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:
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:
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:
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/sec².
Then list 5 possible reasons why your result was different than the expected value.
Transcribed Image Text:**Title: Investigating the Motion of a Toy Ball Down an Inclined Plane**
**Introduction:**
This educational experiment examines the time it takes for a toy ball to roll down an inclined plane. The purpose is to understand the factors affecting descent time on a slope.
**Experiment Setup:**
- **Inclined Plane Dimensions:**
- Length: 67 inches
- Height: 29 inches
- **Procedure:**
- Five trials were conducted measuring the time taken for a toy ball to travel from the top to the bottom of the incline.
**Table of Results:**
| Trial | Time (sec) |
|-------|------------|
| 1 | 2.70 sec |
| 2 | 2.60 sec |
| 3 | 2.34 sec |
| 4 | 2.45 sec |
| 5 | 2.66 sec |
**Diagram Description:**
- The diagram illustrates the inclined plane with a hypotenuse measuring 67 inches and a vertical height of 29 inches. Points on the diagram represent the starting, midpoint, and finishing positions of the ball's journey along the slope.
**Conclusion:**
The experiment provides insights into how gravity and incline affect motion, reflected in the varying times across different trials.
Expert Solution
Step 1
Dear student as you have asked how to calculate a before g(acceleration due to gravity), we will answer this question only and not the full calculation of the entire question.
Now, this is a beautiful setup to calculate acceleration due to gravity i.e. g experimentally. Now the wedge that we have we will roll our body there. Now the wedge angle is not given, that is our main task. If we can calculate the theta, we can calculate the acceleration of the body in terms of g and theta. we can put this acceleration expression in the kinematics equation,
where s = distance the body will travel, here it is 67 inches. t = time required by them to travel the 67 inches. a= acceleration = we will calculate this by Newton's law. u = initial velocity = 0. so as we know theta, t, s we can calculate g. that is why a before g means it wants us to calculate an in terms of g.
![**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/sec².
Then list 5 possible reasons why your result was different than the expected value.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F560885b1-95a6-46a1-8479-9132da42c8bd%2F273000d4-ebf0-4993-bab0-9b92538a2038%2Fso3yvm_processed.jpeg&w=3840&q=75)
