A metal sphere is found floating in a pool. The sphere is 1m in diameter. If it is half submerged determine the weight of the sphere. You may assume the following:
g=10N/kg
density of Water = 1000kg/m^3
Vsphere = 4/3pir^3
I get 13.3 as my final answer, but there is no answer in this book to tell me if I am correct or not >>
R=0.5 m
W= mg
mg =F(buoyant)
W = (1/2) •(4πR³/3) •ρ•g =
=1000•4π•0.5³•10/2•3=
=2618 N
To determine the weight of the sphere, we need to consider the gravitational force acting on it both above and below the water's surface.
First, let's find the volume of the sphere. The volume of a sphere can be calculated using the formula:
V_sphere = (4/3) * pi * r^3
Given that the diameter of the sphere is 1m, we can find its radius by dividing the diameter by 2:
r = 1m / 2 = 0.5m
Now we can substitute the value of the radius into the volume formula:
V_sphere = (4/3) * pi * (0.5m)^3
V_sphere = (4/3) * pi * (0.125m^3)
V_sphere = 0.1665m^3
Since the sphere is half submerged in the water, the volume of the submerged part is equal to half of the sphere's volume:
V_submerged = 0.1665m^3 / 2 = 0.08325m^3
Next, let's find the weight of the submerged part of the sphere. The weight of an object can be calculated by multiplying its mass by the acceleration due to gravity (g). In this case, the mass of the submerged part of the sphere can be found using the density of water:
mass = density * volume
Using the given density of water (1000kg/m^3), we can calculate the mass:
mass = 1000kg/m^3 * 0.08325m^3
mass = 83.25kg
Finally, we can calculate the weight of the submerged part of the sphere:
weight = mass * g
weight = 83.25kg * 10N/kg
weight = 832.5N
Therefore, the weight of the submerged part of the metal sphere is 832.5N.