Question

the students correctly determine that the relationship between spring constant of the spring and the maximum stretch of the spring ( x ) is given by ( x=\frac{mu_{s} m g}{k} ), where ( mu_{s} ) is the coefficient of static friction between the block and the surface. the students create a graph with ( x ) plotted on the vertical axis. (c) i. indicate which measured or calculated quantity could be plotted on the horizontal axis to yield a linear graph whose slope can be used to calculate an experimental value coefficient of static friction ( mu_{s} ) between the block and the surface. you may use the remaining columns in the table, as needed, to record any quantities (including units) that are not already in the table. vertical ( x ) horizontal

Explanation:

Step1: Analyze the given formula

The formula is \(x=\frac{\mu_s mg}{k}\). We can rewrite it in the form \(y = mx + b\) (linear form). Here, if we consider \(x\) as \(y\) (vertical axis), then we need to express the formula in terms of a variable \(X\) (for the horizontal axis) such that \(x = (\text{slope})\times X\). From \(x=\frac{\mu_s mg}{k}\), if we let \(X=\frac{1}{k}\) (where \(k\) is the spring - constant), then \(x=\mu_s mg\times\frac{1}{k}\).

Answer:

Horizontal: \(\frac{1}{k}\) (where \(k\) is the spring - constant)