Question

Graphical analysis is commonly used to determine unknown physical properties. For quantities that are linearly proportional to each other, physicists often use the slope of the best‑fit line to a scatter plot in order to determine the proportionality constant.

A common physics lab experiment involves hanging different masses ?? from a spring of unknown spring constant ?. The resulting spring stretches Δ?? are then plotted versus the weight ??? of each hanging mass, where ? is the gravitational acceleration.

What is the algebraic expression for the slope of the resulting best‑fit line? Assume that the positive ?-direction is downwards

slope:

Answer 1

/ -AY ing Suppose corresponding readings of Extensions Ayi with weights mig are plotted as shown in the figuren. Ay, over y- anir and mig over x-anis than we plot a best fit straight line curve passing through The origin whose Slope = -Ayil mg Now, as per Hooke's lane force x extension og force =-k (endension) .. where ka spring factor So K = forte con hija 1984 al pochy hence in the curve, slope gives the resiprocal of spring factor " Slope = - A4 - spring facto