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Please do it as instructed as its my physics 12 lab which is around 10% of my course please make sure its done neatly ,carefully and correctly. Additionally please make graph on a graph paper . Sorry for inconvenience, thank you in advance :)

o Content Connections The net force on the weight 1s constant and centripetal, F; it 1s caused by two forces at work: the weight of the bob , and the tension in the string Fr. o Content Connections 4. On another piece of graph paper, build this re-graph, find the slope, and make an equation that represents a relationship between Radius and Period T. Show all work below. Slope: Equation: Analysis: From theory, we know that the centripetal acceleration of the pendulum can be determined from its period and radius of orbit, using the following equation: 4m? T2 r a,= Meanwhile, the slope of your re-graph can be represented as follows: r Slope &k = T2 Substituting into the equation above, we get the following: a. = 4n'k Use this equation to calculate the centripetal acceleration of the pendulum weight in this experiment. Show work in the space below: Measured a, = Content Connections The vector addition of the two forces acting on the pendulum weight produces the resultant force F,, which is displayed as a forces triangle: - from this triangle, we can see that F. = F,tand Fr Fg = in turn, this becomes ma. = mg tan@ -> cancelling 'm', we have a. = g tanf R Fe This means that, regardless of the pendulum mass, a constant centripetal acceleration can be achieved by simply maintaining a constant and consistent angle of rotation 6. Data: In this experiment, the following procedures were performed: 1. In making the pendulum, a small weight of was tied to the end of a long string. 2. The string was held at a length of 37 cm from the center of the pendulum weight. This length was recorded in the table below. 3. The pendulum weight was then rotated for 25 complete circular repetitions, while maintaining an average angle of 35 degrees. The time taken to complete the 25 rotations was also recorded in the table below. 4. Procedures 1-3 were repeated for a total of six different string lengths. Note that the 35-degree angle of rotation was maintained for all six lengths. o Content Connections Angle of rotation &: 35 Songlngt | s of | Tine 02| a1 0.37 ' 21.5 0.52 33.1 0.67 37.3 0.79 40.5 0.88 42.5 1.06 46.7 Calculations: 1. Determine the radius r of the pendulum's circular path as well as the period T of its orbital path, and complete columns 2 and 4 of the data table. Show a sample calculation for your radius values below: 2. On a separate piece of graph paper, plot a graph of Radius vs. Period for the conical pendulum, with Radius r as the dependent value (y-axis) and Period T as the independent value (x-axis). Be sure to label each axis and include proper units. Draw a smooth curve through the plotted points. 3. Examine the curve of your graph. It represents a common relationship which should be familiar to you from your previous physics course. Complete the last (5) column of the data table by performing the correct calculation on the x- values so that a straight line re-graph can be drawn. Hint: if you are still unsure how to do this, refer to the Analysis section of this activity. o Content Connections The Conical Pendulum Background A conical pendulum is created by rotating a weight at the end of a string in a circular orbit in such a way that the string traces the shape of a cone, as shown to the right. Looking more closely at the pattern, a triangle can be drawn to represent the following: -> L is the length of string used in the pendulum = 0 is the angle of rotation of the pendulum -> ris the radius of the weight's horizontal circular path - from this triangle, E=sin9 = r=Lsind o Content Connections Next, calculate the expected centripetal acceleration (the accepted value) for a conical pendulum with a constant angle of rotation, using the formula: a. = g tan@ that was developed in the Background section of this activity. Show all work in the space below: Expected a. = Conclusion: Calculate the % error between the accepted value and the measured value of the centripetal acceleration, using the formula: Imeasured value accepted value| % error = x 100 accepted value % error = In a paragraph or two on a separate page, describe what you learned from this activity, and list several sources of error in performing this activity that would lead to maccurate results. In doing so, consider any difficulties that would arise from performing this experiment yourself. Explain what could be done to reduce these inaccuracies. Once completed, be sure to include the conclusion as well as the two graphs in your submission