Newtons second law lab

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Jun 22, 2024

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(1 point) Title of the Experiment: N ewton’s Second Law Student’s name: Isaac Velasco Section SL N : Phy 113 TA’s N ame: Bonfilio N ainggolan Week of the experiment: Lab 4

OBJECTIVE(S) ( 3 points ): The aim of this lab is to confirm N ewton’s second law of motion through measuring gravitational acceleration and learning how to apply the law to systems of masses. EXPERIME N TAL DATA ( 3 points ): Part 1: One way motion without friction. Run 1: Slope of the velocity vs time graph and its uncertainty (extra 200g is on the cart): 0.9770 +/- 0.0006935 m/s^2 Run 2: Slope of the velocity vs time graph and its uncertainty (extra 300g is on the cart): 0.8142 +/- 0.0006039 m/s^2 Part 2: One way motion with friction. Run 1: Slope of the velocity vs time graph and its uncertainty (extra 200g is on the cart): 0.3580 +/- 0.0009778m/s^2 Run 2: Slope of the velocity vs time graph and its uncertainty (extra. 300g is on the cart): 0.1828 +/- 0.0009280 m/s^2 Part 3: Two-way motion: Run 1: slope and its uncertainty (toward the motion sensor): 2.500 +/- 0.0005452 m/s^2 slope and its uncertainty (away from the motion sensor): 0.5129 +/- 0.005665 m/s^2 Run 2: slope and its uncertainty (toward the motion sensor): 3.026 +/- 0.0004698 m/s^2 slope and its uncertainty (away from the motion sensor): 1.177 +/- 0.0001787 m/s^2

Data Analysis (10 points): Part 1: One way motion without friction. Calculate the gravitational acceleration (g) using the formula (6) for each run of Part (1): Run 1: g= 0.9770(250+50)/50= 5.862 m/s^2 Run 2: g= 0.8142(350+50)/50= 6.5136 m/s^2 Calculate the average value of gravitational acceleration for part (1): (5.862 + 6.5136)/2 = 6.1878 m/s^2 Calculate the percent discrepancy between the average value of g and the theoretical value of g, which is 9.81 m/s 2 . (9.81-6.1878)/6.1878 * 100 = 58.54= .59% Part 2: One way motion with friction. Derive equation for the acceleration using equations (2) and (3) from Introduction and Theory. Calculate the theoretical acceleration of the cart. Assume that the kinetic friction force Fk = μk *Mg , where is M is the total mass of the cart and μk the coefficient of kinetic friction which is set up as 0.07 in the virtual lab. Run : 9.81[(50-0.07*250)]/300= 1.063% Run2: 9.81[(50-0.07*350)]/400= 0.63% Calculate the percent discrepancy between the theoretical and experimental values of acceleration: Run 1: (0.3580-1.063)/1.063 * 100= 66% Run 2: (0.1828-0.63)/0.63 *100= 71% Part 3. Two – way motion with friction. Calculate the average acceleration of your two slopes for each run of Part (3): Run1: 2.5+0.5129/2= 1.5096 m/s^2 Run 2: 3.026+1.177/2= 2.1015 m/s^2

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Calculate the mean value of g and its uncertainty: Run 1: 1.5096(550+100)/100= 9.8124 m/s^2 Uncertainty: 0.0005452+ 0.005665/2 = 0.0031051 m/s^2 Run 2: 2.1015(550+150)/150= 9.807 m/s^2 Uncertainty: 0.0004698+ 0.0001787/2= 0.00032425 m/s^2 9.8124+9.807/2= 9.8097m/s^2 Mean of g 0.0031051+ 0.00032425/2 = 0.00171467 m/s^2 mean uncertainty Calculate the discrepancy between theoretical and experimental values of g: (9.81-9.8097)/9.8097 * 100 = 0.31% Results (3 points) Part 1: Part 2: Part 3: M cart, g m hang, g Acceleration, m/s 2 A v e r a g e g r a v i t a t i o n a l acceleration, m/s 2 % discrepancy 250 + 200= 450 g 50 g 0.9770 m/s^2 6.1878 m/s^2 .59% 250 + 300= 550 g 50 g 0.8142 m/s^2 M cart, g m hang, g Acceleration, m/s 2 % discrepancy 250 + 200 = 450 g 50 g 0.3580 m/s^2 66% 250 + 300 = 550 g 50 g 0.1828 m/s^2 71%

