an engineer wishes to determine the spring constant of a helical sprin. she fixe

Question

an engineer wishes to determine the spring constant of a helical sprin. she fixes the top end of the spring to a lab stand and hangs enough weights from 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 63.5cm to 52.6cm when she adds a lab weight whose stamped value is 400g. the uncertainty from the stamped weight is 2%.

1) What is the best estimate of the change in length of the spring when the slotted weights are added?(in cm)

2) Since we are using a simple meter stick, it is reasonable to assume an error of about + or - 0.05cm in any length of measurement. What is the uncertainty of the change in length? (in cm)

3) What is the best estimate for the force exerted on the bottom of the spring by the slotted weight in N?

4) What is the uncertainty of this force, in N?
5) What is the best estimate of the spring constant? (in N/cm)

6) What is the uncertainty in the value of the spring constant? (in N/cm)

Explanation / Answer

a)
x = 63.5 - 52.6 = 10.9
For each 400g weight added the spring is expected to stretch
by 10.9cm.


b)
Since there is uncertainty of the weight is 2% the total uncertainty is
unc = 0.02 + 0.05 = 0.07 cm

c)
F = mg = 0.4kg * 9.81m/s^2 = 3.924 N

d)
F(unc) = 3.924 * 0.07 = 0.275 N

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