A friend and I have been having an ongoing debate for years. We were at a pub on a wharf, watching shipping container ships and cruise ships come into dock, and he posed the question. With no wind, no waves, perfect conditions, could he move the ship at all?
In: Planetary Science
Perfect conditions let you do anything.
Newtons laws hold pretty damn well.
Force = mass x acceleration.
The mass of a containership is quite high, and the force you can apply by hand is pretty small, but it’s not zero. Therefor the acceleration is going to be miniscule, but not zero.
A cargo ship might weigh somewhere in the order of 150,000 tonnes. Metric because conversions are nicer. That’s 150,000,000 kilograms.
A fit person can usually lift their own bodyweight and more in an ideal scenario, so lets say your friend can bench 200lbs, we can convert pounds of force to newtons and get a force of about 900 N.
`F = m*a`
`900 N = 150,000,000 kgs * a`
`a = 0.000006 m/s^2`
`a = 6×10^-6 m/s^2`
We can use one of the kinematic equations to relate acceleration, distance, velocity (initial and final), and time.
For example, how long would it take your friend to move the cargo ship 1 meter?
If we assume the ship starts at rest and the initial velocity is 0, d = 1m, and a = 0.000006 m/s^2, we can use the following formula to calculate time:
`d = vi*t + 1/2*a*t^2`
vi = 0, so we can simplify and rearrange:
`2d/a = t^2`
And solve:
`2(1m /0.000006 = t^2`
`t = 577s`
That means that it would take your friend about 600 seconds or 10 minutes to move the cargo ship by 1m, given there’s no resistance and he can keep up that 900 N of exertion for 10 minutes straight.
Realistically, there’s resistance to movement, and in this case we have friction between the water and the ship (energy required to move along the fluid), and viscous resistance (energy required to move the fluid out of the way). Ketchup might have similar friction to water, but it’d be harder to move out of the way.
If you want the full physics and fluid dynamics lesson, you can find a great document here on the [United States Naval Academy website](https://www.usna.edu/NAOE/_files/documents/Courses/EN400/0207_Chapter_7_Jun20.pdf).
The amount of resistance in a fluid is proportional to the velocity though, and at the abysmally low velocity your friend is able to push at (average speed of about 1/16th of an inch per second), the resistance would also be proportionally low (but not zero).
Without calculating, I’d guestimate that the resistance would double or triple the time required to move the ship 1 meter. And since it’s really hard to exert yourself at full strength for 20-30 minutes straight, probably safe to assume we double the time again.
So within the hour, I expect your friend could move a mid-large size container ship about 1 meter.
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