16.1 Hooke’s Law: Stress and Strain Revisited

Envision holding the end of a ruler with one hand and deforming it with the other. When you let go, you can see the oscillations of the ruler. In what way could you modify this simple experiment to increase the rigidity of the system?

If you apply a deforming force on an object and let it come to equilibrium, what happened to the work you did on the system?

Which of the following represents the distance (how much ground the particle covers) moved by a particle in a simple harmonic motion in one time period? (Here, A represents the amplitude of the oscillation.)

1. 0 cm
2. A cm
3. 2A cm
4. 4A cm

In the formula $F \textrm{ } = \textrm{ } - k x$, what does the minus sign indicate?

1. It indicates that the restoring force is in the direction of the displacement.
2. It indicates that the restoring force is in the direction opposite the displacement.
3. It indicates that mechanical energy in the system decreases when a system undergoes oscillation.
4. None of the above

Fish are hung on a spring scale to determine their mass (most fishermen feel no obligation to truthfully report the mass).

(a) What is the force constant of the spring in such a scale if it the spring stretches 8.00 cm for a 10.0 kg load?

(b) What is the mass of a fish that stretches the spring 5.50 cm?

(c) How far apart are the half-kilogram marks on the scale?

One type of BB gun uses a spring-driven plunger to blow the BB from its barrel. (a) Calculate the force constant of its plunger’s spring if you must compress it 0.150 m to drive the 0.0500-kg plunger to a top speed of 20.0 m/s. (b) What force must be exerted to compress the spring?

When an 80.0-kg man stands on a pogo stick, the spring is compressed 0.120 m.

(a) What is the force constant of the spring? (b) Will the spring be compressed more when he hops down the road?