A spear, mass and gravity......

[Externet]

Hi all.

A spear mass is 1 Kg.  If gravity g is 9.81 m/s² on this planet, its weight is  F=mg = 1 x 9.81 = 9.81 Newtons.  Is that right so far ?

That same spear of 1 Kg underwater weighs 5 Newtons.

Does it mean that the acceleration of gravity is not exactly constant in this planet as it would be then, g = F/m = 5/9.81 = 0.51 m/s²  because differs underwater, part of this same planet ?

 

 

[Markus Hanke]

Water is much more dense than air, so it generates much greater resistance owing to the need of the falling/sinking object to displace it. Gravity is (for all intents and purposes) the same, but there is a counterforce from having to displace the water as the spear sinks, making it appear “lighter” and move slower.

I say “for all intents and purposes”, because the value g=9.81m/s^2 is specific to the Earth’s surface - if you were to go high up (or tunnel deep down), this numerical value will change accordingly. Even on the surface, this value can vary ever so slightly between different locations, depending on how dense the Earth’s crust and mantle are at that place. Also, the Earth isn’t a perfect sphere either. But for most everyday applications, 9.81m/s^2 is a sufficiently good approximation.

[MigL]

Weight is a measure of force, and force has a direction.
Underwater we are subject to a down force just as on land, and an additional upward buoyancy force.
The downward force is reduced by the upward force, so the net force, or weight, is reduced.

Its mass remains unchanged.
Edit : ( I'm at a much simpler level than Markus )

Edited January 30, 2020 by MigL

[Eise]

3 hours ago, Externet said:

Does it mean that the acceleration of gravity is not exactly constant in this planet as it would be then, g = F/m = 5/9.81 = 0.51 m/s²  because differs underwater, part of this same planet ?

I would suggest to think about the crew of a submarine. Do they move normally, or are they lighter as soon as the submarine is under water? So what value of g would they measure? 

Edited January 30, 2020 by Eise

[swansont]

14 hours ago, Externet said:

 That same spear of 1 Kg underwater weighs 5 Newtons. 

You have to be careful with definitions here. W = mg and that is *essentially* unchanged, as Markus notes, as long as you're near the surface. g is basically the same value.

But the net force changes, as MigL notes, owing to the buoyancy from the water, which is equal to the weight of the water displaced, which in this case is 4.81 N. From that you could calculate the volume of the spear, and thus its density (and maybe that could tell you what its made of. It's a little too light to be aluminum*)

 

*edit: solid aluminum

[Externet]

8 hours ago, Eise said:

I would suggest to think about the crew of a submarine.

That is a great "wake-up, brain!"  Thanks.

[J.C.MacSwell]

12 hours ago, swansont said:

You have to be careful with definitions here. W = mg and that is *essentially* unchanged, as Markus notes, as long as you're near the surface. g is basically the same value.

But the net force changes, as MigL notes, owing to the buoyancy from the water, which is equal to the wight of the water displaced, which in this case is 4.81 N. From that you could calculate the volume of the spear, and thus its density (and maybe that could tell you what its made of. It's a little too light to be aluminum)

As Markus alludes to...net forces must also include drag forces.

You are correct of course for an assumed V=0.

But it would approach terminal velocity pretty quickly...becoming net zero.

 

Edited January 30, 2020 by J.C.MacSwell

[mathematic]

Think of a block of wood.  On dry land it has a weight.  But on water it floats, so its "weight" is zero.