I need solution step by step. A student hangs masses on a spring and measures th
ID: 3171874 • Letter: I
Question
I need solution step by step.
A student hangs masses on a spring and measures the spring's extension as a function -of the applied force in order to find the spring constant k. Her measurements are: 200 300 400 500 600 700 800 900 Mass (kg Extension (cm) 5.1 5.5 5.9 6.8 7.4 7.5 8.6 9.4 There is an uncertainty of 0.2 in each measurement of the extension. The uncertainty in the masses is negligible. For a perfect s the extension AL of the spring will be re lated to the applied force by the relation kAL F, where F mg, and AL L- Lon and Lo is the unstretched length of the spring. Use these data and the method of least squares to find the spring constant k, the unstretched length of the spring Lo, and their uncertainties. Find x for the fit and the associated probability.Explanation / Answer
given
F= Y= K*X
SLOPE OF LINE = K = = (NXY - (X)(Y)) / (NX2- (X)2)
N= no of sample
mass F= mg =y extension =x XY X^2 200 2000 5.1 10200 26.01 300 3000 5.5 16500 30.25 400 4000 5.9 23600 34.81 500 5000 6.8 34000 46.24 600 6000 7.4 44400 54.76 700 7000 7.5 52500 56.25 800 8000 8.6 68800 73.96 900 9000 9.4 84600 88.36 SUM 44000 56.2 334600 410.64 k(N/cm)= 1610.357