A cube of wood having an edge dimension of 19.5 cm and a density of 651 kg/m3 floats on water. Required:
a. What is the distance from the horizontal top surface of the cube to the water level?
b. What mass of lead should be placed on the cube so that the top of the cube will be just level with the water surface?

a)   y ’= 0.068 m ,  b)   m_lead = 2,599 kg

Explanation:

a) To solve this exercise, let's use Archimedes' law, which establishes that the pressure of the water is equal to the weight of the dislodged liquid.

Let's write the forces in the equilibrium condition

            B - W = 0

            B = W

Thrust is

            B = ρ_liquid g V_water

Body weight is

             W = m g

the definition of density

           ρ_body = m / V

we substitute

            W = ρ_body g V_body

The volume of the body is

          V_body = L³

The volume of water is

          V_agua = y L²

we substitute

           ρ_liquid g and L2 = rho_body g L3

           ρ_liquid y = ρ_body L

           y = L ρ_body /ρ_liquid

let's calculate

          y = 651/100 0.195

          y = 0.1269 m

this is the distance from the bottom of the cube, the distance from the top of the cube

          y ’= 0.195 -y

          y '= 0.195 - 0.1269

          y ’= 0.068 m

b) In this case the equilibrium equation is

          B - W_body - W_lead = 0

          B = W_body + W_lead

          ρ_liquido g V_liquido = ρ_body g V_body + m_lead g = 0

          ρ_liquid L3 = ρ_body L3 + m_lead = 0

          m_lead = L3 (ρ_liquid - ρ_body)

let's calculate

          m_lead = 0.195 3 (1000 - 651)

          m_lead = 2,599 kg

the order for strong to weak forces such as

strong nuclear force → electromegnetic force → weak nuclear force → gravitational force

the fundamental forces are those forces that act between to objects or element to make interactions. there are four types of fundamental forces such as strong and weak nuclear forces (due to protons and electrons), electromagnetic force (due to the motion of electrons) and gravitational force (due to orbital movement of the planet). if these forces are arranged on the basis of their maximum strength then the order is

strong nuclear force → electromegnetic force → weak nuclear force → gravitational force

answer///terminator or twilight zone;