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Centripetal Force Lab

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Lab Investigation
Purpose: This lab will verify how the centripetal force on a rotating body is affected by the following variables: frequency, speed, mass, and radius of a rotating object.
Available Materials: ● 2 rubber stoppers ● 28 steel washers ● reinforced ceramic tube ● 1.5 m of thread or string ● metre stick ● stop watch [pic]
Lab Procedure:
Remember that a proper scientific method requires identifying the following for each case of the investigation: → Independent Variable → Dependent Variable → Controlled Variables

PART A - Centripetal Force vs Frequency

1. Set up apparatus as illustrated above. Measure 1.0 meter of string from the rubber stopper to the tube (held vertically) using the metre stick. Attach a piece of tape on the string about 1 cm below the bottom of the tube (see diagram pg. 152). This will act as a reference mark.
2. Place 12 washers on the end of the string (using the paper clip).
3. While holding the bottom stack of washers, whirl the rubber stopper in a horizontal circle above your head. Carefully adjust the speed of rotation until you feel very little tension on the string suspending the washers. Let go of the stack of washers and maintain the rotation rate so that the reference tape on the string remains stationary about 1 cm below the tube. Have a lab partner determine the time for 20 complete rotations.
4. Set up a chart as illustrated below.
| | | | |
|Number of Washers |Number of Rotations |Time |Frequency |
|(Force Units) | |(s) |(Hz) |
|12 | | | |
|16 | | | |
|20 | | | |
|24 | | | |
|28 | | | |

Washer Mass (average): ___________ g Rubber Stopper Mass (average): ___________ g

5. Repeat this procedure, adding 4 washers each time until the total of 28 washers (force units) is achieved. Be sure to mass the washers (average) and the rubber stopper.
6. Complete the observation table by calculating the frequency. (Note that if the centripetal force were zero, the number of rotations would be zero.)

PART B - Centripetal Force vs Mass

1. Add one rubber stopper to the stopper already on the end of the string (use tape to accomplish this). This effectively doubles the mass.
2. Place 24 washers on the string. This effectively doubles the total centripetal force when compared to the total centripetal force of 12 washers as in PART A. Make sure the string length remains at 1.0 m.
3. Whirl the two rubber stoppers and vary the rotation rate until the reference tape moves to about 1 cm below the bottom of the tube. Determine the time for a similar number of rotations, and calculate the frequency.
PART C - Centripetal Force vs Radius

1. Attach 12 washers to the end of the string (12 force units). Measure the string such that the radius of rotation is now 0.4 m. Reposition the reference tape accordingly. Rotate ONE rubber stopper at a constant rate as you have done previously, maintaining the reference tape about 1 cm below the tube. Record the time for a given number of rotations, say 10 or 20 revolutions.
2. Set up an observation table like the one shown below. Calculate the frequency and the frequency squared.

| | | | | |
|Radius (m) |Number of Rotations |Time (s) |Frequency (Hz) |Frequency2 (Hz2) |
| | | | | |
|0.40 | | | | |
| | | | | |
|0.60 | | | | |
| | | | | |
|0.80 | | | | |
| | | | | |
|1.00 | | | | |

3. Repeat for radii of 0.60 m, 0.80 m, and 1.00 m (already done).

Analysis A:
7. Plot a graph of force versus frequency. Use graphical techniques to determine the relationship between the centripetal force and the frequency. Write a proportionality statement for this relationship, and determine the constant of proportionality.
8. Using the equation, determine the force (in washer units) required to maintain a rubber stopper of the same mass in a circular path of 1.0 m with a frequency of 6.0 Hz.

Analysis B:
4. Compare this frequency with that in in PART A, using 12 washers and 1 stopper. Based on this information, what conclusion can you make about the relationship between the centripetal force and the mass, provided both radius and frequency are held constant?

Analysis C:
4. Plot a graph of centripetal force (Fc) versus frequency squared (f2). The graph should pass through the origin; in other words, Fc = 0 when f2 = 0. Using the origin and the above data, you can determine four values of f2 for a constant centripetal force of 12 units. Plot four curves of Fc versus f2 on the same graph, one for each radius (see sample illustration below).

Fc ( ( (different radii values) ( 12(------------------o--------------o------------o----------------o ( ( ( ( ( ( ((((((((((((((((((((((((((((((((((((((((( 0 f2 (Hz2)

5. Draw a line parallel to the centripetal force axis, cutting each of the curves. Using interpolation, find for each radius the force required for a constant frequency (f2 = constant).
6. Plot a graph of force (Fc) versus radius (R). Using the graph, determine the relationship between Fc and R.

Conclusions:
Write up as a formal lab with appropriate concluding statements with error analysis.

Use Investigation 3.1.1 in text pages 152 – 153 as your guide.

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