Work and Kinetic Energy Lab Report

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Dec 6, 2023

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Work and Kinetic Energy Giang Nguyen October 30th, 2023 Professor 1301W, Professor: M. Marvin, TA: J. Gehrke Abstract The purpose of the experiment was to determine the coefficient of kinetic friction between a wood block and a plastic surface. It was conducted using a string and pulley system to attach the block to a hanging mass. The hanging mass would then be dropped at a certain height which would cause the block to move. The data collected yielded a mean value of 0.321±0.009 for the friction coefficient, which is relatively close to the literature value of the coefficient with margin of error. Introduction John the carpenter joined a competition to create the best desk for college students and is struggling on making the pull-out keyboard tray. He needs to find the coefficient of the kinetic friction between the plastic sliders and wood tray when they come in contact in order to find the perfect material that leads to a smooth operation of the keyboard tray. In order to calculate the coefficient, John must conduct a series of trials of the wood sliding on the plastic through a pulley system with a hanging force at different heights. Prediction If all the known forces on the wood block are known, the coefficient of friction can be found with a series of equations. Figure 1: Free body diagram of the wood block on a plastic surface attached to a hanging mass. “m” is the mass of the corresponding block, “g” is gravity, and “µ” is the coefficient of kinetic friction.

Shown in Figure 1 are all of the forces acting on the system. In this experiment the potential energy of the system is the gravitational potential energy of the hanging mass which is shown by Equation (1) where m is the mass, g is the acceleration due to gravity and h is the height. The Law of Conservation of Energy states that energy cannot be created or destroyed so the potential energy from the hanging mass when it gets dropped then transfers to the wood block through the pulley and string, causing it to move and turn into kinetic energy. The principle of kinetic energy states that it is proportional to the mass times the square of the velocity, shown in Equation (2). The two equations can then be combined since they have (1) 𝑃𝐸 = 𝑚 2 𝑔ℎ (2) 𝐾𝐸 = 1/2 𝑚𝑣 2 the same amount of energy, however the coefficient of friction must be included in the equation since there is a force resisting against the wood block, so it would then be rearranged into Equation (3). (3) 1 2 (𝑚 1 𝑚 2 )𝑣 2 + 𝜇𝑚 1 𝑔ℎ = 𝑚 2 𝑔ℎ Procedure The experiment was set up by using a wooden block with weights on it that measured 0.375±0.005 kg and attaching it to a string. On the other side of the string was a hanging object that measured 0.170±0.005 kg which was placed hanging off the side of a table with a plastic surface. The string was then placed into a pulley system with each mass on the opposite side. A clear diagram of the system is shown through Figure 1. For each trial, the hanging mass was dropped at different heights of 0.35±0.05 m, 0.45±0.05 m, 0.50±0.05 m, and 0.55±0.05 m and the motion of the block was recorded through the video analysis software, Vernier. Through the software, the position, velocity and time can be recorded throughout the procedure. The maximum velocity that the wooden block reached was obtained to plug into Equation (3) in order to determine the coefficient. Errors that would need to be considered upon this experiment are measurement errors which were included with the mass having an uncertainty of ±0.005 kg and ±0.05 cm for the heights due to constant

change that could occur over the course of the trial. In addition to the precision of the meter stick that the video was scaled to as well as the data points that were taken at every 2 frames of the video. Analysis Figure 2: The velocity vs time graphs of each trial at its corresponding height of where m 2 was dropped. The tip of the graph is the wood block’s maximum velocity which was recorded. Table 1: Measured Values of the Pulley System Maximum Velocity (m/s) Kinetic Energy (J) Height (m) Gravitational Energy (J) Coefficient of Friction “ 𝝁 k ” 0.776 0.164 0.35 0.583 0.325 0.913 0.227 0.45 0.749 0.316 0.944 0.243 0.50 0.833 0.321 0.983 0.263 0.55 0.916 0.323 Figure 1 contains all of the graphs collected from the experiment of each trial and depicts the velocity of the wood block over time. The tip of the graph shows when the hanging block reached the ground and the wooden block began to decelerate. The maximum velocity that the block reached was recorded into Table 1 which includes all of the data and values needed in order to calculate the friction coefficient. Each value

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was plugged into Equation (3) and the corresponding coefficient of friction was calculated and recorded into the table as well. The mean of the values of coefficients obtained was calculated in order to obtain the general coefficient of kinetic friction of the wood block and plastic surface. The friction coefficient was determined to be 0.321±0.009 which is roughly similar to the literature value range of 0.30 to 0.50 for dry wood against hard smooth surfaces (Aira, J.R; Arriaga, F.; Íñiguez-González, G.; Crespo, J (2014). It is hard to compare with a literature coefficient value as there are many types of wood and plastic that could cause varying ranges of friction. The results align with the literature value, in either direction of the uncertainty value. Being able to determine the coefficient of friction is important as friction is a concept that is constantly occurring. Whether it's pushing an object across the floor and the friction is needed in order to figure out how much force should be applied or in engineering where one must create brakes for cars, roller coasters, and wheelchairs to prevent accidents. The results from this experiment proves that with physics, with the application of different equations, a rough estimate of the friction coefficient can be obtained. Although the results agree with the stated literature value, there are some factors that could result in an inaccurate coefficient such as random error due to the video analysis software. If the meter stick shown in the video were inaccurately calibrated to be shorter than 1 m, then the block would appear to be quicker than it actually was, thus resulting in a faster velocity than the actual. For example, if the meterstick was miscalibrated to be 5% smaller than an actual meter, then the measured velocity would be increased by a factor of 5% compared to the actual. Conclusion The experiment was conducted in order to calculate the coefficient of kinetic friction between a wood block and a hard plastic surface. Through different trials, a mean value of 0.321±0.009 was obtained which aligns with the literature value range of 0.3o to 0.50. By obtaining this information, John can collect and compare the coefficients of kinetic friction of different materials in order to determine the best choice and win the competition.

Reference 1 J.R. Aira, F. Arriaga, G. Íñiguez-González, and J. Crespo, View of Static and Kinetic Friction Coefficients of Scots Pine (Pinus Sylvestris L.), Parallel and Perpendicular to Grain Direction | Materiales de Construcción (2014).

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