Pressure and density in flluids

In summary, the conversation discusses a physics problem involving an ice cube floating in a glass of water. The goal is to determine the volume of water that the ice cube displaces. The conversation includes information about densities, Archimedes' Principle, and using equations to calculate the volume.
  • #1
sghaussi
33
0
hi! I was wondering if someone can help me with this physics probelm:


A single ice cube with mass X g floats in a glass completely full of Y cm^3 of water. You can ignore the water's surface tension and its variation in density with temperature (as long as it remains a liquid).

What volume of water does the ice cube displace?



I know these densities -
Water: 1.00 x 10^3 kg/m^3
Ice: 0.92 x 10^3 kg/m^3

density = m / V (m is mass and V is volume)

if I rearrange this equation I get:

V = m / density


I just plugged in my known mass and density for hte ice and i found the volume of the ice. That volume would be the same volume that the ice takes up in the cup of full water, right? I don't think it is because I keep getting hte wrong asnwer. Am even using the write equation? I'm stuck and confused, hope someone can help me! =)
 
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  • #2
water in its liquid form is more dense than water in its solid form (ice), so the ice will be partially submerged. This means the water displaced will be equal or less to the volume of the ice. Use Archimedes' Principle.
 
Last edited:
  • #3
Probably you haven't read our text well before attempting the problems.This problem is a direct application of Archimedes Principle which states that:

"A body whooly or partially immersed inside a liquid is buoyed up by a force which is equal to the weight of the body inside the liquid"

Therefore,as per your problem,in equilibrium,The buoyant force balances the weight of the body:

Weight of the cube= Desnity(cube)(total volume of cube)

Therefore:

[itex]

d_iVg= d_wV_og

[/itex]

[itex]

where V_o=Fraction of volume og cube inside water.
[/itex]



Now calculate V_o ...that will give you the vlume of cube inside water...and that will be the volume occupied by the cube in water...simple isn't it?
 

What is pressure in fluids?

Pressure in fluids is the amount of force exerted per unit area on the walls of a container by the molecules of the fluid. It is measured in units of Pascals (Pa) or Newtons per square meter (N/m²).

How does pressure affect density in fluids?

Pressure has an inverse relationship with density in fluids. This means that as pressure increases, density decreases and vice versa. This is known as Boyle's Law, which states that at a constant temperature, the pressure and volume of a gas are inversely proportional.

What factors affect pressure and density in fluids?

The main factors that affect pressure and density in fluids are temperature, volume, and mass. As temperature increases, the pressure of a gas also increases, while density decreases. Volume and mass also play a role, as a larger volume or mass of fluid will result in a higher pressure and lower density.

What is the difference between absolute pressure and gauge pressure?

Absolute pressure is the total pressure exerted by a fluid, including atmospheric pressure. Gauge pressure, on the other hand, only measures the pressure above atmospheric pressure. This means that gauge pressure can be positive (above atmospheric pressure) or negative (below atmospheric pressure).

How is pressure and density in fluids measured?

Pressure is typically measured using a manometer or a pressure gauge. Density can be calculated by dividing the mass of the fluid by its volume. It can also be measured using a hydrometer, which measures the buoyancy of the fluid to determine its density.

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