Question

I need help finding the spring constant and the elastic pe:

Table 1	Force (N)	Top Spring Position(m)	Bottom Position(m)	Elongation (m)	Elastic PE(J)
Data Point 1	0.3	0.097	0.130	0.033
Data Point 2	0.8	0.104	0.141	0.037
Data Point 3	1.2	0.111	0.150	0.039
Data Point 4	1.6	0.118	0.161	0.043
Data Point 5	2.0	0.125	0.173	0.048
Data Point 6	2.4	0.132	0.184	0.052
Data Point 7	2.8	0.139	0.195	0.056
Data Point 8	3.0	0.146	0.204	0.058
Data Point 9	3.5	0.153	0.213	0.060
Data Point 10	4.0	0.160	0.230	0.070

Answer 1

as seen from the plot, plot of force bs distance is linear in the middle region.

so spring constant can be found approximately by taking its slope.

slope=(3-1.6)/(0.058-0.043)=93.33 N/m

Answer 2

force elongation PE

0.3000000 0.0330000 0.0049500
0.8000000 0.0370000 0.0148000
1.2000000 0.0390000 0.0234000
1.6000000 0.0430000 0.0344000
2.0000000 0.0480000 0.0480000
2.4000000 0.0520000 0.0624000
2.8000000 0.0560000 0.0784000
3.0000000 0.0580000 0.0870000
3.5000000 0.0600000 0.1050000
4.0000000 0.0700000 0.1400000