Lab 2 - Determining g on an Incline (1)

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Jan 9, 2024

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Determining Gravity on an Incline Introduction The objective of this experiment is to both conceptualize and analyze the variation between the force of gravity in its theoretical state and an observed metric of gravity values as they pertain to the motion of an object down an inclined surface until it reaches its terminal position. Under ideal conditions, the measurement of gravity on an incline would be equal to 9.8m/s² and be the sole acting force on acceleration; however, during testing, there are other forces that may impede or amplify the acceleration of the object as it approaches its terminal position (Cano, 2019). Thus, although the expected acceleration of the object should be approximately equal to that of the literature value for gravity during free fall, there may be slight differences which can be compared. In this experiment, the core objective would be not only to study this difference between the observed and theoretical value for gravity but to account for differences that occur as well as their possible cause. To account for this discrepancy, the moving object's acceleration and velocity will be measured at predetermined intervals of time. Due to the inclined nature of the surface in question, the angle of inclination of the surface it travels along would be the primary contributor to acceleration. In tandem with the use of multiple trials at varying angles on inclination, an observed value for gravity will be established and further contrasted with the literature value. Theory Throughout history, numerous scientists have devoted their life’s work towards the pursuit of understanding the ability of a force to exert work on a given object at a continuous pace, over a constant period of time. Any push or pull that is exerting pressure on an object and affecting its velocity is referred to as a force. (Cook, 1965). Forces are employed in practically all computations to form the foundation for what may be called modern physics for kinematics,

and few are as influential as the force of gravity, which was initially postulated by Galileo in the 17th century and proved by Newton later that century. (Cano, 2019). Gravity is the natural force exerted by a planet or other entity that will attract objects toward its center and is classified as an acceleration vector (Cook, 1965). Gravity can be measured to act on an object at a rate of -9.8m/s², Figure 1 illustrates the observed relationship between the forces acting on the object and its direction. (Cano, 2019). Figure 1. Idealistic motion diagram for the movement of an object along an inclined plane. The idealistic model demonstrates the movement of an object down an incline in a vacuum with no external forces acting on the object in motion. As a result, it will possess a g value equivalent to a perfect -9.8m/s². The force of gravity can integrate with other forces of motion to produce greater or less acceleration when an object is suspended in the air or moving down an incline toward the surface or ground level. This notion further implies that although the object may be subject to change, the force in itself will remain constant. This well-known process is also what is examined in this experiment, allowing the value of free-fall acceleration, g, to be calculated using the slope of the acceleration vs. sine of the track angle graph, as well as several physics derivations. Additionally, the outcome can be contrasted with the 9.8 m/s 2 norm for the free-fall acceleration g. One of the primary physics concepts investigated in this experiment includes the incorporation of trigonometry in order to find the angle as well as the mathematical correlation

between the angle of the inline and the cart speeding down the ramp. In essence, the following formula is utilized in order to calculate the sine of the incline angle for each height. The formula for determining the angle θ: ℎ 2 − ℎ 1 = ℎ �� h 2 -h 1 = h 3 sinθ= �� ℎ �� θ=sine -1 �� ℎ �� ( ) The gravity for each angle can be calculated using the angle theta once it has been identified. The average velocity, or a v , is calculated by dividing it by sin theta. The calculation is further defined below, and it can be used to calculate the standard deviation. [ See results and calculations for in depth explanation on average velocity ]. The formula for determining g: �� = �� θ An additional crucial physics concept that is addressed includes the standard deviation. The term "standard deviation" refers to a measurement of the data's disparity from the mean. A low standard deviation shows that the data is grouped around the mean and consequently more dependable, whereas a large standard deviation indicates that the data is considerably more

dispersed and far less accurate. Moreover, in order to effectively calculate the standard deviation, the formula for acceleration is rather beneficial. This formula uses the variables V, for velocity, and T for time. The formula for determining the average acceleration: A avg = �� The formula for determining the standard deviation: ( −µ ) σ = Σ �� 2 Finally, as stated in the Laboratory Guide - Physics the measured values should be presented in the format of, µ ± σ , µ being the mean, and σ being the standard deviation. The uncertainty displays the best estimate of how far the experimental quantity may be compared to its “true value” in this case, in contrast with the 9.8 m/s 2 norm for the free-fall acceleration g. A broad replication of the experiment is necessary. This is because repeating an experiment enables researchers to compute the variance of the data, which may contain any remaining inaccuracies, as well as to enhance the accuracy and trust of the results. Procedure Given that there were four steps in this experiment's method, it was fairly cohesive. Using the menu bar in the upper left corner, which included a sign for the Logger pro interface, the experiment's first step was to validate that the device and system were correctly configured. The motion sensor was also set, and the cart was ready to be installed. The understanding of the system, the acquisition of data, and the types of data that were being acquired were all examined during this phase. The cart was positioned at the top of the incline in the second step, and the application began collecting data by hitting the "collect" button while concurrently displaying two graphs. In order to produce a decent run, this step was modified and performed numerous

times, resulting in a constant slope on the velocity vs. time graph during the cart's motion. The perfect run was selected, recorded, and step two was performed two more times as the experiment called for 3 runs per angle. In order to compute for g on the inclined plane, measurements were taken into account in the fourth stage. Moreover, the incline's length and both endpoints for height were documented. Thereafter, steps 2-3 were repeated four additional times for new inclinations and angles, and step 4 was performed four more times, documenting each changed height. Results and Calculations The following calculations and illustrations were carried out with the intention of simplifying and organizing all recorded data with the intent of displaying the true effects as well as the value of gravity on the inclined surface when acting on a rapidly moving object. Firstly, using the sample calculations below, the values of the angle of inclination were calculated using the inverse sine function and the differences in height. Angle 1 Angle 2

Angle 3 Angle 4 Angle 5

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