# Archimedes Principle Formula

TGIF friends Worldwide, fun physics day, from Dr. TJ Gunn in Houston!………

The Archimedes principle states that the upward buoyancy force exerted on a body partially or completely immersed in a fluid is equal to the weight of the fluid that the body displaces and acts in an upward direction in the center of the mass of the displaced fluid. The Archimedes principle is a fundamental law of physics for fluid mechanics. It was formulated by Archimedes of Syracuse.

**push = density of fluid * gravity acceleration * volume of object.**

The equation is:

p=ρ_{f}*g*V

we have,

p = push

ρ_{f} = density of fluid.

g = gravity acceleration.

V = volume of object.

**Archimedes Principle Questions:**

1)A steel ball of 5cm radius is immersed in water. It calculates the thrust and the resulting force (lead density = 7900kg/m^{3}).

**Answer:** To calculate the resulting push, to calculate the push we must calculate the volume of the ball.

V = 4/3πr^{3}= 4/3π (0,05 m)^{3} = 5.24*10^{-4} m^{3}

and know the density of water (1000 kg/m^{3}).

p = Pf*g*v= 1000 kg/m^{3} * 9.8 m/s² *5,23*10^{-4} m^{3} = 5.1254 N.

p = 5.1254 N.

Let’s go with the resulting force. Here two forces act: the push of the water upwards and the weight of the ball downwards. We still have to calculate this last one:

the density of lead is 7900kg/m^{3}, then the mass of lead is

m_{l} = 7900kg/m m*5.24*10^{-4} m^{3} = 4.1396 Kg

The weight of the ball is

w = m_{l}*g = 4.1396 Kg* 9.8m/s^{2} = 40.568 N

The resulting apparent weight is:

W_{a} = w-p = 40.568 N – 5.1254 N = 35.443 N

W_{a} = 35.443 N.

2) Weigh a cube of 10cm edge into the air resulting in 19 N and then weighed immersed in water giving a value of 17 N. Calculate the apparent weight and the push.

**Answer:** The apparent weight is the weight of the object immersed in a fluid, or in other words, the result of the actual weight and thrust. Therefore, the apparent weight is 17 N .

W_{a} = 17 N.

The push is:

w = 19 N.

W_{a} = w-p-→

p = w-W_{a} = 19 N- 17 N = 2 N

p = 2 N.