A stone falls from rest to the bottom of a water well of depth d. The time t taken to fall is 3.0 ± 0.3 s. The depth of the well is calculated to be 30 m using d = at2. The uncertainty in a is negligible.
The diagram shows an experiment to measure the speed of a small ball falling at constant speed through a clear liquid in a glass tube.
There are two marks on the tube. The top mark is positioned at 15 ± 1 mm on the adjacent rule and the lower mark at 285 ± 1 mm. The ball passes the top mark at 2.50 ± 0.02 s and passes the lower mark at 4.50 ± 0.02 s.
The constant speed of the ball is calculated to be 135 mm s–1.
Which expression calculates the fractional uncertainty in the value of this speed?
The strain energy W of a spring is determined from its spring constant k and extension x. The spring obeys Hooke’s law and the value of W is calculated using the equation shown.
W = kx2
The spring constant k is 200 ± 1 N m–1 and the extension x is 0.040 ± 0.004 m.
What is the percentage uncertainty in the calculated value of W?