The question
Name: ______________________ Date: ____________ Find a spring constant from launch heights (10 points)
Experimental setup
A vertical spring launcher
A toy launcher holds a vertical spring with a light platform on top. A student places a 0.050 kg ball on the platform, pushes it down to compress the spring by x, and releases it. The ball flies straight up and reaches a greatest height h above its launch point (its position with the spring compressed). The student wants to determine the spring constant k. Air resistance is negligible.
| Compression x (m) | Greatest height h (m) |
|---|---|
| 0.010 | 0.027 |
| 0.020 | 0.098 |
| 0.030 | 0.236 |
| 0.040 | 0.401 |
| 0.050 | 0.645 |
(a) Describe a procedure the student could use to collect the data in the table. Name each quantity measured and the equipment used to measure it, and describe what the student could do to reduce experimental uncertainty. [3 points]
(b) Indicate what quantities the student should graph to produce a straight line that could be used to determine k, and explain how k could be found from the graph. [2 points]
(c) On the grid, plot the data points for the quantities you indicated in part (b). Clearly scale and label the axes, including units. Draw a straight line that best represents the data. [3 points]
(d) Calculate the spring constant k using your best-fit line. Use g = 9.8 m/s². [2 points]