Newton's 2nd Law Lab Report

Maxwell Johnson Physics Lab 2215 Newton’s 2nd Law Report 10/04/2023 Newton’s 2nd Law Introduction: Newton’s 2nd Law of physics states that , where F is the nonzero net force ???? = ?𝑎 acting on an object, m is the mass of the entire system, and a is the acceleration of the object. This relationship suggests that acceleration is directly proportional to the magnitude of the force acting on it and inversely proportional to the mass of the object. The overall purpose of this experiment is to investigate Newton’s 2nd law and the relationship between force and acceleration. This experiment was performed with differing variations of mass on a frictionless track with mass on a glider (M) connected by a string and pulley to a falling mass (m), as shown in Figure 2. Because it’s nearly impossible to perfect the experiment with regard to accurate variables and factors in play, it was assumed that there was no friction on the air track, that the track was level, the string was taught and didn’t stretch, and that the masses of the glider and falling mass were accurately recorded. As previously stated, Newton’s 2nd Law is written as (the product of the ???? = ?𝑎 mass and the acceleration of an object). Theoretically, because the only unbalanced force in play is the downward force of gravity due to the falling mass, it can be said that mg = ma, and therefore: . This means that as the mass of the glider, M, increases, then the 𝑎 = ?? ?+? magnitude of the acceleration will decrease. And as the mass of the hanging mass, m, increases, the magnitude of the acceleration will increase. After the experiments were run, the data was analyzed and the following calculations were made–the average or mean ( , the standard deviation or uncertainty ( ), and the percent ? ) σ ? error. These are modeled by the following equations– ??𝑎? (? ) = 1 ? 𝑖=1 ? ∑ ? 𝑖 ??????𝑎𝑖??? ?? ?ℎ? ??𝑎? (σ ? ) = σ ? ? 𝑃?????? ????? = ? ??𝑎????? −? ???????? ? ???????? | | | | | | • 100%

Maxwell Johnson Physics Lab 2215 Newton’s 2nd Law Report 10/04/2023 Figure 1. This is a free-body diagram of the system used in the experiment. The glider is fixated in the vertical direction, and N and Mg cancel out in regards to the net force. This means that the net force in the diagram is equivalent to the weight of the falling mass – mg. This is because the Tension forces ( ) are internal forces of the system. ? 1 & ? 2 Procedure: In this lab, a glider, pulley, motion sensor, air track, and falling mass were set up and connected to Capstone (which connects to our motion sensor to analyze the data recorded). Prior to the first experiment, it was made sure that the air track was level to mitigate any work done by gravity on the glider itself, along with making sure that the air track was on and connected to Capstone. (A) – In the first experiment, the process began with a loaded glider weighing in at 418.1g along with a hanging mass of 10g. After the air track has been turned on, the glider is released from rest while the falling mass immediately pulls it toward the pulley causing the glider to accelerate along the air track. Capstone starts recording data as soon as the glider is let go, and stops right before the glider hits the bumper at the end of the air track. As the glider accelerates, Capstone reads the positional data recorded by the motion sensor, and analyzes said data. (B) – In the second experiment, the process began with a loaded glider weighing in at 418.1g along with a hanging mass of 20g. After the air track has been turned on, the glider is released from rest while the falling mass immediately pulls it toward the pulley causing the glider to accelerate along the air track. Capstone starts recording data as soon as the glider is let go, and stops right before the glider hits the bumper at the end of the air track. As the glider accelerates, Capstone reads the positional data recorded by the motion sensor, and analyzes said data.

Maxwell Johnson Physics Lab 2215 Newton’s 2nd Law Report 10/04/2023 Results: During the data recording process, the equation was used to ? = 1 2 𝑎? 2 + ? 0 ? + ? 0 calculate the acceleration of the glider. After each experiment was run, Capstone provided a graph of the position with respect to time. By using the highlighter tool to apply a quadratic fit to the intended recorded data, capstone provided the equation , where ? = ?? 2 + ?? + ? ? = 1 2 𝑎. The acceleration was then calculated. Loaded Glider with 10g Falling Mass from Rest Trial Measured acceleration ( ) ? ? 2 1 -0.1628 2 -0.1624 3 -0.1096 4 -0.0704 5 -0.1032 Average acceleration -0.1220 Table 1. The data collected in experiment A, where the loaded glider attached to a falling mass of 10g was released from rest. Measured acceleration → 𝑎 = − 0. 1220 ± 0. 018 ( ? ? 2 ) Loaded Glider with 20g Falling Mass from Rest Trial Measured Acceleration ( ) ? ? 2 1 -0.193 2 -0.416 3 -0.362 4 -0.174 5 -0.388 Average acceleration -0.307

Maxwell Johnson Physics Lab 2215 Newton’s 2nd Law Report 10/04/2023 Table 2. The data collected in experiment B, where the loaded glider attached to a falling mass of 20g was released from rest. Measured acceleration → 𝑎 = − 0. 307 ± 0. 051( ? ? 2 ) Empty Glider with 10g Falling Mass from Rest Trial Measured acceleration ( ? ? 2 ) 1 -0.268 2 -0.149 3 -0.356 4 -0.370 5 -0.374 Average acceleration -0.303 Table 3. The data collected in experiment C, where the empty glider attached to a falling mass of 10g was released from rest. Measured acceleration → 𝑎 = − 0. 303 ± 0. 043( ? ? 2 ) Loaded Glider with 10g Falling Mass with an Initial Velocity Trial Measured acceleration ( ? ? 2 ) 1 -0.220 2 -0.222 3 -0.220 4 -0.224 5 -0.208 Average acceleration -0.219 Table 4. The data collected in experiment D, where the loaded glider attached to a falling mass of 10g with an initial velocity. Measured acceleration → 𝑎 = − 0. 219 ± 0. 0028( ? ? 2 )

Maxwell Johnson Physics Lab 2215 Newton’s 2nd Law Report 10/04/2023 cannot conclude that the goal was met, and therefore cannot describe any mathematically and physically proven relationships.