Question

A cube of wood 15.0 cm on each side is tied to the bottom of a tank filled with water to a depth of 50 cm. The tension in the string is found to be 6.615 N. Please answer each of the following questions. Note: 1 atm = 1.013 x 105 Pa a) What is the density of the wood? b) What is the absolute pressure at the bottom of the tank.

Answer 1

(a). The density of the wood is
`1479.48*10^(2)\ Kg/m^3`

(b). The absolute pressure at the bottom of the tank is
`1.06200*10^(5)\ Pa`.

Step-by-step explanation:

Given that,

Side of cube = 15.0 cm

Depth = 50 cm

Tension = 6.615 N

We need to calculate the volume of the wood

Using formula of volume

`V = a^3`

`V=(15.0*10^(-2))^3`

`V=0.003375\ m^3`

We need to calculate the density of the wood

Using buoyant force

`\rho_(w)gh=mg+T`

`\rho_(w)gh=\rho_(c)Vg+T`

Put the value into the formula

`\rho_(c)=(\rho_(w)gh-T)/(Vg)`

Put the value into the formula

`\rho_(c)=(1000*9.8*50*10^(-2)-6.615)/(0.003375*9.8)`

`\rho_(c)=1479.48*10^(2)\ Kg/m^3`

(b). We need to calculate the absolute pressure at the bottom of the tank

Using formula of absolute pressure

`P=P_(atm)+\rho gh`

Put the value into the formula

`P=1.013*10^(5)+1000*9.8*0.5`

`P=1.06200*10^(5)\ Pa`

Hence, (a). The density of the wood is
`1479.48*10^(2)\ Kg/m^3`

(b). The absolute pressure at the bottom of the tank is
`1.06200*10^(5)\ Pa`.