In an experiment, students are to calculate the spring constant k of a vertical
ID: 1704471 • Letter: I
Question
In an experiment, students are to calculate the spring constant k of a vertical spring in a small jumping toy
that initially rests on a table. When the spring in the toy is compressed a distance x from its uncompressed
length L0 and the toy is released, the top of the toy rises to a maximum height h above the point of maximum compression. The students repeat the experiment several times, measuring h with objects of various masses taped to the top of the toy so that the combined mass of the toy and added objects is m. The bottom of the toy and the spring each have negligible mass compared to the top of the toy and the objects taped to it.
(a) Derive an expression for the height h in terms of m, x, k, and fundamental constants.
With the spring compressed a distance x = 0.020 m in each trial, the students obtained the following data for different values of m.
(b)
i. What quantities should be graphed so that the slope of a best-fit straight line through the data points
can be used to calculate the spring constant k ?
ii. Fill in one or both of the blank columns in the table with calculated values of your quantities,
including units
(d) Using your best-fit line, calculate the numerical value of the spring constant.
(e) Describe a procedure for measuring the height h in the experiment, given that the toy is only momentarily at that maximum height.
PLEASE HELP ME ASAP!!!
Explanation / Answer
a) spring potential energy is PE = 1/2 KX2
mgh = 1/2 kX2 and from that we get h = kX2/(2mg)
b) i You should really include all quantities so that you get a best fit line.
ii. You can calculate k using the forumla from A. use k = 2mgh/X2 to save time.
c)youd plot those points on the graph then draw the line.
d)and the line through will be K. itll be an almost horizontla line.
e) I'm lazy so I would say stick paper on the wall and stick a pen or maker or something on the top of it and set it so that when it is released it will mark the paper. Then measure the highest mark.
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