$2$ Measuring the Spring Constants

In this lab you will record and analyze a video of a puck attached to two springs on a flat table: you will use one large puck with a central peg, to which you will attach the springs from the two rails opposite each other lengthwise along the table. This two spring system $($with spring constants $\backslash ($ k$\_\{1\}\backslash )$ and $\backslash ($ k$\_\{2\}\backslash ))$ also obey's Hooke's law, providing a restoring force toward equilibrium. This means it effectively acts the same as a one spring system with spring constant $\backslash ($ k$=$k$\_\{1\}+$k$\_\{2\}\backslash ),$ but the individual spring constants $\backslash ($ k$\_\{1\}\backslash )$ and $\backslash ($ k$\_\{2\}\backslash )$ need to first be measured.

Energy conservation is an incredibly useful tool for analyzing the motion of objects subjected to conservative forces, but if the object is in an equilibrium state then you must resort to thinking about the forces acting on it instead. To measure the spring constants accurately, you will be hanging known masses from the springs and measuring the stretched lengths.

Question $6$: For a mass $\backslash ($ m $\backslash )$ hanging from the end of a spring with spring constant $\backslash ($ k $\backslash ),$ what are all the forces acting on the mass? Draw a free body diagram and label the forces.

Question $7$: What is the net force $\backslash (\backslash$vec$\{$F$\}\_\{\backslash$text $\{$net $\}\}\backslash )$ when the mass is hanging motionless on the spring?

Question $8$: What is the statement of Newton's Second Law for this hanging mass? Assuming you know the mass and the you can measure the spring's extension length, solve for the spring constant $\backslash ($ k $\backslash ).$