a rectangular box measures 5 x 1 x .5 m. what mass may be loaded in it (including the mass of the box) before it sinks in a lake?
mass=density*volume
volume=5*1*5=25m3
density=1000kg/m3
mass=1000*25=25000kg
To determine the maximum mass that can be loaded into the rectangular box before it sinks, we need to consider the buoyant force acting on the box. The buoyant force is the upward force exerted on an object immersed in a fluid, in this case, water.
To calculate the buoyant force, we need to know the density of water and the volume of the box that is submerged when it is loaded. The density of water is approximately 1000 kg/m³.
Given:
Dimensions of the box:
Length (L) = 5 m
Width (W) = 1 m
Height (H) = 0.5 m
To calculate the volume of the box, we multiply the length, width, and height:
Volume (V) = L * W * H
To determine the submerged volume, we multiply the volume of the box by the density of water:
Submerged Volume (SV) = V * density of water
To calculate the buoyant force, we multiply the submerged volume by the acceleration due to gravity (approximately 9.8 m/s²):
Buoyant Force = SV * 9.8
The weight of the box and its contents must be less than or equal to the buoyant force for the box to remain afloat. Therefore, we can calculate the maximum mass that can be loaded into the box by dividing the buoyant force by the acceleration due to gravity:
Maximum Mass = Buoyant Force / 9.8
Now, let's substitute the given values and calculate the maximum mass:
Volume = 5 m * 1 m * 0.5 m = 2.5 m³
Submerged Volume = 2.5 m³ * 1000 kg/m³ = 2500 kg
Buoyant Force = 2500 kg * 9.8 m/s² = 24,500 N
Maximum Mass = 24,500 N / 9.8 m/s² ≈ 2500 kg
Therefore, the maximum mass that can be loaded into the rectangular box (including the mass of the box) before it sinks in the lake is approximately 2500 kg.