Newton's second law states that the resultant of the forces acting on the sphere is equal to the product between its mass m and its acceleration a:
There are two forces acting on the sphere: its weight W, directed downward, and the buoyancy B, directed upward. So Newton's second law becomes
(1)
We already know the weight of the sphere:
, from which we can also find the mass of the sphere:
The buoyancy is equal to the mass of the water displaced:
where
is the water density
V is the volume of water displaced, which corresponds to the volume of the sphere, since the sphere is underwater
g is the gravitational acceleration
The radius of the sphere is
, so its volume is
So now we can rewrite Newton's second law (1) as
and solve it to find the acceleration of the sphere, a:
and this acceleration is directed downward, since it has the same sign of g.
There are two forces acting on the sphere: its weight W, directed downward, and the buoyancy B, directed upward. So Newton's second law becomes
We already know the weight of the sphere:
The buoyancy is equal to the mass of the water displaced:
where
V is the volume of water displaced, which corresponds to the volume of the sphere, since the sphere is underwater
g is the gravitational acceleration
The radius of the sphere is
So now we can rewrite Newton's second law (1) as
and solve it to find the acceleration of the sphere, a:
and this acceleration is directed downward, since it has the same sign of g.
