Upthrust and Archimedes' principle

Under ordinary condition, water has density 1000 (unit)

• Pa

A cube of metal with density 5000 kg m^-3 is placed on a still pound. What will be its subsequent motion? (hint: the density of water is 1000 kg m^-3)

• It will float at the surface

• It will descend into the pound and stop moving before reaching the bottom.

• It will descend at a constant rate and sink all the way to the bottom.

• It will accelerate and sink all the way to the bottom.

• 10 N

• 20 N

• 2 N

• 5 N

Consider the pressure due to a solid and the pressure due to a fluid on a horizontal surface. Which of the following is a difference between the two?

• The pressure due to solid is a constant but the pressure due to fluid is not.

• The pressure due to solid is directional but the pressure due to fluid is the same in all directions.

• The pressure due to solid is independent of the material's density

You consider an imaginary cylinder when deriving the formula for fluid pressure. Which of the following is not true?

• The force on the bottom area is equal to the weight of the fluid in the cylinder

• The weight of the fluid in the cylinder is Ahρg, ρ being the density of the fluid

• Since the bottom surface is imaginary, there is no pressure on it

• The pressure at depth h is hρg, ρ being the density of the fluid

What does Archimedes' principle tell you?

• The upthrust on an object is equal to the weight of that object

• The upthrust on an object is equal to the weight of the fluid displaced

• It only applies to objects fully submerged in the fluid

• The upthrust on an object depends on the density of the object, but not that of the fluid

When considering the upthrust on an object, we simplify the object to a cube. Which of the following steps is wrong? (ignore air pressure)

• force at top surface = hρgA

• force at bottom surface = (h-x)ρgA

• resultant force = xρgA

• identify Axρ as the volume of the fluid displaced

Consider the derivation in the previous question. Which of the following is correct?

• We considered a cuboid because Archimedes' principle only applies to cuboids

• The fluid exerts no force on the sides of the cuboid

• The fluid particles collide with the sides of the cuboid and exert a force; therefore the cuboid will move horizontally

• To calculate the total pressure on the upper surface, we need to add air pressure to hρg