Simple harmonic motion rise and fall of water

[thereddevils]

Homework Statement

The rise and fall of water in a harbour is simple harmonic. The depth of water varies between 5.0 m at low tide and 9.0 m at high tide. The time between sucessive low tides is 12 hours. A ship, which requires a minimum depth of 6.0 m approaches the harbour at low tide, how long the ship has to wait before entering the harbour?

Homework Equations

The Attempt at a Solution

A hint to start?

 

[Shivpal]

The time period of oscillations is given to you as 12hrs, the amplitude is (9-5)/2 = 2 meters, now for the tide to be at least 6m (minimum need for ship to pass), your oscillator must be 1m away from the lowest position moving toward the center.

 

[thereddevils]

The time period of oscillations is given to you as 12hrs, the amplitude is (9-5)/2 = 2 meters, now for the tide to be at least 6m (minimum need for ship to pass), your oscillator must be 1m away from the lowest position moving toward the center.

Thanks Shivpal, but i don get the meaning of this sentence.

'your oscillator must be 1m away from the lowest position moving toward the center.'

 

[thereddevils]

Thanks Shivpal, but i don get the meaning of this sentence.

'your oscillator must be 1m away from the lowest position moving toward the center.'

Never mind, i got it.

 

[rwisz]

I would approach this problem by first understanding the concept of simple harmonic motion. This type of motion is characterized by a periodic back-and-forth movement, where the object's displacement from its equilibrium position is directly proportional to the restoring force acting on it. In this case, the water in the harbour is experiencing simple harmonic motion as it rises and falls with the tides.

To solve the problem, we can use the formula for the period of simple harmonic motion, which is T=2π√(m/k), where T is the period, m is the mass of the object, and k is the spring constant. In this case, we can consider the water in the harbour as the object, and the restoring force acting on it is the gravitational force.

We know that the time between successive low tides is 12 hours, or 43200 seconds. We also know that the depth of water varies between 5.0 m and 9.0 m. Using this information, we can calculate the period of the water's motion as T=2π√(m/g), where g is the acceleration due to gravity and m is the mass of the water. We can then solve for m by using the average depth of water (7.0 m) and the density of water, which is 1000 kg/m^3.

Once we have calculated the period, we can use it to find the time it takes for the water to reach a depth of 6.0 m. This will be half of the period, since the water reaches its maximum depth and then returns to its minimum depth in one full cycle. We can then subtract this time from the time between successive low tides to determine how long the ship will have to wait before entering the harbour.

In summary, as a scientist, I would approach this problem by first understanding the concept of simple harmonic motion and using relevant equations to calculate the period of the water's motion. From there, we can determine the time the ship will have to wait before entering the harbour.