# Archimedes Principle

A crane is used to lower a vertical cylindrical pillar into a reservoir. The pillar has a mass of 4 tonnes and is submerged to a depth of 2.5m. It has a diameter of 1.1m.

The specific gravity of fresh water is $$1125kg/m^3$$, and $$9.81m/s^2$$.

Use a free body diagram to show the forces acting on the pillar when submerged and calculate the upthrust, the tension in the rope in air and the tension in the cable when submerged.

I have this for Upthrust:

$$Fbuoy = Pf \cdot Vd \cdot g$$ $$\pi r^2h$$ $$3.14 \cdot .55^2 \cdot 2.5 = 2.375m^3$$ $$1.125 \cdot 2.375 \cdot 9.81 = 26.2N$$

$$Upthrust = 26.2N$$

Tension in air

$$T = w - Fb$$ $$\pi r^2h$$ $$3.14 \cdot .55^2 \cdot 2.5 = 2.375m^3$$ $$Volume = 2.375m^3$$ $$w = m \cdot g$$ $$w = 4 \cdot9.81 = 39.24kN$$ $$w = 39.24kN$$ $$Fb = Pf \cdot Vd \cdot g$$ $$1.29 \cdot 2.375 \cdot 9.81 = 30N$$ $$T = w - Fb$$ $$T = 39.24 - 30 = 9.24N$$

$$Tension in air = 9.24N$$

Tension in water

$$T = w - Fb$$ $$\pi r^2h$$ $$3.14 \cdot .55^2 \cdot 2.5 = 2.375m^3$$ $$Volume = 2.375m^3$$ $$w = m \cdot g$$ $$w = 4 \cdot 9.81$$ $$w = 39.24kN$$ $$Fb = Pf \cdot Vd \cdot g$$ $$Fb = 1.125 \cdot 2.375 \cdot 9.81$$ $$T = w - Fb$$ $$T = 39.24 - 26.2 = 13.04N$$

$$Tension in the cable when sumerged = 13.04N$$

Are these correct?

If not could someone help?

I have been trying to complete Archimedes Principle but just getting a little stuck on the calculations.