First go over the overview of the experiment, the experiment, and the results of the experiment (data tables 1-3) then answer the few questions regarding the results of the experiment (NOTE you are NOT doing the experiment, just simply answering the questions, the experiment is just for reference)

Overview/ Experiment: Explore the influence of mass, length, and angular displacement on the period of a simple pendulum. You will use the devised relationships to calculate the acceleration due to gravity and compare this to the accepted value.

The Experiment:

1. Using the measuring tape, measure a piece of string that is approximately 150 cm in length.
2. Securely attach the 50 g hanging mass to one end of the string.

Note: The hanging mass will hereafter be referred to as the bob.

1. Suspend the string from the pendulum support so that the distance from the attachment point to the center of the bob is exactly 1.50 m (150 cm).
2. Use tape to affix the protractor to the wall behind where the string is attached to the support so that the center hole of the protractor is located directly behind the pivot point as shown in Figure 9.

Note: The string should hang straight down so that the string aligns with the 90 mark on the protractor. See Figure 9 for correct placement of the protractor.

Figure 9.

Protractor aligned behind string and center hole behind pivot point.

INSTRUCTOR NOTES

Note that the following instructions are telling you to displace the bob a certain number of degrees from the vertical. For the first trial, that means starting from the 85 degree mark, NOT the 5 degree mark. This lab works best for small amplitudes of swing. Figure 10 is a little misleading because the initial angle is much larger than you will use.

1. Displace the bob by 5 from the vertical as measured using the protractor and hold it there as shown in Figure 10. Release the bob and observe its swing for one cycle, so that the bob returns to its starting point. Record your observations of the motion inData Table 1.

Note: Keep the string straight as the bob is displaced by holding the bob to create the desired angle. The pendulum must swing without obstruction and should not strike the background as it swings.

INSTRUCTOR NOTES

For this next part, remember that a complete cycle is from release point back to release point. You will time 10 complete cycles, then divide by 10 to get the time forthe period. (which is the time it takes to complete one cycle)

1. Use the digital stopwatch to time the bob as it swings through ten complete cycles. Record the time to the nearest 0.1 seconds inData Table 1.
2. Repeat steps 7-8 two additional times for a total of three trials.
3. Displace the bob by 10 from the vertical as measured using the protractor and release. Record your observations of the motion inData Table 1.
4. Use the digital stopwatch to time the bob as it swings through ten complete cycles. Record the time to the nearest 0.1 seconds inData Table 1.
5. Repeat steps 10-11 two additional times for a total of three trials.
6. Displace the bob by 20 from the vertical as measured using the protractor and release. Record your observations of the motion inData Table 1.
7. Use the digital stopwatch to time the bob as it swings through ten complete cycles. Record the time to the nearest 0.1 seconds inData Table 1.
8. Repeat steps 13-14 two additional times for a total of three trials.
9. Calculate the average of the three time trials for each angle and record to the nearest 0.1 seconds inData Table 1.
10. Calculate the period for each angle by dividing the average time by 10 and record to the nearest 0.1 seconds inData Table 1.

Part 2: Effect of Length of Period

1. Copy the data recorded in Data Table 1 for the bob displaced by 10 toData Table 2.
2. Detach the string from the pendulum support and adjust the length so that the distance from the attachment point to the center of the bob is exactly 1.00 m (100 cm) as measured using the tape measure.

Note: Do not cut the string. Instead, wrap the excess string around the top of the bob, or otherwise out of the way, so that it does not interfere with the swinging of the pendulum as shown in Figure 11.

1. Repeat steps 10-12 for the 1.00 m length pendulum and record all measurements inData Table 2.
2. Detach the string from the pendulum support and adjust the length so that the distance from the attachment point to the center of the bob is exactly 0.50 m (50 cm) as measured using the tape measure.
3. Repeat steps 10-12 for the 0.50 m length pendulum and record all measurements inData Table 2.
4. Calculate the average of the three time trials for each length and record to the nearest 0.1 seconds inData Table 2.
5. Calculate the period for each length by dividing the average time by 10 and record to the nearest 0.1 seconds inData Table 2.

Part 3: Effect of Mass on Period

1. Copy the measurement data for the 50 g hanging mass and 1.00 m length fromData Table 2toData Table 3.
2. Remove the 50 g hanging mass from the string and replace with the 100 g hanging mass.
3. Detach the string from the pendulum support and use the measuring tape to adjust the string length so that the distance from the attachment point to the center of the bob is exactly 1.00 m (100 cm).
4. Repeat steps 10-12 for the 100 g mass and the 1.00 m length and record the measurements in Data Table 3.
5. Attach the 50 g hanging mass to the bottom hook of the 100 g hanging mass and adjust the length of the string so that the distance from the attachment point to the center of the bob is exactly 1.00 m (100 cm).

Note: Measure the distance to the center of mass of the pendulum bob as shown in Figure 12. If your hanging weight set does not include bottom hooks, use a small section of string to tie the 100 g mass to the 50 g mass.

1. Repeat steps 10-12 for the 150 g bob and the 1.00 m length and record the measurements inData Table 3.
2. Calculate the average of the three time trials for each mass and record to the nearest 0.1 seconds inData Table 3.
3. Calculate the period for each mass by dividing the average time by 10 and record to the nearest 0.1 seconds inData Table 3.

Results of the experiment (data table 1-3)

Angle () 5 10 20 Time 1 (5) Time 2 (s) 23.8 Time 3 (s) 25.2 Average time (s) 24.3 Period (5) 2.4 Observations very slow swing 24 .4 l25.2 |24.5 2.5 slow swings 24.3 25.1 24.5 2,5 faster swings Data Table 4: Acceleration Due to Gravity for 0 = 109, m = 50 g Length (m) Period squared (m/s2) g (calculated) (m/s2) Ag (calculated) (m/s2) % Error (calculated) 1.50 g (graph) (m/s2) % Error (graph) 24 1.00 28 0.50 .17Data Table 3: Mass and Period for 0 = 109, L = 1.0 m Mass (g) Time 1 (s) Time 2 (s) Time 3 (s) Average time (s) Period (s) Observations 50 18.9 19.2 18.8 19 1.9 slow 100 19.2 19.3 19.1 19.2 1.9 a little fast 150 19 19.2 19.3 19.2 1.9 a little fast\fLength (m) 1.50 1.00 0.50 Time 1 (s) Time 2 (s) Time 3 (5) Average time (5) Period (5) Observations 23.8 18.9 24.4 19.2 25.2 18.8 24.5 h 2.5 slow swings fast swings 17 17.1 16.9 17 ' 1.7 ' [faster swings l 472 L = T2