Lab 4.2 Terminal Velocity (1)

A.M.D.G. Lab 4.2 Terminal Velocity NAME: DATE: PERIOD: When you solve physics problems involving free fall, often you are told to ignore air resistance and to assume the acceleration is constant and unending. In the real world, because of air resistance, objects do not fall indefinitely with constant acceleration. One way to see this is by comparing the fall of a baseball and a sheet of paper when dropped from the same height. The baseball is still accelerating when it hits the floor. Air has a much greater effect on the motion of the paper than it does on the motion of the baseball. The paper does not accelerate very long before air resistance reduces the acceleration so that it moves at an almost constant velocity. When an object is falling with a constant velocity, we prefer to use the term terminal velocity , or v T . The paper reaches terminal velocity very quickly, but on a short drop to the floor, the baseball does not. Air resistance is sometimes referred to as a drag force . Experiments have been done with a variety of objects falling in air. These sometimes show that the drag force is proportional to the square of the velocity. The direction of the drag force is opposite to the direction of motion. Mathematically, the drag force can be described using F drag = – cv 2 . The constant c is called the drag coefficient and depends on the size and shape of the object. When falling, there are two forces acting on an object: the weight, mg , and air resistance,– cv 2 . At terminal velocity, the downward force is equal to the upward force, so mg = cv 2 . Since g and c are constants, the terminal velocity is affected by the mass of the object. Rewriting the equation to solve for v T 2 yields ࠵? " # = ࠵? ࠵? ࠵? In this experiment, you will measure terminal velocity as a function of mass for falling coffee filters and use the data to determine the slope of the graph. Materials Coffee filters Mass Balance Meter stick Video camera Computer with video analysis software Procedure 1. Measure the mass of a coffee filter and record it on the data table. 2. Record a video of the falling coffee filter, observing the rules for video analysis: meter stick in the frame, motion perpendicular to the camera axis, drop from head height and record to the ground. 6 11/16/23 Eddie Elias, Jones Harrison, Carter Bruns 11-16-2023 6

3. Repeat step #2 for 2, 3, 4, 5 and 15 coffee filters. Be sure to name your videos with the number of filters since it will be difficult to determine afterward. Analysis 1. Use either Logger Pro or Video Physics software to analyze your videos. You will want to find the terminal velocity of each stack of filters and record that value in the data table. The easiest way to find the terminal velocity is to make a linear regression line on the position vs time graph and adjust the endpoints of the range to the linear portion of the data. The slope of this regression line will be the terminal velocity. Fill in the column with the square of the terminal velocities. 2. Open a blank Logger Pro file and enter the V T 2 in the x column and the mass values in the y column for the first 5 data points (coffee filters 1-5). 3. Place a linear regression line over the data and record the slope of this regression line. 4. Use the slope of the regression line to predict the terminal velocity of a stack of 15 coffee filters. 5. Do video analysis of your last video (15 filters) and determine the terminal velocity using the same procedure in step 1 above. 6. Compare the predicted terminal velocity to the actual terminal velocity for the 15 filters by calculating a % error. Try to explain the discrepancy. Data and Calculations Trial # of filters mass V T V T 2 1 1 2 2 3 3 4 4 5 5 6 15 Slope of V T 2 vs m graph = ______ Predicted value for the V T for 15 filters = _________ Measured value of V T for 15 filters = ________ Percent Error = ________ 11.3 g 0.7 g 2.6 g 3.3 g 4.0 g -1.01 -2.01 2.0 g -2.01 -2.03 -2.44 1.02 4.04 4.04 4.12 5.95 -3.49 12.18 -3.49 -3.48 g -3.49 0.2874%