A rectangular piece of Styrofoam of mass 3.0 kg floats with 5.0% of its volume underwater. What is the maximum mass that the Styrofoam can support without sinking?
to sink it, if 1/20th of its volume supports 3kg, then all of its volume would support 20*3kg total, or a net load added of 19*3kg
To determine the maximum mass that the Styrofoam can support without sinking, we need to consider the buoyant force acting on it. Buoyant force is the upward force exerted on an object immersed in a fluid, and it is equal to the weight of the fluid displaced by the object.
The volume of the Styrofoam submerged underwater can be calculated by multiplying the total volume of the Styrofoam by the percentage that is underwater. Given that 5.0% of the Styrofoam's volume is underwater, we can calculate:
Volume underwater = 5.0% * Total volume of Styrofoam
Next, we need to determine the density of water, as it affects the buoyant force. The density of water is approximately 1000 kg/m^3.
The buoyant force is given by the equation:
Buoyant force = Density of fluid * Volume underwater * Acceleration due to gravity
The acceleration due to gravity is approximately 9.8 m/s^2.
Now, the buoyant force opposes the gravitational force acting on the Styrofoam, which is given by the equation:
Gravitational force = Mass of Styrofoam * Acceleration due to gravity
For the Styrofoam to float, the buoyant force must be greater than or equal to the gravitational force. Therefore, we can set up the following inequality:
Buoyant force ≥ Gravitational force
Substituting the equations for the buoyant force and gravitational force, we get:
Density of fluid * Volume underwater * Acceleration due to gravity ≥ Mass of Styrofoam * Acceleration due to gravity
Simplifying this equation, we find:
Density of fluid * Volume underwater ≥ Mass of Styrofoam
Plugging in the known values, we have:
1000 kg/m^3 * (5.0% * Total volume of Styrofoam) ≥ Mass of Styrofoam
Now, we can solve this equation to find the maximum mass that the Styrofoam can support without sinking.