LABREPORT8JACKSONMITTON

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Indiana University, Bloomington *

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201

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Mechanical Engineering

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Dec 6, 2023

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docx

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Jackson Mitton Lab Partner: Eric Cheng 10/25/2023 Lab Report 8 The Ballistic Pendulum Introduction: This lab focuses on the conservation of momentum as well as the conservation of energy. This lab experiment is focused on a steel ball shot from a spring gun. Equations for determining the velocity, the projectile motion and range of the steel ball. Experimental Methods: When initially loading the ballistic pendulum, we found that to get the most precise data, you should load the steel ball WITH the spring rather than loading the spring and then loading the steel ball. When loading the ball with the spring, you get the most accurate data and closer values that can be comparable to the prelab. While calculating our S value, we found that it was longer than the 2-meter stick that was provided for this experiment. So, to place down the sheet of paper to measure the steel ball’s landing spot, we put down the two-meter stick right up against the table directly under the barrel of the pendulum, and then used the meter stick at the very end of the 2-meter stick (measuring 300cm) to find where our calculated S value would appear on the floor. When putting the piece of paper down on the floor to record the landing spot of the ball, we first found where our S value was on the “3-meter” stick, out the piece of paper right up next to it and centered it with the exact point of the S value. Results: Recorded mass of Steel ball (m): 66.8 g Recorded mass of pendulum (M): 247.4g Recorded Radius of Pendulum (R): 28.35 cm + 0.05cm Recorded (d): 94.85 + 0.05 cm Determining the Height: Trial Recorded Angle Calculated 1-cos 1 39.1 0.224 2 36.1 0.192 3 38.2 0.214 4 38.5 0.217 5 39.9 0.233 Calculated average of 1-cos: 0.216 (st dv. 0.0153) Standard error using σ √ N = 0.006834

Calculating the height = R ( 1 − cos ) = 28.35 ( 0.216 ) = 6.124 cm Calculating the uncertainty of the height √ ( δ ( 1 − cos ) ( 1 − cos ) ) 2 +( δR R ) 2 = 0.0316 cm Determining the Velocity: Using the values recorded at the beginning of the experiment, and the newly calculated value of h, we can now calculate the velocity of the steel ball using this equation: v = M + m m √ 2 gh Calculations: v = .2474 + 0.0668 0.0668 √ 2 × 9.8 × 0.06124 = ± 5.153 m / s δv = v ( 1 2 δh h ) = 5.153 ( .5 × .000316 .06124 ) = ± 0.0133 m / s Predicting the range: Using this equation after determining the velocity, we can predict the range: S = v √ 2 d g Calculations: S = 515.3 √ 2 × 94.85 980 = 226.715 cm δS = S √ ( δv v ) 2 + ( 1 2 ∙ δd d ) 2 = 226.715 √ ( 0.0133 5.153 ) 2 + ( 1 2 ∙ 0.05 94.85 ) 2 = ± 0.5882 cm Now after the original experiment, the ball landed at roughly 227.05 + 0.05 cm This is a picture of our paper. The small line that says estimated under it is the calculated value, where the dark dot is the landing spot of the steel ball.

Conclusion: Our calculated S value of 226.715 cm and its uncertainty fit within the calculated field of the actual landing range. The steel ball landed roughly 0.3 cm outside of our exact calculated value, but it still fits into our calculated uncertainty, meaning that the S value was correctly calculated as well as the height value. Therefore, we can accept our calculated prediction of the range value.

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