Question

Styrofoam has a density of 32kg/m3 . What is the maximum mass that can hang without sinking from a 50-cm-diameter Styrofoam sphere in water

Answer 1

The maximum mass that can hang without sinking from a Styrofoam sphere in water can be determined by considering the buoyant force exerted by the water on the sphere.

Step-by-step explanation:

The maximum mass that can hang without sinking from a Styrofoam sphere in water can be determined by considering the buoyant force exerted by the water on the sphere. Buoyant force is equal to the weight of the water displaced by the sphere. The weight of the water displaced can be calculated using the volume of the sphere and the density of water.

The volume of a sphere with radius r is given by V = (4/3)πr^3. Therefore, the volume of the Styrofoam sphere with a diameter of 50 cm is V = (4/3)π(25 cm)^3.

Since the density of Styrofoam is given as 32 kg/m3, we can calculate the mass of the Styrofoam sphere using its volume and density. Mass = density x volume = 32 kg/m3 x (V/1000000 m3).

To calculate the weight of the water displaced by the sphere, we use the density of water (1000 kg/m3) and the volume of the sphere. Weight = density x volume = 1000 kg/m3 x (V/1000000 m3).

Therefore, the maximum mass that can hang without sinking from the Styrofoam sphere is the mass of the Styrofoam sphere minus the weight of the water displaced.

Answer 2

To calculate the maximum mass that can hang without sinking from a Styrofoam sphere in water, we need to use the concept of buoyancy. The buoyant force can be calculated using Archimedes' principle, which states that the buoyant force is equal to the weight of the fluid displaced by the object. The density of the Styrofoam is given as
`32 kg/m^3`. The maximum mass that can hang without sinking from the Styrofoam sphere in water is 65.4 kg.

To calculate the maximum mass that can hang without sinking from a Styrofoam sphere in water, we need to use the concept of buoyancy. Buoyancy is the upward force exerted on an object submerged in a fluid, such as water. The buoyant force can be calculated using Archimedes' principle, which states that the buoyant force is equal to the weight of the fluid displaced by the object.

The density of the Styrofoam is given as 32 kg/m3. Let's assume the diameter of the Styrofoam sphere is 50 cm, which means the radius is 25 cm or 0.25 m.

The volume of the Styrofoam sphere can be calculated using the formula V = (4/3) * π * r3, where V is the volume and r is the radius. Plugging in the values, we get V = (4/3) * 3.14 * (0.25)3 = 0.0654 m3.

The mass of the water displaced by the Styrofoam sphere can be calculated using the formula m = ρ * V, where m is the mass, ρ is the density, and V is the volume. Plugging in the values, we get m = 1000 kg/m3 * 0.0654 m3 = 65.4 kg.

Therefore, the maximum mass that can hang without sinking from the Styrofoam sphere in water is 65.4 kg.