Linear kinematics lab report

Name: Date: Lab #1: Linear Kinematics INTRODUCTION In this experiment you will attempt to reproduce Galileo's results using the inclined plane. You will test three hypotheses relating to motion on an incline. You will learn to draw a "best fit" or regression line of experimental data. You will discover that reaching conclusions about motion is not as easy as it seems at first. Although you will be using an electronic stopwatch, it is not much more accurate than Galileo's water clock. Galileo designed experiments to study accelerated motion using the inclined plane. His reasoning suggested that objects rolling down a ramp behaved similarly to objects in freefall so that he could understand freefall by studying ramps. This experiment is designed to reproduce a portion of Galileo's experiments. Galileo performed many more trials than you will, but did not have the sophisticated tools that you have to analyze the data. He deduced that an object which is uniformly accelerated will travel a greater distance in each successive time interval such that the distance traveled is directly proportional to the square of the time. He also discovered that the speed of a falling object depends only on the height from which it falls. One of Galileo's contributions to the experimental method was the idea of holding one or more variable constant while noting the effect when another variable is changed. In this lab you will need to determine whether or not a graph expresses a linear relationship. To do this you must draw what is known as a "best fit" straight line, also called a "regression line". The purpose of the graph is to visually display relationships which may not be apparent from data tables. Experimental errors which are always present may obscure the relationships. The best fit line averages out the errors. There are ways of calculating a regression line. You can find the formula in any statistics text. Most of the time an "eyeball" line will suffice. Many computer graphing software programs such as Excel will draw a regression line for you. The software will quickly draw the line and calculate its slope, intercept, and regression coefficient. The regression coefficient is used to determine how nearly the points fall on a straight line, or how nearly linear they are. A perfect correlation will have a regression coefficient of R = 1.000 . . . Normally in the physical sciences we would like to have a "confidence level' of 0.01 or better. That means that a coefficient of R = .990 or higher gives us the confidence to say that a relationship is linear within a margin of tolerable error. Without computer software you will need to draw the lines "by hand" and then make a judgement about whether the points are "linear". This judgement depends upon the nature of the experiment and how far you are willing to go in saying the relationship is linear. In other words, "how close is close enough"? The answer depends on your confidence and your judgement. 1|Page Here are two examples of graphs. The regression line has been drawn for each by the computer, but the regression coefficients have been left out for now. Clicking on the graph will give a full set of statistics for each graph so you can see how the numbers relate to your own judgement. The easiest way to draw the best fit line is to enter the data into the computer and let the software do the work. If you don't have the software or don't know how to use it you can still estimate the regression line. Imagine that the points enclose an area, then cut that area in half. If you use a ruler to draw the line you can move it around until you find a place where approximately half the points are on each side of the line. Here is the d vs. t graph with the imaginary area outlined. The more linear the data, the narrower the area and the easier it is to draw the line. Here is the d vs. t2 graph with the imaginary area outlined. In this experiment there are FOUR VARIABLES. 1. The distance along the ramp which the balls roll. 2|Page 2. 3. 4. The steepness of the incline which is measured by the ratio of height to length of the ramp. The height from which the ball is released on the ramp. The time required for the ball to roll a certain distance down the ramp. NOTES ON DISTANCE AND TIME MEASUREMENT Measuring distance and time require different skills as well as different instruments. There are unique problems associated with each type of measurement. You should be able to make distance measurements to one digit more than the least count of the meter stick or ruler. Typically this will be 0.1 mm.(0.01 cm or 0.001m.) on a ruler with a least count of 1 mm. Try to estimate the decimal fraction "between the mm. marks" on the ruler. Be sure to measure and record all data to the correct number of significant figures. Time measurements require coordination between the event and the timer in a different way because an event happens only once in time. You get only one chance at a time measurement (not counting video tapes and other recordings.) It is best to use a "starting gate" to avoid imparting to the can any uphill or downhill motion. The starting gate is a pencil or small ruler which holds the can in place, to be lifted when time starts. Think of how the gates at a parking garage operate.