Names:___________________________________________________ Date:__________ Physics Period:________ Terminal Velocity Lab Objectives Determine how air resistance and mass affect the terminal velocity of a falling object. Determine the drag coefficient of a coffee filter. Background Often in physics discussions, you are told to ignore air resistance and to assume the acceleration is constant. In reality, air resistance causes objects not to fall indefinitely with constant acceleration. This is observed 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. 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 describe it with the term terminal velocity. The paper reaches terminal velocity very quickly, but on a short drop to the floor the baseball does not. Air resistance is often referred to as a drag force. The direction of the drag force is opposite to the direction of motion. Mathematically, the drag force can be described using Fdrag = -bv. The constant b is called the drag coefficient, and is dependent on the size and shape of the object. The variable v is the velocity of the object. When falling there are two forces acting on an object: the weight, mg, and air resistance, -bv. At terminal velocity, the downward force is equal to the upward force, so mg = -bv. Since g and b are constants, the terminal velocity is proportional to the mass of the object. 1 Procedure 1. Connect the motion sensor to the support rod, pointing down. Set it to wide beam. 2. Open DataStudio and select the motion sensor probe. Click Create an Experiment. Drag and drop Position over Graph to create a Position vs. Time graph. 3. Hold the coffee filter under the motion sensor. Click Start. Release the coffee filter. Practice until you achieve a nice, smooth graph. 4. The velocity of the coffee filter can be determined from the slope of the line on the Position vs. Time graph. At the start of the graph, there should be a region of increasing slope (increasing velocity), and then the plot should become linear. Since the slope of this line is velocity, the linear portion indicates that the filter was falling with a constant or terminal velocity during that time. Select that portion of your graph and click the Size to Fit button. Next select Fit, then Linear. Record the slope in your data table. 5. Repeat to fill the data table. Delete All Data Runs between trials. 6. Calculate Average Terminal Velocity. Calculate the Drag Force (Fdrag = mg). Data Table Number of Filters Mass (kg) Drag Force (N) Terminal Velocity Trial 1 (m/s) Terminal Velocity Trial 2 (m/s) Average Terminal Velocity (m/s) 2 3 4 5 7 9 2 Graph In our experiment, Fdrag was the independent variable. However, sometimes is it beneficial for analysis purposes to graph the independent variable on the y- axis. In Excel, create a scatter plot of Fdrag vs. Terminal Velocity Use the average terminal velocity. Since Terminal Velocity is to be on the x-axis, enter this data in column A. Include all the necessary elements: title, labeled axes with units, line of best fit (linear), equation and R2. Print your graph and staple it to this packet. Analysis Use your graph to determine the drag coefficient b. Here’s how: 1. The magnitude of drag force can be found with the equation: Fdrag = bv so, if you divide both sides of the equation by v, b = Fdrag v 2. The slope of your line of best fit is y or x Fdrag v 3. Therefore, the slope of your line is equal to b. Write your constant b including the correct units. ______________________ 3 Questions 1. What is the initial velocity of the coffee filter? 2. What is the acceleration of the coffee filter the instant it is dropped? 3. When the coffee filter reaches terminal velocity, what is the net force acting on it? 4. If there were no air resistance, how would the velocity of a falling coffee filter compare to that of a brick? 5. Draw a free-body diagram of a skydiver for the following situations. To the side of each diagram include the velocity, acceleration, and Fnet vectors. a. The instant she jumped out of the plane. She was in freefall. b. She reached terminal velocity. c. She opened her parachute. d. With her parachute open, she now reached a slower terminal velocity. 4