Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN: 9780190698614
Author: Sadiku, Matthew N. O.
Publisher: Oxford University Press
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Use the middle of the 5 measurements for your calculations. Use the equation: \[ a = g \sin(\theta) \] to find the acceleration due to gravity. Of course you'll need the equations of kinematics to determine the acceleration "a" first before finding \( g \). Again compare your result to the actual value of 9.80 m/sec\(^2\). Then list 5 possible reasons why your result was different than the expected value.
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Transcribed Image Text:Use the middle of the 5 measurements for your calculations. Use the equation: \[ a = g \sin(\theta) \] to find the acceleration due to gravity. Of course you'll need the equations of kinematics to determine the acceleration "a" first before finding \( g \). Again compare your result to the actual value of 9.80 m/sec\(^2\). Then list 5 possible reasons why your result was different than the expected value.
**Experiment #2** In this section of the experiment, we will locate a smooth surface at an angle and measure the distance between the starting and finishing points of the hill. Then we'll place a ball at the top of the hill, let it go, and time how long it takes for the ball to roll down the hill, and repeat until we get 5 measurements total. **Diagram and Calculations:** 1. **Triangle Setup:** - Triangle ABC with: - \( AB = 29 \text{ in} \) - \( AC = 67 \text{ in} \) - \(\sin \theta = \frac{AB}{AC} = \frac{29}{67} = 0.4328\) - \(\theta = \sin^{-1}(0.4328) \approx 25.6^\circ\) 2. **Kinematic Equation:** - Given: - \(a = g \sin \theta\) - \(u = 0\) - Equation: - \( s = ut + \frac{1}{2} at^2 \) - \( s = \frac{1}{2} g \sin \theta t^2 \) - \( g = \frac{2s}{\sin \theta t^2} \) 3. **Time of Top Going Down Hill:** | Trial | Time (sec) | |-------|------------| | 1 | 0.80 sec | | 2 | 0.60 sec | | 3 | 0.74 sec | | 4 | 0.46 sec | | 5 | 0.66 sec | 4. **Average Time and Calculations:** - Average time \( t = \frac{0.74 + 0.84 + 0.46 + 0.66}{5} = 0.5 \text{ sec} \) - Distance \( s = 67 \text{ in} = 1.7018 \text{ m} \) - \(\sin \theta = 0.4328\) - \( g = \frac{s}{\sin \theta t^2} = \frac{2(1.7018)(0.5^2)}{
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Transcribed Image Text:**Experiment #2** In this section of the experiment, we will locate a smooth surface at an angle and measure the distance between the starting and finishing points of the hill. Then we'll place a ball at the top of the hill, let it go, and time how long it takes for the ball to roll down the hill, and repeat until we get 5 measurements total. **Diagram and Calculations:** 1. **Triangle Setup:** - Triangle ABC with: - \( AB = 29 \text{ in} \) - \( AC = 67 \text{ in} \) - \(\sin \theta = \frac{AB}{AC} = \frac{29}{67} = 0.4328\) - \(\theta = \sin^{-1}(0.4328) \approx 25.6^\circ\) 2. **Kinematic Equation:** - Given: - \(a = g \sin \theta\) - \(u = 0\) - Equation: - \( s = ut + \frac{1}{2} at^2 \) - \( s = \frac{1}{2} g \sin \theta t^2 \) - \( g = \frac{2s}{\sin \theta t^2} \) 3. **Time of Top Going Down Hill:** | Trial | Time (sec) | |-------|------------| | 1 | 0.80 sec | | 2 | 0.60 sec | | 3 | 0.74 sec | | 4 | 0.46 sec | | 5 | 0.66 sec | 4. **Average Time and Calculations:** - Average time \( t = \frac{0.74 + 0.84 + 0.46 + 0.66}{5} = 0.5 \text{ sec} \) - Distance \( s = 67 \text{ in} = 1.7018 \text{ m} \) - \(\sin \theta = 0.4328\) - \( g = \frac{s}{\sin \theta t^2} = \frac{2(1.7018)(0.5^2)}{
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