Copy of Physics Lab 2

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University of Maryland, College Park *

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131

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Mechanical Engineering

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Apr 3, 2024

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pdf

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Introduction: Human bodily fluids have resistive forces that act on them as cells travel throughout the bloodstream. For this week's lab on analyzing the motion of objects through fluids, we tested the resistive forces acting on a model in order to determine the terminal velocity. In the experiment, we represented bacteria and red/white blood cells moving across the bodily fluids as a marble that goes through fluid resistances which in our lab model we represented as soap. The fluid-to-fluid friction force or viscosity was used in order to see the amount of force the cell will have to exert to continue moving through the viscous fluid. In our first model, we used the marbles and dropped it into the fluid at different angles to calculate the acceleration. Using this we determined if the forces acting on the marble are drag force or viscous force. The second model analyzes the impact of resistive forces and velocity on different numbers of coffee filters falling from the same height through the air. Procedure: In this week’s experiment, we gathered data to determine how viscous forces affected terminal velocity. In doing so, we created a model by holding a cylinder filled with liquid soap at 5 different angles and dropping a marble into the liquid soap. We held the cylinder at angles of 30°, 45°, 60°, 75°, and 90° and used a protractor to measure our angles correctly. As we dropped the marble into the soap, we recorded our process with the computer camera on the Virtual Dub software until the marble hit the bottom. Afterwards, we uploaded our recordings to ImageJ, we manually tracked our videos using video capture. We measured our distances in intervals of 3 cm based on the graduation marks on our graduated cylinder. This also allowed us to see the seconds it took for our marble to travel through each interval. From this, we were allowed to create tables consisting of time, distance traveled, and velocity. Also we used the other group's data in order to figure out the terminal velocity of the coffee filter and graphed the data based on their observed solutions and data collected. Model:

Figure 1: Free Body Diagram of the model used in experiment Our free body diagram illustrates that the forces acting on the marble include, gravity (mg), the resistive force caused by the drag or viscous force acting on the marble by the fluid in which the marble is falling in, and the normal force of the side of the cylinder propping the marble up. Using this free body diagram, we were then able to determine the equation F net = F resistive - mg(sin(θ)). Since our marble reaches a terminal velocity v t , by nature it implies that at v t acceleration is 0. Given the nature of the marble in the cylinder and the coffee filter scenarios, we determined that in the marble in the cylinder scenario, the viscous force is predominating and the drag force is largely negligible. In the coffee filter scenario, the reverse is true. The drag force is predominating, and the viscous force is largely negligible. As a result, this can lead to the following two equations, v t = to determine viscous force and to ?𝑔 6πµ? ?𝑖?(θ) 𝑣 ? 2 = 2?𝑔 𝐶ϱ𝐴 𝑁 determine drag force. Based on our scenario in which the marble falls through the cylinder, and therefore the viscous is dominant, the sine value of the angle at which the cylinder is titled affects the terminal velocity. In the coffee filter scenario, the number of filters and the resulting mass is the primary independent variable affecting the terminal velocity. Experimentally, the terminal velocity can be seen when the speed no longer changes, ipso facto of the term, terminal velocity. Data: Figure 2: Sin(angle) vs Terminal Velocity Angle sin(θ) Terminal Velocity (cm/s) 90° 1 3.822920473 75° 0.9659 2.196735727 60° 0.866 1.008008074

45° 0.707 0.583169888 30° 0.5 0.384261343 Figure 3: Sin (θ) vs. Corresponding Terminal Velocity Graph Figure 4: Terminal Velocity for Coffee Filters Figure 5: Graph for Number of Filters vs. Terminal Velocity Number of Coffee Filters Avg Terminal Velocity (cm/s) (Avg Terminal Velocity) 2 (Cm/s) 2 3 7.916 cm/s 62.663056 (cm/s) 2 5 10.02 cm/s 100.4004 (cm/s) 2 7 10.773 cm/s 116.057529 (cm/s) 2 9 11.359 cm/s 129.026881 (cm/s) 2 11 12.02 cm/s 144.4804 (cm/s) 2

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