Styrofoam has a density of 300kg/m3. What is the maximum mass that can hang without sinking from a 30.0cm -diameter Styrofoam sphere in water?
To find the maximum mass that can hang without sinking from a Styrofoam sphere in water, we need to consider the buoyant force acting on the sphere. The buoyant force is equal to the weight of the water displaced by the sphere.
First, we need to calculate the volume of the Styrofoam sphere. The formula for the volume of a sphere is given by V = 4/3 * π * r^3, where r is the radius of the sphere.
Given the diameter of the Styrofoam sphere is 30.0 cm, the radius (r) is half of the diameter, which is 15.0 cm or 0.15 m.
Substituting the values into the formula, we have:
V = 4/3 * π * (0.15)^3
V ≈ 0.141 m^3
Now we can calculate the weight (W) of the water displaced by the Styrofoam sphere using the formula:
W = ρ * V * g
where ρ is the density of water and g is the acceleration due to gravity.
The density of water is approximately 1000 kg/m^3, and the acceleration due to gravity is approximately 9.8 m/s^2.
Substituting the values into the formula, we have:
W = 1000 * 0.141 * 9.8
W ≈ 1379 N
The buoyant force acting on the Styrofoam sphere will be equal to this weight, and for the sphere to remain afloat, the maximum mass that it can support without sinking is the weight divided by the acceleration due to gravity:
Mass = W / g
Mass ≈ 1379 / 9.8
Mass ≈ 140.71 kg
Therefore, the maximum mass that can hang without sinking from a 30.0 cm-diameter Styrofoam sphere in water is approximately 140.71 kg.