To find the equation of the line of best fit for the relation between weight and stretch of a spring, you can apply Hooke's Law, with the slope of the line representing the spring constant. Convert the given measurements to standard units and use least squares regression to find the line.
To determine the equation of the line of best fit for the data provided by the student measuring the stretch of a spring with hanging objects of different masses, we first need to understand that this is an application of Hooke's Law, which states that the force (F) needed to extend or compress a spring by some distance (x) is directly proportional to that distance. In mathematical form, Hooke's Law is expressed as F = kx, where k is the spring constant, and x is the extension or compression of the spring.
The student's data can be modeled as F = kx, where the weight (mass × gravity) of the object is the force (in Newtons) and the stretch (in meters) is x. However, since the data is given with weight in grams and stretch in centimeters, we should convert weights to Newtons (1g = 0.001kg, and weight = mass × 9.8m/s² for Earth's gravity) and stretches to meters for consistency and to find k. After converting the data and plotting it on a graph, the line of best fit can be determined using statistical methods, such as least squares regression.
This line will provide the spring constant as the slope of the line and will result in an equation of the format y = mx, where m is the value of k, and y is the stretch in response to force x.