Question

For my experiment my line of best fit equation was y= 23.6x + 0.19. Compare the best-fit linear equation with Hooke’s law formula. I know this does not support Hooke's law because my y intercept needs to be zero, but what might be the limitations of the experiment and on possible causes of measurement uncertainty?

Answer 1

We have linear best -fit equation for Hooke's law:

In which the Y-values represent the force on the spring and X-values represent the spring displacement .

The slope of the linear best-fit line is:

The Y-intercept of the linear best-fit line is:

Therefore, the linear best-fit equation is:

We know Hooke's law is given as:

Comparing equations (1) and (2) gives the slope of the linear best-fit line is equal to spring constant:

Therefore, the experimental spring constant of the spring is .

The Y-intercept of the linear best-fit is , which indicates the initial force already acting on the spring. In real experiments, spring has some weight but in theory we neglect the spring weight itself. So this spring weight reflects in the form of Y-intercept in the experiment. To get accurate measurement, spring weight should be added to hanging mass, which possibly gives us Y-intercept zero.

Another reason for this uncertainty is measurement error. To minimize the uncertainty and get Y-intercept zero, possible care should be taken while taking measurements in the experiment.