Daniel O. answered • 10/27/12

Math and Physics Tutor, with a math and physics degree

Since the forces on the ball will be balanced (ie. we know the buoyant force will act upwards, but this must be balanced by the tension acting downwards, or else the cord would snap and the ball would float up) this means the tension in the rope is equal to the buoyancy force. The buoyant force acting on the object is equal to the weight of water displaced - note that the buoyancy force is only related to weight of water displaced, not depth, so the pool depth and cord length are irrelevant.

The net buoyancy force will be equal to the weight of water displaced minus the weight of the ball.

We use the formula: **F _{B }= Vg(ρ_{water} - ρ_{ball})** where V is the volume (of water displaced, equal to the ball's volume),

**g = 9.81m/s**, ρ is density (

^{2}**ρ**,

_{water}= 1000kg/m^{3}**ρ**0.3g/cc

_{ball}=**= 300kg/m**).

^{3}**Vgρ**gives the weight of water displaced (buoyancy force) and

_{water}**Vgρ**gives the weight of the ball.

_{ball}

Volume of the ball/water displaced is the volume of a sphere, and the radius is 1/2 diameter, so 23cm or **r = 0.23m**

**V = 4/3 * pi * r ^{3} = 4/3 * pi * 0.23^{3} = 0.050965**

**m**

Now from the formula for net buoyancy force,

^{3}**F**

_{B}= 0.050965 * 9.81 * (1000 - 300) = 349.98NSince the tension must equal the net buoyancy force for the ball to remain stationary, **T = 350N**

Sinesipho S.

09/23/17