Lab 9_ Rolling Energy

Lab 9: Rolling Energy Aashna Arora Physics 141 Introduction The purpose of this lab is to delve into the intricacies of energy in rolling objects. I will examine the relationship between shape, linear speed and energy per unit mass. Through this, I will consider the following two equations and 𝐾 = 1 2 𝑚(𝑣 𝑐𝑜𝑚 ) 2 + 1 2 𝐼 𝑐𝑜𝑚 ω 2 . By designing and conducting experiments, I aim to explore key 𝐾 𝑖 + 𝑈 𝑖 = 𝐾 𝑓 + 𝑈 𝑓 concepts including the effect of shape on linear speed for rolling objects possessing the same energy per unit mass, compare the speed of a non rolling object sliding frictionlessly to that of a rolling object both possessing the same energy per unit mass, and finally investigate the impact of static friction on the acceleration of a rolling object moving down a straight, planar ramp. Through the execution of these experiments and then the following analysis of the data, I will be able to construct a comprehensive lab report that includes the experimental setup, necessary data collection and analysis, along with a thorough comparison between theoretical values and obtained results. I will calculate percent errors to understand deviations between experimental and theoretical values and by doing so I aim to deepen my understanding of the complexities behind energy in rolling objects and contribute to the broader realm of scientific knowledge. Procedure Equipment: ● iPhone 13 with frame by frame timestamping and slow mo video recording options ● A tennis ball ● A hollow straw ● A cup lid ● A quarter ● A pink rectangular eraser ● A 20 in x 30 in poster board with straight easy to easy gridlines ● A range of 5-10 books to be used as a ramp ● A 12 in metal ruler Activity 1: Effect of Shape on Linear Speed for Rolling Objects: 1. I will get three different rolling objects with known theoretical moments of inertias. For example, I will use a solid spherical ball, a hollow straw and a cup lid. 2. I used the poster board as a ramp and fixed the ramp at an incline with a fixed angle. 3. I measured the height of the ramp and recorded it as the initial potential energy of the rolling object. 4. I then release each rolling object from the same height on the ramp and then record the time it takes for the object to reach the bottom of the ramp.

5. I then will calculate the linear speed of each object using the measured time and the distance traveled along the ramp. 6. I then will analyze the results and compare the speeds with their theoretical values based on their moments of inertia. 7. I then will calculate the percent errors between the experimental and theoretical values. Activity 2: Comparison of Sliding and Rolling Objects: 8. Then, I will get a non rolling object such as an eraser and a similar object that can slide frictionlessly such as a coin. 9. I will set up a flat surface with the poster board on a table or on the floor and mark the starting point. 10. I will raise the poster board to a specific height, using that data to determine the initial potential initial energy. 11. I will release the objects simultaneously from the starting point and then measure the time it takes for each object to reach a designated endpoint. 12. I will then calculate the linear speed of each object using the time and distance traveled. 13. I will compare the speeds determined above and then analyze the results and calculate the percent difference in speed between the sliding and rolling objects. Activity 3: Static Friction and Acceleration on a Ramp: 14. I then set up a straight ramp inclined at a fixed angle. 15. I will place the rolling object with a known moment of inertia at the top of the ramp. 16. I measured the height of the ramp and recorded it as the initial potential energy of the object. 17. I will release the object and measure the time it takes to reach the bottom of the ramp. 18. I will calculate the linear speed of the object and then calculate the theoretical acceleration of the object based on the angle of the ramp and then compare it with experimental acceleration. 19. I will discuss the role of static friction in affecting the acceleration of the rolling object. 20. I will analyze the results and calculate the percent difference between the experimental and theoretical accelerations. Results Activity 1

The above photos show the frame just after the hollow straw was released and the frame right before the straw reached the end of the poster board. The distance traveled was 0.762 meters and the time elapsed was 1.18 seconds. Activity 2: The above photos show the frame just after both the eraser and the coin were released and the frames right before the coin and eraser reach the end of the poster board. The distance traveled for both was 0.762 meters and the time elapsed for the coin was 1.51 seconds and the time elapsed for the eraser was 1.36 seconds. Activity 3:

The above photos show the frame just after the tennis ball was released and the frame right before the tennis ball reached the end of the poster board. The distance traveled was 0.762 meters and the time elapsed was 1.02 seconds. Analysis Activity 1: This picture shows how I determined the distance the rolling objects traveled.

The above calculations show how I determined the theoretical velocity of the cup lid to be 0.24 m/s. The above calculations show how I determined the theoretical velocity of the hollow straw to be 0.23 m/s. The above calculations show how I determined the percent error of the tennis ball to be 34.8%.

The above calculations show how I determined the percent error of the cup lid to be 36.7%. The above calculations show how I determined the percent error of the hollow straw to be 39.1%. Activity 2: The above photo shows how I determined the distance traveled to be 0.252 m. The calculations above show that the linear speed for the eraser is 0.19 m/s and the linear speed for the quarter is 0.17 m/s.

The experimental acceleration is calculated to be . 0. 24 𝑚/𝑠 2 The theoretical acceleration is calculated to be . 0. 35 𝑚/𝑠 2 The percent difference is calculated to be 37.3%. Conclusion The purpose of this lab was to understand the intricacies of energy in rolling objects. In this lab, I explored the effect of shape on linear speed, I compared sliding and rolling objects, and investigated deeper into static friction and acceleration on a ramp. I analyzed the linear speeds of rolling objects with different speeds but the same overall energy per unit mass. I collected experimental results for a tennis ball, a cup lid, and a hollow straw which I then compared with their theoretical values through determining their moments of inertia. I calculated the percent errors and observed that the rolling object’s shape had an

impact on its linear speed with percent errors ranging from 34.8% to 39.1%. This shows that there are significant differences between the two values. I then looked at the speeds of non rolling objects and a sliding object. Both objects had the same overall energy per unit mass and a percent difference was calculated and determined to be 11.1%. This comparison highlighted that the non rolling object had a slightly higher speed compared to a rolling object with the same energy per unit mass. I also explored static friction and acceleration on a ramp to determine the role of static friction in affecting the acceleration of a rolling object. The experimental acceleration was compared to the theoretical acceleration and it was observed that the former value was lower than the latter which suggested an influence of static friction. Overall, these experiments provided insights into the complexities between shape, energy, speed, and friction in rolling objects.The percent errors and percent difference calculations allowed for numerical assessments of the deviations between experimental and theoretical values.