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Use the middle of the 5 measurements for your calculations. Use the equation: azgsim( a-g sin(e) to find the acceleration due to gravity. Off 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

Use the middle of the 5 measurements for your calculations. Use the equation: azgsim( a-g sin(e) to find the acceleration due to gravity. Off 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

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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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.
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)}{
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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