 1.78 2.11 1.82 v avg 1.12 0.95 1.10 Does the velocity change for increasing numbers of filters? If yes, how does it change, i.e., does it increase or decrease? Yes, the velocity decreases as the number of filters increases. The velocity you calculated is called the terminal velocity. What do your results tell you about how the terminal velocity changes with the mass (or weight)? Terminal velocity decreases with an increase in mass (or weight). Heavier objects reach lower terminal velocities.

6 If two people with identical parachutes jump out from a plane at the same time, who will hit the ground first? Explain. Both will reach the same terminal velocity, so they will hit the ground simultaneously. SUMMARY: In a few sentences, explain what you learned from this experiment. The experiment showed that as the number of filters increased, the terminal velocity decreased, indicating a relationship between mass and terminal velocity. The results aligned with the expectation that heavier objects have lower terminal velocities.

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