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UA11

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May 14, 2024

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Lab #6: Conservation of Energy PHYS-UA11

Objective and Description In this experiment, students further develop their skills with the Capstone interface in order to observe the Conservation of Energy. This lab consists of three parts. In the first part, a rubber tube is dropped through the photogate sensor that students were introduced to in previous experiments. In the second part, a 0.1kg hanging mass and the photogate are used, which students have been previously introduced to. However, they are used in a new way, as the mass is set up in such a way that it can be treated as a pendulum. Finally, in the last part, a 0.5kg weight is attached to a spring and allowed to oscillate, while its motion is detected with the motion sensor. Through each experiment, the application of the conservation of energy in a physical sense can be evaluated. Theory In previous experiments, the work-energy theorem, which shows that the integration of Newton’s Second Law yields W=∆KE, was observed. This experiment expands upon that observation to state that this work, or line integral, may have two different possibilities. In one instance, the work depends on the path and is considered non-conservative , while in the other, it is path-independent and therefore, conservative . From the second case, the work can be derived such that the potential energy is equal to the kinetic energy, or, U f + KE f = U i + KE i Where each side is the total mechanical energy, E . If E is conserved such that E f =E i , this is referred to as the conservation of energy . Procedure The procedure was followed fairly closely to that of the write-up with a few differences. For section 3, we only used heights of 15cm and 25cm and did not include 35cm. We also only used the rubber tube and not the paper tube. One significant mistake that occurred during this part happened due to

being new to the calipers. When measuring the diameter of the tube, the inches side was accidentally used instead of the centimeters side. This is a serious problem because this diameter is entered as the Flag Width in Capstone. As a result, all of the data was off and my partner and I had to repeat this step. In section 4, we ensured to not make the same mistake. For this section, we also only used heights of 7cm and 15cm. For section 5, it only took 3 tries to get a fully successful run. Data and Calculations Section 3 v t (m/s) Trail h = 15 cm h = 25 cm 1 1.58 2.31 2 1.47 1.86 3 1.43 2.27 4 1.49 2.12 5 1.41 1.86 Table 1. Theoretical velocity, v f h = 15 cm h = 25 cm = = 1.71 m/s 𝑣 = 2𝑔ℎ 2(9. 8𝑚/𝑠 2 )(0. 15𝑚) = =2.21 m/s 𝑣 = 2𝑔ℎ 2(9. 8𝑚/𝑠 2 )(0. 25𝑚) Table 2. Section 4 v t (m/s) Trail h = 7 cm h = 15 cm 1 1.00 1.50

2 0.97 1.47 3 0.98 1.48 4 1.05 1.43 5 1.04 1.47 Table 3. Theoretical velocity, v f h = 7 cm h = 15 cm = = 1.17 m/s 𝑣 = 2𝑔ℎ 2(9. 8𝑚/𝑠 2 )(0. 07𝑚) = = 1.71 m/s 𝑣 = 2𝑔ℎ 2(9. 8𝑚/𝑠 2 )(0. 15𝑚) Table 4. Section 4 Figure 1. Highest point (H) 0.766m Distance= H–L =0.766m–0.367m =0.399m Lowest Point (L) 0.367m Max down v after H -0.83 m/s Amplitude=A Distance=2A A= =0.200m 0.399𝑚 2 Max v after L 0.83 m/s Table 5.

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