Chapter 16: Oscillatory Motion and WavesContent check — College Physics, Chapter 16: Oscillatory Motion and Waves

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?

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?

Engineering Application

Each piston of an engine makes a sharp sound every other revolution of the engine. (a) How fast is a race car going if its eight-cylinder engine emits a sound of frequency 750 Hz, given that the engine makes 2000 revolutions per kilometer? (b) At how many revolutions per minute is the engine rotating?

As usual, the acceleration due to gravity in these problems is taken to be $g=9.80\text{m}/{\text{s}}^2$, unless otherwise specified.

What is the length of a pendulum that has a period of 0.500 s?

As usual, the acceleration due to gravity in these problems is taken to be $g=9.80\text{m}/{\text{s}}^2$, unless otherwise specified.

What is the period of a 1.00-m-long pendulum?

As usual, the acceleration due to gravity in these problems is taken to be $g=9.80\text{m}/{\text{s}}^2$, unless otherwise specified.

The pendulum on a cuckoo clock is 5.00 cm long. What is its frequency?

As usual, the acceleration due to gravity in these problems is taken to be $g=9.80\text{m}/{\text{s}}^2$, unless otherwise specified.

(a) A pendulum that has a period of 3.00000 s and that is located where the acceleration due to gravity is $9\text{.}\text{79}{\text{m/s}}^2$ is moved to a location where the acceleration due to gravity is $9\text{.}\text{82}{\text{m/s}}^2$. What is its new period? (b) Explain why so many digits are needed in the value for the period, based on the relation between the period and the acceleration due to gravity.

As usual, the acceleration due to gravity in these problems is taken to be $g=9.80\text{m}/{\text{s}}^2$, unless otherwise specified.

(a) What is the effect on the period of a pendulum if you double its length?

(b) What is the effect on the period of a pendulum if you decrease its length by 5.00%?

As usual, the acceleration due to gravity in these problems is taken to be $g=9.80\text{m}/{\text{s}}^2$, unless otherwise specified.

At what rate will a pendulum clock run on the Moon, where the acceleration due to gravity is $1\text{.}\text{63}{\text{m/s}}^2$, if it keeps time accurately on Earth? That is, find the time (in hours) it takes the clock’s minute hand, which on Earth makes one revolution per hour, to make one revolution on the Moon.

As usual, the acceleration due to gravity in these problems is taken to be $g=9.80\text{m}/{\text{s}}^2$, unless otherwise specified.

If a pendulum-driven clock gains 5.00 s/day, what fractional change in pendulum length must be made for it to keep perfect time?

The length of nylon rope from which a mountain climber is suspended has a force constant of $1.40\times {10}^4\text{N/m}$

(a) What is the frequency at which he bounces, given his mass plus and the mass of his equipment are 90.0 kg? Ignore the change in gravitational potential energy after the cord begins to stretch.

(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? Hint: Use conservation of energy.

(c) Repeat both parts of this problem in the situation where twice this length of nylon rope is used.

Engineering Application

Near the top of the Citigroup Center building in New York City, there is an object with mass of $4\text{.}\text{00}\times {\text{10}}^5\text{kg}$ on springs that have adjustable force constants. Its function is to dampen wind-driven oscillations of the building by oscillating at the same frequency as the building is being driven—the driving force is transferred to the object, which oscillates instead of the entire building. (a) What effective force constant should the springs have to make the object oscillate with a period of 2.00 s? (b) What energy is stored in the springs for a 2.00-m displacement from equilibrium?

Medical Application

Ultrasound of intensity $1\text{.}\text{50}\times {\text{10}}^2{\text{W/m}}^2$ is produced by the rectangular head of a medical imaging device measuring 3.00 by 5.00 cm. What is its power output?

Astronomy Application

Energy from the Sun arrives at the top of the Earth’s atmosphere with an intensity of $1.30{\text{kW/m}}^2.$ How long does it take for $1.8\times {10}^9\text{J}$ to arrive on an area of $1\text{.}00{\text{m}}^2$?