Why does a heavier sphere fall faster in a liquid ?

[KingCrimson]

why do heavier balls fall faster in liquids ?, if F=mg-drag, a heavier ball would have greater mg, but the acceleration is given by F=ma, therefore mg-drag = ma, a = (mg-drag)/m.
I can't see how a heavier ball would fall faster.

 

[Bandersnatch]

You've got $a=g-F_D/m$. (minus is up here) If you increase mass, g is reduced more or less?

 

[TESL@]

$F=ma=mg-F_b-F_d$ where $F_b$ is bouyant force and $F_d$ is drag.

Then; $a=g-F_b/m+F_d/m$, so if you have two balls of same volume but different mass, the larger mass will have a higher acceleration.

 

[KingCrimson]

You've got $a=g-F_D/m$. (minus is up here) If you increase mass, g is reduced more or less?

g is constant, but Fd/m is reduced, I see it now :D thanks.

 

[PJC01]

The reason for this is due to the concept of buoyancy. When an object is submerged in a liquid, it experiences an upward force called buoyant force, which is equal to the weight of the displaced liquid. This force acts in the opposite direction to the force of gravity, and it reduces the overall weight of the object in the liquid.

When we consider the equation F=ma, the acceleration is inversely proportional to the mass of the object. This means that for a given force, a heavier object will have a smaller acceleration compared to a lighter object. However, in the case of a heavier ball falling in a liquid, the buoyant force acting on the ball is also greater due to its larger mass. This means that the net force acting on the ball is greater, resulting in a larger acceleration.

In other words, the heavier ball has a greater weight and experiences a greater buoyant force, which results in a larger net force and therefore a greater acceleration. This is why a heavier ball falls faster in a liquid.