Calculating spring constant experientially with the methods of compression and collision (the question on the experiment is bolded in the description)

Question

In an experiment, the spring constant (k) was calculated by gathering data on force and displacement from a compression (Part 1) and a collision (Part 2).

In both parts, the spring constant (k) was found by dividing the force by the displacement, but Part 2 (collision) gave a much higher standard deviation. What are three reasons why this could be so?

Procedure of Part 1 (compression) and Part 2 (collision) detailed below for reference:

Procedure for Part 1 (compression)

1. Start recording data. Push the iOLab slowly toward the box by about a half-centimeter or so, and hold it steady for a couple of seconds.

2. Slowly release the pressure on the iOLab and let it return to equilibrium.

3. Using the selection tool, select the data where the spring is compressed to its maximum. Using Hooke’s law solve for k.

Repeat this procedure at least four times for five total values of k for the short spring. Find the mean k value of the data that you obtained, and find the standard deviation (σk) of that data.

Procedure for Part 2 (collision)

1. In this part of the experiment, we are going to roll the iOLab and spring and have it bounce off of the box.

2. Set the iOLab with wheels down and the spring facing the box about 10 cm away.

3. Practice pushing the device so that it rolls, hits the box and bounces backward in a straight line.

4. Once you have a good feel for it, make sure to zero your force sensor and record a single push and collision.

5. You will need to use the zooming function of the iOLab software to zoom in both the force and position graphs. If you do not zoom in enough, it will be very hard to read.

6. Use the selection tool to select the part of the force graph representing the collision. Write down the value of the force (Fy) at the very bottom of the graph.

7. On the position graph, note the position of the start of the collision ry(start), and the position when the collision is at its maximum force ry(max). ∆r = ry(max) − ry(start).

8. Once you have all of this data, you can find k by using Hooke’s Law: k = −F/∆r. Repeat this procedure at least four times for five total values of k for the short spring. Find the mean k value of the data that you obtained, and find the standard deviation (σk) of that data.

Answer 1

(1) Friction losses from the box and the ground that is if it is touching the ground.

(2) The impact is not completely elastic. Restitution coefficient of impact is not 1.0.

(3) There is variability in the start of position, that would be your ry variable