Question

If the mass of a hanger were negelected when the graph of force vs displacement was plotted, what effect if any, would that have on the value of the slope, and hence the spring constant? Explain.

Answer 1

addition or ignoring the mass of hanger would result in the change of every value lying on the axis of the force to change by a constant amount = mg (m=mass of hanger, g= acceleration due to gravity). But since spring constant is a measure of change in displacement with respect to change in force, it will remain unchanged and so will be the slope.

For eg. when mass of hanger is considered let any two measurements be (x1,F1) and (x2,F2).

then slope=k=((F2-F1)/(x2-x1)).

now when mass of hanger is not considered measurements would be (x1,F1+mg) and (x2,F2+mg).

then slope=k=[{(F2+mg)-(F1+mg)}/(x2-x1)]=((F2-F1)/(x2-x1)). (same as before)