PHYS 1433 Lab 4 Linear uniformly accelerated motion

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Mechanical Engineering

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Dec 6, 2023

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10/03/23 PHYS 1433 Lab 4: Linear Uniformly Accelerated Motion Objective: In this lab experiment our group determined the principals of a projectiles positions by finding the relationship between gravity and the horizontal/vertical directions of motion, and whether they are independent of projectile mass or not. The acceleration of the moving projectile was measured in order to verify the accelerated motion. Theoretical Background: As an object changes position, the value of its position coordinates will change with time. This change in value due to its change in position is known as displacement which is expressed as △ X = X 2 – X 1 . When the object changes its initial position with time, this is known as velocity in the formula; V = △ X/ △T. In determining acceleration, we use the formula A = V 2 – V 1 / t 2 – t 1 , and for average acceleration the formula A = v-v( Initial )/t can be used. By receiving the data calculated we can create a graph needed for finding the slope which would be equal to the acceleration’s magnitude. Procedure: 1. We began by setting up the dynamic tracks and photogates to determine the distances between photogates as shown in figure 1. 2. The length of the flag was measured, and the data results were recorded in the given table. 3. Two photogates were utilized in the experiment. Photogate #1’s accessory plug was inserted into Digital channel 1 on the computers workshop software. 4. Photogates #2’s accessory was then plugged into digital channel 2 workshop software. 5. Photogate #2 was then placed at the distance X = 0.50m below photogate #1, 6. The given object was set up at its starting position, then released from that same point over a repeated number of times as specified in the given table. Graphs:

0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 0.64 0.66 0.68 0.7 0.72 0.74 0.76 0.78 0.8 f(x) = 0.18 x + 0.53 R² = 0.96 Velocity V. Time (T ) △ Time, t,s Velocity,m/s 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 f(x) = 0.62 x R² = 1 Distance V. Time Time t, s Distance x,n Sample Calculations:

TIME △ T 0 , S TIME △ T, S Velocit y V= △ L/ △ T , m/s Time Betwee n Photoga tes t, S Accele ration A from (4), m/s^2 Dista nce betw een phot ogate s x, m Distan ce X from (6), x,m % differ ence for X Dista nce X from (8), m Velocit y V0= △ L/ △ T , m/s 0.08 0.0573 0.69 0.8356 0.2273 0.5 0.4943 1.14% 0.447 6 0.5 0.0849 0.0567 0.7 1.0111 0.2265 0.6 0.5014 17.9% 0.464 9 0.47 0.0832 0.0536 0.74 1.1296 0.2301 0.7 0.5658 20.6% 0.522 0.471 0.086 0.0525 0.76 1.2845 0.2296 0.8 0.6407 23.3% 0.552 7 0.465 0.0857 0.0506 0.79 1.4161 0.2288 0.9 0.7123 23.2% 0.599 2 0.466 Average Acceleration {m/s^2} Slope of Graph {m/s^2} Acceleration from slope of Graph {m/s^2} Percent Difference for Acceleration 0.2285 0.1792 0.619 15.56

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Conclusion: To conclude, we measured the acceleration of a moving cart and acceleration by determining how long it took for an object to pass through both photogates. After gathering data for the table our group assumed that the velocity of an object clearly affects its acceleration. Despite the distance, time, and velocity having varying units throughout the experiment, the acceleration remained roughly similar, as shown in the table for the average. Though, when calculating the percent difference for acceleration it came out to be 15% which is 5% higher than the acceptable error which means a mistake was made somewhere in the experiment, meaning the kinematic equation was not verified. { Slope = 0.1792 m/s^2 / Acceleration from graph = 0.619 m/s^2}

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