Consider the geometry shown in Figure P5.41. The cube is level with the surface

Question

Consider the geometry shown in Figure P5.41. The cube is level with the surface of the liquid.

a. If the mass M is 300 kg, calculate the density of the cube.

b. For the density calculated in part A, will the cube float or sink if the mass is removed? If it floats, is it stable? Why or why not?

c. Repeat part a, but this time let the partially submerged object be spherical, with its center level with the surface of the liquid.

d. Repeat part b for the spherical object investigated in part c.

e. Repeat part a, but this time let the center-line of the cube be located 3 m below the surface of the liquid.

Consider the geometry shown in Figure P5.41. The cube is level with the surface of the liquid. If the mass M is 300 kg, calculate the density of the cube. For the density calculated in part A, will the cube float or sink if the mass is removed? If it floats, is it stable? Why or why not? Repeat part a, but this time let the partially submerged object be spherical, with its center level with the surface of the liquid. Repeat part b for the spherical object investigated in part c. Repeat part a, but this time let the center-line of the cube be located 3 m below the surface of the liquid.

Explanation / Answer

a)

weight of M = 300*9.81 = 2943 N

so.. weight of the cube = 2943 + volume * density * g = 2943 + 1 * 1000*9.81 = 12753 N

so.. mass of cube = 12753 / 9.81 = 1300 kg

so.. density = mass / volume = 1300 kg / 1 m^3 = 1300 kg / m^3

b) if the mass is removed then the cube will sink

c)

weight of M = 300*9.81 = 2943 N

so.. weight of the cube = 2943 + volume * density * g = 2943 + 0.5 * 1000*9.81 = 7848 N

so.. mass of cube = 7848 / 9.81 = 800 kg

so.. density = mass / volume = 800 kg / 1 m^3 = 800 kg / m^3

d)

if mass is removed ... for fully sinking ...

upthrust = 1 * 800 * 9.81 = 7848 N

so.. total upward force = 7848 N

so.. total downward force = weight of the block = mass of cube * g = 800 * 9.81 = 7848 N

so.. the cube will float ...

it is not stable .. because the upward force is equal to downward force .. so block can be pulled anywhere

inside the water and it will stay there

e)

weight of M = 300*9.81 = 2943 N

so.. weight of the cube = 2943 + volume * density * g = 2943 + 1 * 1000*9.81 = 12753 N

so.. mass of cube = 12753 / 9.81 = 1300 kg

so.. density = mass / volume = 1300 kg / 1 m^3 = 1300 kg / m^3

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

---