A certain coiled wire with uneven windings has the property that to stretch it an amount s from its relaxed length requires a
force that is given by , so its behavior is different from a normal spring. You suspend this device vertically, and its
unstretched length is 25 cm.
(a) You hang a mass of 18 grams from the device, and you observe that the length is now 29 cm. What is b, including
units?
(b) Which of the following were needed in your analysis in part (a)?
(A) The Momentum Principle
(B) The fact that the gravitational force acting on an object near the Earth's surface is approximately mg
(C) The force law for an ordinary spring ( )
(D) The rate of change of momentum being zero
(c) Next you take hold of the hanging 18 gram mass and throw it straight downward, releasing it when the length of the
device is 33 cm and the speed of the mass is 5 m/s. After a very short time, 0.0001 s later, what is the stretch of the
device, and what was the change in the speed of the mass (including the correct sign of the change) during this short
time interval? It helps enormously to draw a diagram showing the forces that act on the mass after it leaves your
hand.
Section 4.8