Problem

A block of wood of mass 55.0 g floats in a swimming pool, oscillating up and down in simpl...

A block of wood of mass 55.0 g floats in a swimming pool, oscillating up and down in simple harmonic motion with a frequency of 3.00 Hz.

a) What is the value of the effective spring constant of the water?

b) A partially filled water bottle of almost the same size and shape as the block of wood but with mass 250. g is placed on the water’s surface. At what frequency will the bottle bob up and down?

Step-by-Step Solution

Solution 1

Step #1 of 6

THINK:

To find the spring constant, we have to relate the mass and frequency.

Step #2 of 6

RESEARCH:

The angular frequency is given by

And frequency is

Step #3 of 6

SIMPLIFY:

The spring constant can be expressed as

The new frequency can be expressed as

Step #4 of 6

CALCULATE:

(a) Spring constant can be calculated as

Step #5 of 6

(b) Frequency of the bottle bob can be calculated as

Step #6 of 6

ROUND:

The result should be rounded to three significant figures.

a) The spring constant

b) The frequency is

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Solutions For Problems in Chapter 14

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