A hollow plastic sphere is held below the surface of a freshwater lake by a cord anchored to the bottom of the lake. The sphere has a volume of 0.600m^3 and the tension in the cord is 840N . What is the mass of the sphere?
is this how i would find the mass?
(4/3)X3.14X(.600)^3?
and to find the buoyant force exerted by the water on the sphere.
(.600)(9.8)?
please just tell me if im on the right track
Your buoyant force is
Fb = (water density)(volume)x g,
but the water density in SI units is 1000 kg/m^3, not 1. So Fb = 5886 N
If the mass of the sphere is M g, a vertical force balance requires that
M*g + T = Fb
M = (1000kg/m^3*0.6*m^3*g - 840 N)/g
= 600 kg - 840/g = 514 kg
Yes, you are on the right track. To find the mass of the hollow plastic sphere, you can use the formula:
mass = volume * density
However, you need to know the density of the plastic used to make the sphere. Without that information, you won't be able to calculate the mass accurately.
Regarding the formula you mentioned:
(4/3) * π * (0.600)^3
This formula is used to find the volume of a solid sphere, not the mass. So, you would need the density of the plastic and then apply the formula mass = volume * density.
To find the buoyant force exerted by the water on the sphere, you need to use Archimedes' principle, which states that the buoyant force on an object submerged in a fluid is equal to the weight of the fluid displaced by the object. The formula is:
buoyant force = density of fluid * volume of fluid displaced * acceleration due to gravity
In this case, the fluid is freshwater, so you can use its density, which is approximately 1000 kg/m^3. The volume of fluid displaced is the volume of the sphere, which is given as 0.600 m^3. And the acceleration due to gravity is 9.8 m/s^2.
Therefore, the formula for the buoyant force would be:
buoyant force = (density of freshwater) * (volume of sphere) * (acceleration due to gravity)