1. a)Use Newton’s 2nd law to show how the spring force balances the weight of a
ID: 2037724 • Letter: 1
Question
1. a)Use Newton’s 2nd law to show how the spring force balances the weight of a mass hanging on the spring. For your equation use the following variables: Mass hanging on the spring, mhang, the acceleration due to gravity, g, displacement of the spring in the vertical direction, ?y, and k for the spring constant.
b) For our experiment, we will change the mass hanging on the spring, mhang, and measure the displacement, ?y, after the spring achieves equilibrium. The spring force will balance the force of gravity acting on the mass hanging on the spring. We will plot our results of changing mhang, and measuring ?y. We will use a linear fit to find the spring constant, k. If you are confused about this, refer to Using graphical analysis to compare theory to experiment, in the Introduction. In order to find the relation between the slope and the spring constant we will need to answer the following questions:
I. Which variable in your equation from the previous question is the dependent variable? Would this be plotted on the x or y-axis?
II. Which variable in your equation is the independent variable? Would this be plotted on the x or y-axis?
III. Rearrange your equation from the previous question to match the equation of a line, y = mx+b
IV. Based on your answer to part c, what do you expect the y-intercept to be?
V. Based on your answer to part c, what is the slope m, in your equation? Solve for the spring constant k, in terms of the slope m.
Explanation / Answer
Let us consider two instances, (making the assumption for now that the force response for spring extension is linear. )
when mass is m1 , the extension was y1
when mass is m2 . the extension was y2
y is the dependent variable
m is the independent variable
(y1-y2)/((m1-m2)g) = slope
from y = mx +b
y = (y1-y2)/((m1-m2)g)*m +b
we would observe that b = 0
so,
y = (y1-y2)/((m1-m2)g)*mg
thus here , (y1-y2)/((m1-m2)g) = 1/k = 1/(spring constant)
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