Question

A block of wood with the density of 780 kg/m^3 has a cubic shape with sides 0.259m long. A cord of negligible mass is used to tie a piece of lead to the bottom of the wood. The lead pulls the wood into the water until it is just completely covered with water. What is the mass of lead? Density of water 1000kg/m^3 and density of lead 11300 kg/m^3

Answer 1

3.828 kg

Step-by-step explanation:

m - mass of lead

gravitational acceleration =9.81 ms⁻²

Vwood - volume of the wood cube

d(water) - density of water

d(wood) - density of wood

Vwood=
`(0.259 m)^(3) =0.0174 m^(3)`

Archimedes' principle states that the upward buoyant force that is exerted on a body immersed in a fluid, whether fully or partially submerged, is equal to the weight of the fluid that the body displaces

assuming the equillibrium state

weight of lead + weight of wood = upthrust for the cube

`\\m*g+Vwood*d_(wood)*g=Vwood*d(water)*g\\m*9.81 + 0.0174*780*9.81 = 0.0174*1000*9.81 \\m=3.828 kg`