contestada

A raft is made of solid wood and is 2.31 m long and 1.59 m wide. The raft is floating in a lake. A woman who weighs 130 lb steps onto the raft. How much further into the water does the raft sink? You do not need the thickness of the raft or the density of the wood to solve this problem if you find the symbolic solution first.

Respuesta :

cjmejiab

To solve this problem we will apply the principle of Archimedes.

We know that in the equilibrium condition the weight of the object is equivalent to the Buoyant Force exerted by the water to generate buoyancy.

The weight of the system is equivalent to,

[tex]Weight = mg[/tex]

[tex]W = 58.97*9.8[/tex]

[tex]W = 577.906N[/tex]

Now the definition of the Bouyant force is equivalent to

[tex]F_B = \rho_w g V_D[/tex]

Here,

[tex]\rho_w[/tex]= Water Density

g = Gravity

[tex]V_D[/tex]= Volume of Object

The volume will be equal to the dimensions of the raft x h (h will be the height that the raft sinks)

[tex]V_D= (2.31)(1.59)h[/tex]

[tex]V_D = 3.679h[/tex]

At equilibrium

[tex]W= F_B[/tex]

[tex]W = \rho_w g V_D[/tex]

[tex]577.906 = (1000)(9.8)(3.679h)[/tex]

[tex]h = 0.016m[/tex]

[tex]h = 1.6cm[/tex]

Therefore the height that the raft sinks is 1.6cm

According to the Archimedes principle, weight is equal to the Buoyant Force at equilibrium. The given raft will sink up to 1.6 cm in the water.

Apply the Archimedes principle to solve the given problem. According to the Archimedes principle, weight is equal to the Buoyant Force at equilibrium.

[tex]W = F_b[/tex]...........1

Where,

[tex]W[/tex] = Weight = [tex]mg[/tex] = [tex]58.97 \times 9.8 = 577.9\rm \ N[/tex]

[tex]F_b[/tex] = Buoyant force

Buoyont force can be calculated by the formula,

[tex]F_b = \rho _w gV_d[/tex]

Where,

[tex]\rho _w[/tex] - Density of water =

[tex]g[/tex] - gravitational acceleration

[tex]V_d[/tex] - Volume of Raft = [tex]2.31 \times 1.59 \times h = \bold {3.679 \it h}[/tex]

Put the values in the equation (1) and solve for [tex]h[/tex],

[tex]\begin{aligned}577.9 &= 1000 \times 9.8 \times 3.679h\\h& = 1.6\rm \ cm \end {aligned}[/tex]

Therefore, the given raft will sink up to 1.6 cm in the water.

Learn more about the Archimedes principle,

https://brainly.com/question/787619

Otras preguntas