College Physics
11th Edition
ISBN: 9781305952300
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
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How can find g? And what does it mean to compare my results to the actual value of 9.80 m/sec2
![### Transcript for Educational Website
#### Diagram and Calculations
**Triangle Diagram:**
- A right triangle with:
- Side \( AB = 29 \, \text{in} \)
- Side \( AC = 67 \, \text{in} \)
**Trigonometric Calculations:**
- \[
\sin \theta = \frac{AB}{AC} = \frac{29}{67} = 0.4328
\]
- \[
\theta = \sin^{-1}(0.4328) = 25.6^\circ
\]
#### Inclined Plane Diagram
- **FBD** (Free Body Diagram):
- \( N \): normal reaction
- \( W \): weight
- \( mg \sin \theta \): component of weight down the plane
**Newton's Second Law:**
- \[
F = ma
\]
- \[
mg \sin \theta = mka
\]
- \[
a = g \sin \theta
\]
#### Table of Trials
| Trial | Time (Sec) |
|-------|------------|
| 1 | 0.80 sec |
| 2 | 0.60 sec |
| 3 | 0.34 sec |
| 4 | 0.16 sec |
| 5 | 0.66 sec |
#### Kinematic Equations
- **Given:**
- \( a = g \sin \theta \)
- \( u = 0 \)
- **Equations:**
- \( S = ut + \frac{1}{2} at^2 \)
- \( S = \frac{1}{2} g \sin \theta t^2 \)
- \( g = \frac{2S}{\sin \theta t^2} \)
This information provides a detailed analysis of an object on an inclined plane, demonstrating calculations involving trigonometry, Newton's Laws, and kinematic equations. The experimental trials and times can be used for further analysis or validation of theoretical principles.](https://content.bartleby.com/qna-images/question/560885b1-95a6-46a1-8479-9132da42c8bd/dd2a6bc3-6bf1-4b5b-b9ac-6d97e7f8a2a6/e0qv0ha_processed.jpeg)
Transcribed Image Text:### Transcript for Educational Website
#### Diagram and Calculations
**Triangle Diagram:**
- A right triangle with:
- Side \( AB = 29 \, \text{in} \)
- Side \( AC = 67 \, \text{in} \)
**Trigonometric Calculations:**
- \[
\sin \theta = \frac{AB}{AC} = \frac{29}{67} = 0.4328
\]
- \[
\theta = \sin^{-1}(0.4328) = 25.6^\circ
\]
#### Inclined Plane Diagram
- **FBD** (Free Body Diagram):
- \( N \): normal reaction
- \( W \): weight
- \( mg \sin \theta \): component of weight down the plane
**Newton's Second Law:**
- \[
F = ma
\]
- \[
mg \sin \theta = mka
\]
- \[
a = g \sin \theta
\]
#### Table of Trials
| Trial | Time (Sec) |
|-------|------------|
| 1 | 0.80 sec |
| 2 | 0.60 sec |
| 3 | 0.34 sec |
| 4 | 0.16 sec |
| 5 | 0.66 sec |
#### Kinematic Equations
- **Given:**
- \( a = g \sin \theta \)
- \( u = 0 \)
- **Equations:**
- \( S = ut + \frac{1}{2} at^2 \)
- \( S = \frac{1}{2} g \sin \theta t^2 \)
- \( g = \frac{2S}{\sin \theta t^2} \)
This information provides a detailed analysis of an object on an inclined plane, demonstrating calculations involving trigonometry, Newton's Laws, and kinematic equations. The experimental trials and times can be used for further analysis or validation of theoretical principles.
![**Experiment 2:**
Find a smooth surface that is positioned at an angle (a long board, a slide at a playground, a sloped driveway, etc.). Measure the distance from the starting point up the hill to the finishing point down the hill. Place a smooth running toy at the top of the hill, and let go. Measure the time it takes for the toy to roll down to the bottom of the hill. Repeat 4 more times. 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\(^2\).](https://content.bartleby.com/qna-images/question/560885b1-95a6-46a1-8479-9132da42c8bd/dd2a6bc3-6bf1-4b5b-b9ac-6d97e7f8a2a6/gqloxzo_processed.jpeg)
Transcribed Image Text:**Experiment 2:**
Find a smooth surface that is positioned at an angle (a long board, a slide at a playground, a sloped driveway, etc.). Measure the distance from the starting point up the hill to the finishing point down the hill. Place a smooth running toy at the top of the hill, and let go. Measure the time it takes for the toy to roll down to the bottom of the hill. Repeat 4 more times. 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\(^2\).
Expert Solution
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Going through your solution, i see you have done it correctly throughout you need to convert inches in meters and taking time t=0.34 s as per your you'll get the answer.
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