Imagine the smoke rising from a small fire or a cigarette, at first the smoke will travel straight up in a linear manner (laminar flow) but then it begins to mix, swirl, and bellow, this is caused by the chaotic mixing and re-mixing of smoke with slightly different velocities and temperatures. For our experiment we look at how weight, size and shape of an object traveling through the air effects the acceleration of that object. Because the force of air resistance depends on whether laminar or turbulent flow is being experienced, we would expect to find accelerations that depended on not only weight but also on shape and size. Experimental Design Our setup included a motion sensor pointed straight up, placed on the floor. An object was released at about two meters above the sensor such that the sensor recorded the position of the object as it fell. Objects were chosen such that they reached terminal velocity within our data set. This data was sent to Attitudes on the computer where the acceleration could be calculated. Once the acceleration was found, we can use Newton’s 2nd Law (F=ma) and Terminal Velocity resistance)] to determine the forces acting on the object.
Our two models are defined with: Laminar Flow (for a sphere): F = 6 nor here n is viscosity, r is the radius of the sphere, and v is the relative speed of the sphere Turbulent Flow (for a sphere): p Cd rev where r and v are the same as above, p is the density of air, and Cd is the drag coefficient We also get, using Newton’s 2nd and Terminal Velocity: so, at V=Vt MGM=inner (for laminar flow) MGM” (1/2) art p Cd rev (for turbulent flow) Once we can predict the force values for each of these types of flow we can use the Reynolds number to find the ratio of laminar flow to turbulent flow: (p d where d is the diameter of the sphere, v is the relative velocity, p is the density of IR, and n is viscosity For Eerier turbulent flow primarily acts Procedure (past tense) Set up motion sensor Place motion sensor on the ground pointed straight up Make sure there is a 50 CM wide column of free space surrounding the motion sensor up from the floor. Include at least one test with a hand to make sure the motion sensor is tracking position. Measure Object Object should approximate a sphere Find object that you think will reach terminal velocity when dropped from about 2. Mm. Measure its circumference at the widest point use this to calculate the maximum radius Mass the object Run Tests Drop the object right above the motion sensor from a height of around 2. Mm.
Look at the data to see if the motion sensor recorded the full drop any movement side to side will cause the data to be confused Analyze Data Once a good data set is recorded, find the average slope of the position graph for the period where it seems the object reached terminal velocity the position graph should start out parabolic but then should transition to a line before it reaches the ground/motion sensor as it reaches terminal velocity. Record the radius, ass, and terminal velocity in your lab notebook Repeat Repeat steps 2-4 for the same object with 4 different masses tape one penny to the bottom most point each time to increase the mass Repeat steps 2-4 for different objects with 4 different radii Repeat steps 2-4 for a cone shaped object, vary the radii 4 times. Results and Analysis “This section will be a combination of data presented in tables or plots and a discussion of those results. One without the other isn’t going to work out.
You must present data in the form of plots or tables AND discussion of that data, referable keeping data and discussion nearby. ” “Plots and tables should be numbered and captioned. ” Conclusion “The first sentence is a broad summary of what you set out to do. This is followed up by a more detailed summary of results than that in your abstract (since that only hits on key results).