Experimental Design and LinearizationName: ______

The purpose of experimentation is to answer a scientific question using repeatable and controllable measurements. While you may be familiar with the scientific method, you may not know much about experimental design. Here are some guidelines that can help when designing an experiment:

  1. What question are you trying to answer?
  2. How can we answer it?
  3. What can we measure to answer it? (______)
  4. What are things that we can measure in physics?
  5. What is different between each experiment? (______)
  6. What needs to be the same between each experiment? (______)

Problem 1: Each of you should have a car design, unique from everyone else. As a group, what questions could you answer about your car design using experimentation?

Problem 2: Design a simple procedure that could be used to collect data to answer your question. Be sure to address what your independent, dependent and control variables are.

Problem 3: Collect data for your car and graph it on the axis below. What graphical shape does your data appear to follow?

Linearization

Since most of us are familiar with using the slope-intercept form of a line and finding the slope of a line it is usually easier to analyze linear data than any other. Unfortunately, not all physical data is linear. However, there are techniques that can help us translate non-linear data into linear data.

How to linearize data:

  1. Determine an equation that relates all of your experimental variables.
  2. Line up your equation from step 1 with the general equation for a line (y = mx + b).
  3. Match the variables from your equation with those in the equation for a line.
  4. y- variable: usually by itself on one side of the equation.
  5. b (y-intercept): anything being added to the end of the equation (can be zero).
  6. m (slope): all the constants (including variables that don’t change in your experiment)
  7. x- variable: everything else
  8. Calculate your new x and y variables and find the best-fit line.

Problem 4: The relationship between the distance traveled by an object on an inclined plane and the time traveled is given by the equation where Δx is the distance, a is the acceleration and t is the time. Using linearization, what variables should you graph to get a linear set of data?

Problem 5: What would the slope of your best-fit line tell you from the experiment? Does your y-intercept make sense?

Problem 6: Graph your linearized data.