Lab 7 archimedes Physics 103A.docx (1)

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Feb 20, 2024

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Physics Laboratory Report Title Archimedes' Principle and Density Lab number and Title: Lab 7: Archimedes' Principle and Density Name: Hari Patel Group ID: 2 Date of Experiment: 2/1/24 Date of Report Submission: 2/8/24 Course & Section Number: PHYS103A006 Instructor’s Name: Aidan Thayer Partners’ Names: Aaron Avezov, Benjamin Cerda-Albornoz, Samantha Chauca 1. INTRODUCTION (10 points) 1.1 OBJECTIVES 1. To understand Archimedes’ Principle (Physical Law of Buoyancy) 2. To measure the density of unknown substances by two methods: Archimedes’ Principle and density definition. (Lab manual) 1.2 THEORETICAL BACKGROUND This experiment focuses on Buoyant forces which is described when an object is submerged in fluid. This fluid exerts an upward force against the gravitational force that acts on the object. This is classified as a buoyant force and according to Archimedes’ Principle, a buoyant force acting on a submerged object equals the weight of the fluid displaced by the given object. 1. B = WL = mLg = ρLVOg (Buoyant Force) 2. W = mg = ρOVOg (Weight) 3. B = W - W’ (Buoyant Force in fluid) 4. (ρO / ρL) = (W / W - W’) (Archimedes’ Principle) 2 EXPERIMENTAL PROCEDURE (10 points) The procedure was the same as in the lab manual. 3 RESULTS (30 points in total)
3.1 EXPERIMENTAL DATA (15 points) Table 1 Cylinder ID Height(m) Diameter(m) Vo (m^3) W (N) in air W’ (N) in liquid 1 W’ (N) in liquid 2 Small 0.0127 0.0255 6.4E-6 0.1769 0.1055 0.1157 Medium 0.0255 0.0254 1.29E-5 0.3446 0.2099 0.2345 Large 0.0382 0.0254 1.9E-5 0.5134 0.3235 0.354 Table 2 Block ID Vo (m^3) W(N) W’(N) Density by Archimedes’ Principle Density by Density Definition Substance Y 3.2E-5 0.8623 0.5460 2.721 2.755 Aluminum W 3.24E-5 2.4922 2.17112 7.76 7.844 Iron X 3.19E-5 2.6683 2.3521 8.43 8.53 Brass U 3.29E-5 3.4257 3.1186 11.15 10.6 Lead Percent Difference = (M-A)/A * 100 Aluminum- 2.721-2.755/2.755 *100%= 1.23% Iron- 7.76-7.844/7.844 *100%= 1.07% Brass- 8.43-8.53/8.53 *100%= 1.17% Lead- 11.15-10.6/10.6 *100%= 5.19%
Small cylinder in air Small cylinder in water Medium cylinder in air Medum cylinder in water
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Large cylinder in air Large cylinder in water Small cylinder in ethanol Medium cylinder in ethanol
Large cylinder in ethanol Y block in water W block in water X block In water
U block in water Y block in air W block in air X block in air
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U block in air CALCULATION (15 points)
4 ANALYSIS and DISCUSSION (20 points) The density values that were calculated using Archimedes’ Principle, were very close to the density definition values. Although the values were not exact, they were still close enough to where our group was able to determine the substance. This deviation can be a result of human error in calculations and experimentation. 1. Despite the fact that the experimental numbers were not accurate, the cause might have been a human error when experimenting and calculating. Nonetheless, the experimental results in the first half of this experiment were very close to the accepted values. We were able to validate Archimedes' principle by comparing these figures and computations and we were able to determine that our values fell in the range of Archimedes’. Another possible explanation for our error could be that the blocks weren’t fully submerged, which could cause changes in our values. 2. In part II of the experiment our measured density values were very close to the acceptable values with the largest percentage difference being 5.19% and the other blocks had just over 1% difference. Overall, our values confirm that Archimedes’ Principle is an accurate method for measuring fluid density. 3. According to Archimedes, the mass of the water being displaced is equal to the weight of the ice cube, thus even if an ice cube floats in a glass of water that is completely full and the ice melts, the glass won't overflow. The melting process causes the ice to continue until it reaches the water's density. 4. Humans will float much easier in salt water when compared to freshwater since salt water has a lower density than freshwater. 5. Since the balloon's volume is intended to change, it will rise higher when it is allowed to expand. A balloon that has a higher volume and a lower density will rise further than a rigid balloon. 5 CONCLUSIONS (10 points)
In this experiment, we learned that when an object is submerged, there is a buoyant force that acts upon the object directly against gravitational forces. This experiment also was successful in explaining and proving Archimedes principle as it helped in finding the density of objects and identifying the substances. This is significant topic that engineers may have to utilize when working in the field. Our values for density were very close to the actual values which confirms that our experiment was successful. In future experiments, the groups should make sure that the object is fully submerged in the water and standing still. 6 Attachment of Raw Data (5 points)
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