1. A bathroom spring scale obeys Hooke’s law and is depressed 0.750 cm by its maximum load of 120 kg. What is the springs effective force constant?
2. Fish are hung on a spring scale to determine the mass (most fishermen feel no obligation to report the mass truthfully). (a) What is the force constant of the spring in such a scale if it 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?
3. A stroboscope is set to flash every 8.00 x 10^(-5) s. What is the frequency of the flashes?
4. A spring has a length of 0.200 m when a 0.300 kg mass hangs from it, and a length of 0.750 m when a 1.95 kg mass hangs from it. (a) Draw a graph of force versus length (i.e. length on the horizontal axis). As always, use graph paper for accurate graphs. (b) What is the force constant of the spring? (c) Use your (very accurate and readable) graph to find the unloaded length of the spring.
5. The length of nylon rope from which a mountain climber is suspended has a force constant of 1.40 x 10^4 N/m. (a) What is the frequency which which he bounces, given his mass plus equipment to be 90.0 kg? (b) How much would this rope stretch to break the climber’s fall, if he free-falls 2.00 m before the rope runs out of slack? Be careful on this. You will use conservation of energy, but here you have two kinds of potential energy (that of gravity and that of the “spring”.) Draw “before” and “after” diagrams to show what is happening. The solution will involve a quadratic equation. (c) Repeat both parts of this problem in the situation where twice this length of nylon rope is used.
6. Pendulum clocks are made to run at the correct rate by adjusting the pendulum’s length. Suppose you move from one city to another where the acceleration of gravity is slightly greater, taking your pendulum clock with you. Will you have to lengthen or shorten the pendulum to keep the correct time, other factors remaining constant? Explain.
7. A Foucault is just an ordinary pendulum, but very large, so that it will oscillate for a very long time after set in motion. It was invented to demonstrate that the Earth is rotating: the plane of swing of the pendulum slowing rotates relative to the Earth’s surface. (A) A typical Foucault pendulum has a length of 15.0 m and a pendulum bob of mass 20.0 kg. What is the period of such a pendulum? (B) If the pendulum were oscillating with an amplitude of 3.0 degrees, what would be the total energy of the system? (Hint: what is the maximum change in height of the bob?)
9. When a 20-kg child stands in the middle of a trampoline, the surface of the tramp is depressed by 0.40 m. (Assume that the upward force of the trampoline acts like a spring, varying linearly with distance from its upstretched position.) (A) If the child begins oscillating up and down with some small amplitude, what is her frequency of oscillation? (B) If the amplitude of oscillation is 0.20 m, what is the total mechanical energy of the child + trampoline system?
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