A ball of Styrofoam (ρ = 100 kg/m3) is totally submerged in water. The ball has a mass of 300.0 g (it could be a pretty big block).
What is the volume of the ball?
If a string holds the ball when it’s in the water, what’s the tension in the string?
mass=density*volume
.3kg=100kg/m^3 * V
solve for volume
volume=.3/100 m^3=.003 m^3
To find the volume of the ball, we can use the formula:
Volume = Mass / Density
Given that the mass of the ball is 300.0 g and the density of Styrofoam is 100 kg/m3, we need to convert the mass to kilograms:
Mass = 300.0 g = 0.3 kg
Now we can plug the values into the formula:
Volume = 0.3 kg / 100 kg/m3 = 0.003 m3
Therefore, the volume of the ball is 0.003 cubic meters.
Now let's determine the tension in the string when the ball is submerged in water.
When an object is in a fluid, such as water, it experiences an upward buoyant force equal to the weight of the fluid it displaces. This is known as Archimedes' principle.
The buoyant force (Fb) acting on the submerged object is given by:
Fb = Density of fluid * Volume * Acceleration due to gravity
In this case, the fluid is water and its density is approximately 1000 kg/m3.
Fb = 1000 kg/m3 * 0.003 m3 * 9.8 m/s2
Fb = 29.4 N (rounded to one decimal place)
The tension in the string will be equal to the buoyant force acting on the ball, which is 29.4 N.