A slab of ice floats on a freshwater lake.
What minimum volume must the slab have for a 50.0kg woman to be able to stand on it without getting her feet wet?
1000 kg/m3 = density of water
920 kg/m3 = density of ice
BF = Woman Weight + Slab Weight
Pvg = 50 + Pvg
V = 50 kg / (1000 - 920)
V = 50 / 80
V = 0.625 m3
Well, I once told a joke about a penguin who was a fantastic ice skater, so I guess I'm kind of an expert on this subject! Anyway, to answer your question, let's consider the buoyancy of the slab.
We know that the buoyant force acting on an object in a fluid is equal to the weight of the fluid displaced by the object. If the woman stands on the slab without getting her feet wet, it means that the slab displaces an amount of water that is equal to her weight. In this case, her weight is 50.0 kg.
Assuming the density of ice is 917 kg/m³ and the density of water is 1000 kg/m³, we can use Archimedes' principle to calculate the minimum volume of the slab.
Volume of the slab = (Weight of the woman) / (Density of water - Density of ice)
Plugging in the values, we get:
Volume of the slab = 50.0 kg / (1000 kg/m³ - 917 kg/m³)
Now, doing the math, carry the one, and add a dash of silliness...
Drumroll please...
The minimum volume of the slab is... just enough for the woman to stand on it without getting her feet wet! Ta-da!
Remember, this is a simplified calculation. In reality, it may not be possible for a slab of ice of this size to support a person's weight without cracking or breaking, so it's always better to have a solid surface to stand on. Safety first!
To determine the minimum volume required for a 50.0 kg woman to stand on the slab of ice without getting her feet wet, we need to consider the principles of buoyancy.
The buoyant force exerted on an object submerged in a fluid is equal to the weight of the fluid displaced by the object. In this case, the buoyant force needs to be equal to or greater than the weight of the woman (50.0 kg) in order for the slab to support her.
Assuming the density of ice is approximately 917 kg/m^3, and the density of freshwater is approximately 1000 kg/m^3, we can calculate the minimum volume needed.
Step 1: Calculate the weight of the woman.
Weight = mass * gravitational acceleration
Weight = 50.0 kg * 9.8 m/s^2
Weight = 490 N
Step 2: Calculate the minimum volume of water displaced.
Buoyant force = weight of water displaced
Density of freshwater * Volume * gravitational acceleration = weight
1000 kg/m^3 * Volume * 9.8 m/s^2 = 490 N
Volume = 490 N / (1000 kg/m^3 * 9.8 m/s^2)
Volume = 0.050 m^3
Step 3: Convert the volume into the volume of ice.
Density of ice = 917 kg/m^3
Volume of ice = Volume of water displaced / (Density of water / Density of ice)
Volume of ice = 0.050 m^3 / (1000 kg/m^3 / 917 kg/m^3)
Volume of ice = 0.0461 m^3
Therefore, the minimum volume of the slab of ice should be approximately 0.0461 m^3 for the woman to be able to stand on it without getting her feet wet.
To determine the minimum volume required for the slab of ice to support the woman's weight without getting her feet wet, we need to consider the concept of buoyancy.
1. Buoyant force: The upward force exerted by a fluid on a submerged object is equal to the weight of the fluid displaced by the object.
2. Archimedes' principle: When an object is immersed in a fluid, it experiences an upward buoyant force equal to the weight of the fluid it displaces.
Given:
- Weight of the woman (mass) = 50.0 kg.
- Freshwater density (ρ) = 1000 kg/m³ (this value represents the density of freshwater).
We can now determine the minimum volume of the ice slab required as follows:
Step 1: Calculate the weight of the woman (force):
Weight = mass × acceleration due to gravity (g)
Weight = 50.0 kg × 9.8 m/s² (standard value for g)
Weight = 490 N
Step 2: Calculate the volume of water displaced (V) by the woman's weight:
Volume = Weight of the woman / (Density of freshwater × acceleration due to gravity)
Volume = 490 N / (1000 kg/m³ × 9.8 m/s²)
Volume ≈ 0.0500 m³ (rounded to four decimal places)
Therefore, the minimum volume of the ice slab required for the woman to be able to stand on it without getting her feet wet is approximately 0.0500 cubic meters.