An engineer wishes to determine the spring constant of a helical spring. She first puts enough weights on the spring to pull the coils apart. Using a simple wooden meter stick with millimeter marks, she finds that the elevation of the end of the spring changes from 63.5 cm to 52.6 cm when she adds a lab weight whose stamped value is 400 grams. The uncertainty of the stamped weight is 2%. Take g = 9.81 m/s2 with negligible uncertainty.
a) What is the best estimate of the change in length of the spring when the slotted weights are added?
b) Since we are using a simple wooden meter stick, it is reasonable to assume an error of about 0.05 cm in any length measurement. What is the uncertainty of the change in length? (in cm)
c) What is the best estimate for the force exerted on the bottom of the spring by the slotted weight, in N?
d) What is the uncertainty of this force, in N?
e) What is the best estimate of the spring constant?
f) What is the uncertainty in the value of the spring constant?