A steel bowl has a mass of 14 kg and will displace a volume of 0.17m^3. What is the extra mass that can be added to the bowl before it will sink when floating in water of density 1000kg m^-3 ?
X kg = mass added.
Dbmax = Dw.
Dbmax = Density of bowl with X kg added.
Dw = Density of water.
Dbmax = (14+X)kg / 0.17m^3 = 1000kg/m^3
(14+X)/0.17 = 1000
14 + X = 170
X = 170 - 14 = 156 kg added.
To find the extra mass that can be added to the steel bowl before it sinks when floating in water, we need to consider the concept of buoyancy.
Buoyancy is the upward force exerted on an object submerged in a fluid. When an object is partially or fully submerged in a fluid, the buoyant force counteracts the gravitational force acting on the object, making it seem lighter.
Here's how you can calculate the extra mass that can be added:
1. Calculate the buoyant force acting on the steel bowl:
Buoyant force = density of fluid x volume of fluid displaced x acceleration due to gravity
The density of water is given as 1000 kg/m^3, and the volume of fluid displaced is given as 0.17 m^3. The acceleration due to gravity is approximately 9.8 m/s^2. So, the buoyant force is:
Buoyant force = 1000 kg/m^3 x 0.17 m^3 x 9.8 m/s^2
2. Calculate the gravitational force acting on the steel bowl:
Gravitational force = mass x acceleration due to gravity
The mass of the steel bowl is given as 14 kg, and the acceleration due to gravity is approximately 9.8 m/s^2. So, the gravitational force is:
Gravitational force = 14 kg x 9.8 m/s^2
3. Find the extra mass that can be added before the bowl sinks:
Extra mass = Buoyant force - Gravitational force
By subtracting the gravitational force from the buoyant force, we can determine the additional mass that can be added to the steel bowl without it sinking.
Now, plug in the values and evaluate the equation to find the answer to your question.