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- 1. Mass and the Terminal Velocity<br />Introduction:<br />Figure 1: Showing a picture of a cupcake holder that is adding masses with changing its shapes and areasTerminal velocity is achieved in free-fall when the objects weight (mass x gravity) equates to the drag force of the air. This causes a net force of zero and the object stops accelerating. An increased weight will mean a higher terminal velocity while an increased drag means a lower terminal velocity. In this lab, the cupcake is falling in free fall towards the motion detector, in which the data of position and the time will be recorded in the logger pro. The aim of the experiment is to see how mass affect terminal velocity while the research question of the experiment is how changing the mass affect terminal velocity? Assume that the equation is correct and the experiment is going to investigate about the nature of things falling.<br />The equation o the theory is:<br />Mg=CD×A×ρ2×(v×v)<br />Equation 1<br />To find the terminal velocity:<br />v2= 2mgAρCD<br />Equation 2<br />The independent variable of the experiment is mass (m) of the cupcake holder and the dependent variable is V2. The expectation or the prediction of the experiment is as the mass is doubled, the terminal velocity will be doubled as well. This is because as it falls down it takes longer for the drag force to compensate.<br />Controlled Variable:<br /><ul><li>The gravity on Earth = 9.8 m/s²
- 2. Room temperature = 26 C°
- 3. Area and shape of the cupcake holder = 0.0043 m</li></ul>Diameter = 7.4 cm<br />Height = 3.4 cm<br />Diameter = 4.6 cm<br />Figure 2: Diagram of the measurements taken of cupcake holder.<br />Procedure:<br />Motion DetectorCupcake HolderTableThe motion detector was put on the floor to record the data as the cupcake holder is free falling to the logger pro. Firstly, control the cupcake holder to drop on the floor straight to the motion detector and it will record the position and time the cupcake holder takes to fall for three trials. Add more mass to the cupcake holder and measure the mass of it without changing its shapes and areas, do the same thing as a cupcake holder that do not added. Do this with three different trials for five different mass, and average the slope of the data. <br />Figure 3: Showing the cupcake is falling down to the motion detector.<br />Data Collection:<br />Table 1: The table shows the mass and the terminal velocityMass(±0.01g)TrialVelocity(±0.04 m/s)Average Velocity (±0.04 m/s)0.5111.611.6621.6831.690.8612.352.3322.3132.321.2412.542.5422.5432.561.5512.812.8422.9032.811.8213.123.1523.1333.212.0213.313.3123.2933.32<br />Table SEQ Table * ARABIC 1: The table indicates the average of the different velocity that is measured of each sample of the three trails. The average of each of the three trials is already calculated for each sample velocity.<br />Sample Calculation:<br />Average Velocity:<br />= Sum of velocity Number of velocity<br />= 1.61+ 1.68 + 1.693<br />= 1.66<br />Uncertainty of Velocity<br />= Range 2<br />= 2.90-2.81 2<br />= 0.04<br />Data Analysis:<br />Figure SEQ Figure * ARABIC 4: The graph shows the relationship between position and the time it takes capcake paper to fall in the right time.<br />Figure SEQ Figure * ARABIC 5: Indicate the terminal velocity with the mass on the x axis. However, the graph uses proportional fit to see. It needs to calculate to the linear line in the below graph.<br />Data Collection:<br />Table 2: The table shows the mass and the V²Mass(±0.01g)V² (±0.2 m/s)0.512.760.865.431.246.451.558.071.829.922.0210.96<br />Table SEQ Table * ARABIC 2: The table indicates the calculated column of velocity that is squared to get new numbers which make the slope from the proportional line to linear line.<br />Sample Calculation:<br />CD = 20.0018(9.8)0.00431.2(9.92)<br />CD = 0.689<br />Uncertainty:<br />Highest V²=2m+0.0001gA-0.0005P(CD-0.1)Lowest V²=2m-0.0001gA+0.0005P(CD+0.1) <br /> =20.0018+0.0001(9.8)0.0043-0.00051.2(0.689-0.1) =20.0018-0.0001(9.8)0.0043+0.00051.2(0.689+0.1)<br /> =6.927 =6.572<br />Range:<br />=Highest V²-Lowest V²2<br />=0.298-0.1232<br />=0.09<br />Data Analysis:<br />Figure SEQ Figure * ARABIC 6: indicates the calculated velocity and the mass with the linear line. However, the graph shows that there are some errors because there is rarely a point that is close enough to the linear line.<br />Conclusion and Evaluation: <br />From the graph, the equation states that V² = 5.1997m+0.3331 in which it shows the result that prove the hypothesis in which if mass is increasing then the terminal velocity would be increased as well. <br />Example to prove the hypothesis is accurate:<br />If Mass = 10 kgIf Mass = 20 kg<br />Then, V² = 210(9.8)0.00431.2(0.0689)Then, V² = 220(9.8)0.00431.2(0.0689)<br /> V = 61.39 m/s V = 86.82 m/s<br />From the solved equations from above shows that if the mass increased then the velocity will be increased from 61.39 m/s to 86.82 m/s which give the accuracy of the theory in which the more mass it has, the more velocity it takes to fall down. Even though the result from sample equation above can proves the hypothesis, but the level of confident is low. In the Figure 6, it shows the large uncertainty bars which it can show the quality of the data. Although, the second data in the graph can clearly shows how inaccurate the graph has because the data is not near in the linear fit. The reason that can cause the level of uncertainty to be high is because of the data recorded and the calculation of the uncertainty for the data. Therefore, to improve the experiment, one should take more careful data and carefully calculate the calculations for the experiment.<br />

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