a slab of ice floats on a freshwater lake what is the minimum volume must the slab have for a 45kg women to be able to stand on it without getting her feet wet?
To figure out the minimum volume the slab of ice must have for a 45 kg woman to be able to stand on it without getting her feet wet, we need to consider the principles of buoyancy.
The buoyant force exerted on an object submerged in a fluid (in this case, freshwater) is equal to the weight of the liquid displaced by the object. In order for the woman to stand on the ice without getting wet, the buoyant force on the ice must be equal to or greater than her weight.
1. Find the weight of the woman: The weight of the woman is given as 45 kg.
2. Calculate the buoyant force required to support her weight: The buoyant force is equal to the weight of the liquid displaced by the ice slab. Since the density of freshwater is about 1000 kg/m^3, the buoyant force can be calculated as Buoyant force = Weight of the woman = 45 kg × 9.8 m/s^2.
3. Determine the volume of the slab required: The volume of water displaced by the ice slab must be equal to or greater than the calculated buoyant force divided by the density of freshwater. Thus, Minimum volume of the slab = Buoyant force / Density of freshwater.
Plugging in the values:
Minimum volume of the slab = (45 kg × 9.8 m/s^2) / (1000 kg/m^3)
Simplifying the expression:
Minimum volume of the slab = 4.41 m^3
Therefore, the minimum volume the slab must have for the woman to be able to stand on it without getting her feet wet is approximately 4.41 cubic meters.
To determine the minimum volume required for the slab of ice to support a 45kg woman without getting her feet wet, we need to consider the principles of buoyancy.
Buoyant force is the force exerted by a fluid on an immersed object. When an object is submerged in a fluid, it experiences an upward force equal to the weight of the fluid displaced by the object. This force helps objects float.
In this case, the woman is standing on the slab of ice, which floats on the freshwater lake. The slab of ice displaces a volume of water in order to float. The buoyant force exerted by the water on the ice slab must be greater than or equal to the weight of the woman (45kg) for her not to get her feet wet.
Let's break down the process of finding the minimum volume required:
1. Determine the weight of the woman:
The weight of the woman is given in the question as 45kg.
2. Calculate the weight of the water displaced:
The weight of the water displaced by the ice slab is equal to the weight of the woman, using the principle of buoyancy. Water has a density of approximately 1000 kg/m³.
3. Calculate the volume of water displaced:
Using the equation for density (density = mass / volume), we can rearrange it to find the volume:
Volume = mass / density
4. Calculate the minimum volume required for the slab of ice:
The volume required for the slab of ice is equal to the volume of water displaced.
By following these steps, you can determine the minimum volume required for the slab of ice to support the woman without getting her feet wet.
Weight of ice slab + weight of woman = buoyancy force
(ice density)*V*g + Mg = (water density)*V*g
[(Water density)-(Ice density)]*V = M = 45 kg
V = 45 kg/[(Water density)-(Ice density)]
= 45kg/(1000 - 917)kg/m^3 = 0.54 m^3