DISCUSSIO N A N D CO N CLUSIO N (10 points): The objective of this lab was to validate Newton's Second Law of Motion by measuring the acceleration due to gravity and understanding its application in different systems of masses. This involved conducting three parts of an experiment: one-way motion without friction, one-way motion with friction, and two-way motion with friction towards and away from a motion sensor. Newton's Second Law of Motion states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass F = ma. By analyzing the motion of a cart under different conditions, we aimed to measure the gravitational acceleration and observe how varying forces and masses affect the cart's motion. The mean value of gravitational acceleration (g) calculated in Part 1 was 6.1878 m/s^2 which is significantly lower than the theoretically accepted value of 9.81 m/s^2. This discrepancy is attributed to experimental errors and also extra weight being provided onto the cart. 1. One-Way Motion Without Friction - A cart was placed on a track with additional weight added to it, and allowed to move without any intentional frictional forces. - The cart's acceleration was measured, and the gravitational acceleration was calculated. The average value of 6.1878 m/s^2 suggests that adding weight to the cart or other factors might have affected the motion despite the aim to minimize them. 2. Part 2: One-Way Motion With Friction - The same cart with the same weight was subjected to motion on a track where friction was intentionally present. M cart, g m hang, g Average gravitational acceleration, m/s 2 % discrepancy 550 g 250+300 100 g 50+50 9.8097 +/- 0.00171467 m/s^2 0.31% 550 g 250 +300 100 g 50+50

- The presence of friction reduced the cart's acceleration compared to Part 1. This demonstrates Newton's Second Law, as the net force acting on the cart was reduced by the frictional force, leading to a lower acceleration. 3. Two-Way Motion With Friction - The cart was moved towards and away from a motion sensor, experiencing friction in both directions, while weight was added to the cart. - The cart's acceleration varied based on its direction of motion relative to the sensor. Moving towards the sensor likely showed higher deceleration due to friction acting opposite to the motion, while moving away showed less deceleration. - What will happen to an object when you apply one force to it? When only one force is applied to an object, it accelerates in the direction of the force, as per Newton's Second Law. - What will happen to an object when you apply five forces to it? When multiple forces are applied, the object accelerates in the direction of the net force, which is the vector sum of all individual forces. - How will the acceleration of an object change as the net force acting on it stays constant but its mass changes? As mass increases, acceleration decreases, and vice versa. - How will the motion of an object change if it has a constant mass but the magnitude of the net force on it changes? If the mass is constant, increasing the net force increases acceleration, while decreasing the net force reduces acceleration. - Effect of Doubling Mass with Constant N et Force? Doubling the mass halves the acceleration. - Effect of Halving N et Force with Constant Mass? Halving the net force reduces the acceleration proportionally. - Acceleration in Part 3? Acceleration was greater when moving towards the motion sensor due to additional deceleration from friction. - Comparing Parts 1 and 2? Acceleration was greater in Part 1 due to the absence of friction. In Part 2, friction reduced the net force and thus the acceleration. - N eglecting N ormal Force? The normal force does not affect the horizontal motion analyzed in this experiment and therefore is not included in the equations for horizontal forces and acceleration. This lab effectively demonstrated Newton's Second Law by analyzing the motion of a cart under different conditions. Despite experimental discrepancies, the results highlighted the impact of friction and mass on acceleration. The significant difference between the experimental and theoretical values of gravitational acceleration suggests the

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need for improved accuracy in future experiments. Overall, the lab reinforced the understanding of how forces and masses interact to influence the motion of objects.

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