I-2 Final Proposal

PHYS 1251 Describing Motion Along a 2D Plane Section 1: During the investigation, students were expected to access a ball and its motion up and down an incline. This concept can answer the guiding question, “does a ball on an incline have the same acceleration on its way up as its way down?” As Newton second law states, force is equal to the mass and acceleration. The larger the mass, the more force that is required to create acceleration. The ball in this case did not have a large mass (around 20.0 grams ( g )), so the force was relative to the size for this investigation. To evaluate the ball’s acceleration, there are several factors that need to be calculated, such as the position of the ball. The ball’s position can be classified as a vector because it has a direction. To trace this vector, a Tracker software recorded the position and time of the ball – key points of data to collect as they help determine velocity. Velocity is the change in position over a change in time. As the software recorded the ball, it captured points along a manually entered distance. Using this information, the group calculated the velocity of the ball leading to the ability to determine acceleration. Acceleration is the change in velocity over a given time. Given that the relative force of Earth’s gravity is constant, the ball should be expected to experience the same acceleration uphill as it does downhill. Section 2: As previously mentioned, this investigation utilized Tracker software that was connected to a camera and displayed a video image on a computer screen. The camera captured a ball being pushed up an incline and allowed to freely fall down the incline, twice. After setting the point and distance in the software, it created a series of data points which were exported to an Excel document. Using this information, the velocity was calculate using the equation ( x f − x i ) ( t f − t i ) . Let “x” equal the position and “t” equal time. In the Excel document, velocity and time data points were used to create a graph and create what is known as a linear regression. Finally, from this regression, the acceleration was determined along with the uncertainties of both the uphill and downhill points. As with any investigation, there were some sources of error that needed to be reduced such as the inclination and choosing one person to place force on the ball. Firstly, by completing the trial twice at different inclines, once at 70˚ and again at 43.5˚, this allowed the investigation to have variety. If the ball had the same acceleration upwards and downwards as a smaller angle, then a larger angle would most likely not make a difference. Secondly, by ensuring only one person applied force to the ball, the acceleration would not increase/decrease due to the amount of force applied. It kept the force consistent, essentially. For the sake of reference, the 70˚ angle will be referred to as “angle A” and the 43.5˚ will be referred to as “angle B”. Section 3: A ball on an incline has the same acceleration as it goes uphill as it goes downhill. In this investigation, the uncertainties for both accelerations upward and downhill inclines of angles A and B were combined by using δc = √ ( δa ) 2 + ( δb ) 2 . To find the overall uncertainty, we then used

C = √ δc ( δa a ) 2 +( δb b ) 2 . Following these equations, this produced an uphill uncertainty of (0.05± 0.04) m/s² and a downhill uncertainty of (0.10 ± 0.04) m/s². Since the uncertainties do not have a significant difference, they can be considered statistically similar. Figure 1: position and time graph for 70˚ for Figure 2: position and time graph for 43.5˚ for upward and downward. upward and downward. Figure 3: velocity/time graph for 70 ˚ downhill Figure 4: velocity/time graph for 43.5˚ downhill Figure 5 : velocity/time graph for 70 ˚ upward Figure 6: acceleration/time graph for 43.5 ˚ upward Upward data for angles 70˚and 43.5˚ Downward data for angles 70˚ and 43.5˚ Acceleration 0.05 m/s 0.10 m/s Uncertainty 0.04 m/s 0.04 m/s Regression 70-degree angle, Uphill = 0.0956 Downhill = 0.5806 43.5-degree angle, Uphill = 0.0674 Downhill = 0.5529