Physics 161 Lab 5, Elastic Constant of a Spring

Physics 161 Lab 5, Elastic Constant of a Spring

Objective In this experiment you are going to calculate the stiffness of a spring using two experiments and then compare the results of the two experiments.

Turn in There is no preliminary survey for this lab. The lab exercise for this lab will be due in one week after posting. The lab exercise can be accessed on Canvas by clicking the “Assignments” link on the front page.

Introduction When you stretch or compress a spring it wants to recover its equilibrium length. It fights against the force you just applied. The elastic force done by the spring is described by Hooke’s law

[1] Where the negative sign indicates that the force is in the opposite direction compared to the displacement direction, k is the elastic constant (or spring constant) of the spring, and is the displacement from its equilibrium position. The equilibrium position is the position of the end of the spring when there is no external force acting on it to make it stretch or compress. Imagine you hang a spring vertically. If you attach a mass at the bottom of the spring, this will stretch. Following Hooke’s law the displacement (amount stretched) is proportional to the force applied. In this particular case the force is the weight of the mass you attached to the spring (mg). If a mass is suspended by a spring and is not accelerating then Newton’s 2nd Law of Motion dictates that all upward forces balance all downward forces. Consider this and use Eq. [1] to solve for k and find its value by knowing the mass your attached to the spring, and measuring the displacement.

Task A: 1) Each spring has a hook on one end and a loop on the other end. You can use either the loop or the hook to hang the spring vertically so that masses can be attached to it. A couple of ways to do this: hang the hook over a coat hanger or tie a piece of string through the loop and then hang the loop of string on something like a door handle.

2) Measure the relaxed length of the spring and record value on a piece of paper. 3) Hang a mass that is less than 400 g from the spring and allow it to stretch out. A typical coffee cup is ~ 400 g.

4) Measure the new stretched length of the spring. 5) Repeat steps 3) and 4) for 9 additional masses. Try to find objects ranging in mass from ~400 to ~10 grams, as this will give you a good spread of data. Once this step is completed you will have 10 data points.

Task B: 1) Attach the second spring to the first one so that you have two vertically oriented springs from which you can hang masses from. 2) Do the steps 2), 3), 4) and 5) that you did in Task A, only this time the mass weight will be stretching two springs instead of one.

F = ! k "x

!x