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For my project, I need to create a lock gate which will be used for the Panama Canal. One of the many thing my teacher said, was that for the design of the lock gate, the gate should not fail when it gets bumped by a large ship (like a cruise ship).

All the information that we need to calculate, like the mass of a common cruise ship can be found on the internet or other places. We came to the conclusion that the mass of a cruise ship, in the worst case scenario, is equal to $65.000.000 \text{ kg} + 158.200.000\text{ kg} = 223.200.000\text{ kg}$.

The $65.000.000$ is the mass of a common cruise ship and the $158.200.000$ is the maximum mass a cruise ship can hold. The average speed of a cruise ship is equal to about $7 \text{ m/s}$.

We can now calculate the kinetic energy, which is:

$$E_k = \frac12mv^2$$

$$E_k = \frac12\cdot223.200.000\cdot7^2$$

$$E_k =5.468.400.000\text{ J}$$

But after this, I got stuck. A tip from my teacher was that we also need to use the formula $W = F\cdot s$, whereas $s$ is the indentation of the lock gate. How do I know that the lock gate will not fail? I wanted to try something like this:

$$\frac12mv^2 = F \cdot s$$

But I'm not sure if this is right. What is the right approach to know if a lock gate will fail or not against a bump of a cruise ship?

Edit

Here is the information about the lock gate:

The lock gate itself is 31 m x 10 m x 57 m and is hollow in the inside. This leaves a 30 m x 9 m x 56 m gap:

enter image description here

The thickness of the edge is 0,5 m everywhere. The outer case is made of steel and has crossed steel beams.

Qmechanic
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Adnan
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1 Answers1

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I don't know what source you used to get the masses of a "common" cruise ship and its contents. 158,000 metric tons seems like a lot of stuff to cram into one ship. What happened? Did all the passengers bring lead suitcases on this trip?

The Spirit-class cruise ships can fit in the canal locks and they have a deadweight of only 7500 tons. I estimate the empty weight of one of these ships at about 37,500 tons, or about 45,000 tons for the fully-loaded vessel.

https://en.wikipedia.org/wiki/Spirit-class_cruise_ship

You can't use the gross tonnage figures to estimate weight since the gross tonnage is a measure of the internal volume of the vessel.

https://en.wikipedia.org/wiki/Gross_tonnage

Many of the largest cruise ships cannot fit in the lock chambers of the canal because they are physically too large. The lock chambers are 1000 feet long by 110 feet wide, and the widest vessel which is normally accommodated cannot be wider than 105 feet.

user16622
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