In an experiment similar to the one you did in lab, the following data was recor

Question

In an experiment similar to the one you did in lab, the following data was recorded for a spring obeying Hooke's Law. After a careful inspection of the data, formally report your best estimates for the spring constant k in N/m, and the equilibrium position r_e in meters. See the Excel sheet provided for a copy of this table. b) What was the linear correlation coefficient, R^2, for the data you used to find k and r_e? R^2 = (To 4 decimal places) c) As in lab, this 9.96 gram spring and an attached 81.76 gram brass cylinder is spun in a centripetal motion device. After the analysis, an experimental effective mass of system is found. m_eff, exp = 88.23 g. The spring is oddly shaped however, and we are not sure how much it contributes to the effective mass. We still assume theoretical effective mass is m_eff, acc = m_cyl + n = m_s where we want to find n. Perform a series of percent fractional errors scanning these possible n's: 0, 1/4, 1/3, 1/2, 2/3, 3/4, and 1. (You just need one sample calculation.) What seems to be the most likely value for n?

Explanation / Answer

ans (a)

For the mass spring system:

Applied weight w = k(r-re) = kr-kre ---(1)

where k is the spring constant and r is the extension.

This equation is of the form y=mx+b

Here, the sprign constant k= ( W2-W1)/ (r2-r1)

Choosing w2=24N r2=0.1700m and w1=20 N , r1=0.1439

we get: k =156.2567 N/m

Now using equ(i)

re= r- w/k

Using the data: r2=0.17 m , w2=24 kg and the calculated value of k, we get

re=0.17 - (24/156.2567)=0.0134 m

Ans (b)

From the graph: the coefficient of regression R2=0.6046

Ans (c)

Effective mass (actual) of the system is defined as : meff,acc= mCylin + n* ms, --(2)

Now percent fractional error= ( meff ,acc-meff,exp)/ meff,acc X100 % --(3)

Obeserved meff,exp= 88.23g --(4)

For the different values of n, meff,acc , are found from equ(2) and PFE are calculated

n meff,acc=81.27 +n*9.96 PFE

0 81.27 8.56

1/4 83.76 5.34

1/3 84.59 4.30

1/2 86.25 2.30

2/3 87.91 0.36

3/4 88.74 0.57

1 91.23 3.29

The likely value of n is 2/3

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