A 10cm solid wooden cube is floating on the surface of water. Its height above w

Question

A 10cm solid wooden cube is floating on the surface of water. Its height above water is 3.0 cm. a) What is the gauge pressure on the bottom of the cube? b) What is the buoyant force on the cube? c) What is the density of the wooden cube? The speed of water flow in a horizontal pipe is 1.2 m/s at point A, where the cross sectional area is 4.0 times 10^-4 m^2. a) What is the volume rate of the water flow? What is the mass rate of the water flow? b) What is the speed of flow at point B with half the cross sectional area? at point C with half the inner diameter? c) Among the three points A, B, and C, where is the pressure the highest? What are the relations between the Celsius, the Fahrenheit and the Kelvin temperatures? When the temperature drops in a process from 327 degree C to 27 degree C, what is its initial temperature in the Kelvin scale? What is the change of its temperature? What is the temperature coefficient of linear expansion ?What is the temperature coefficient of volume expansion? What is the relation between them for solids? What is the equivalence between heat and mechanical work? What is implied by their equivalence? What is the specific heat capacity What is the latent heat of a phase transition?

Explanation / Answer

11.a)

The height of cube below water is h = 10 cm - 3 cm = 7 cm = 0.07m

At the bottom of the cube the pressure is

P = P0 + wgh, where P0 is atmospheric pressure and w is the density of water.

So, P = 101325 N/m2 + (1000 kg/m3)(9.8 m/s2)(0.07 m)

or, P = 1.02X105 Pa

***************************************************************************************************

11.b)

The volume of water displaced by the cube is,

V = 10cmX10cmX7cm = 700cm3 = 700X10-6m3

So, the buoyant force is the weight of the water displaced, so we have buoyant force as,

F = Vwg = ( 700X10-6m3)(1000 kg/m3)(9.8 m/s2)

or, F = 6.86 N

***************************************************************************************************

11.c)

The buoyant force F balances the weight of the cube.

The volume of the cube is Vc = (10cm)3 = 1000X10-6m3

Let the density of the cube be c, then wieght of the cube will be,

Wc = Vccg

This weight is equal to the weight of the displaced water or the buoyant force.

So, Vwg = Vccg

or, (700X10-6m3)(1000 kg/m3) = (1000X10-6m3)c

or, c = 700 kg/m3 is the density of the cube.

***************************************************************************************************

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.