a rectangular box of negligible mass measures 5m long,1m wide and 0.5m high. How many kilograms of mass can be loaded into the box before it will sink in a freshwater lake?
Vb = L*W*h = 5 * 1 * 0.5 = 2.5 m^3 = Vol. of the box=Vol. of water displaced.
Mass = Vb*Dw = 2.5m^3 * 1000kg/m^3 =
2500 kg.
Well, I have to say, that is quite the deep question! To determine how many kilograms of mass can be loaded into the box before it sinks, we need to consider the volume of water it will displace.
If we calculate the volume of the box by multiplying its length, width, and height (5m x 1m x 0.5m), we find that it has a volume of 2.5 cubic meters.
Now, since the density of freshwater is approximately 1000 kilograms per cubic meter, we can conclude that the box can hold a maximum of (2.5 cubic meters) x (1000 kilograms per cubic meter) = 2500 kilograms of mass before it sinks.
So, it seems like this box can handle quite the load, but remember, don't go overboard or it might just end up a sinking ship!
To determine the maximum mass that can be loaded into the rectangular box before it sinks in a freshwater lake, we need to consider the buoyant force acting on the box. The buoyant force is equal to the weight of the water displaced by the submerged portion of the box.
First, let's calculate the volume of the box. The volume (V) of a rectangular box is given by the formula V = length × width × height.
V = 5m × 1m × 0.5m
V = 2.5 m³
Freshwater has a density of approximately 1000 kg/m³.
Now, let's determine the weight of the water displaced by the submerged portion of the box. The weight (W) of an object is given by the formula W = mass × gravity, where gravity is approximately 9.8 m/s².
Since the box will fully submerge when it sinks, the weight of the water displaced will be equal to the weight of the box and the maximum mass it can hold.
W = mass × gravity
mass = W / gravity
The weight of the water displaced is equal to the volume of water (V) multiplied by the density of freshwater (ρ) and the acceleration due to gravity (g).
W = V × ρ × g
mass = (V × ρ × g) / g
mass = V × ρ
Substituting the values into the equation:
mass = 2.5 m³ × 1000 kg/m³
mass = 2500 kg
Therefore, the rectangular box can hold a maximum mass of 2500 kilograms before it sinks in a freshwater lake.
To determine the mass that can be loaded into the box before it sinks, we need to consider the buoyant force exerted by the freshwater lake on the box.
First, let's calculate the volume of the box:
Volume = length × width × height
Substituting the given dimensions:
Volume = 5m × 1m × 0.5m
Volume = 2.5 cubic meters
The density of freshwater is approximately 1000 kg/m³.
Now, let's calculate the buoyant force:
Buoyant force = density of fluid × volume × gravitational acceleration
Substituting the values:
Buoyant force = 1000 kg/m³ × 2.5 m³ × 9.8 m/s²
Buoyant force ≈ 24,500 N
For the box to remain afloat, the weight of the box and the mass loaded into it should not exceed the buoyant force.
The weight is given by:
Weight = mass × gravitational acceleration
Since the box has a negligible mass, we can neglect its weight. Therefore, the total weight is only determined by the mass of the contents.
To find the maximum mass, we need to equate the weight to the buoyant force:
mass × gravitational acceleration = buoyant force
Rearranging the equation:
mass = buoyant force / gravitational acceleration
Substituting the values:
mass = 24,500 N / 9.8 m/s²
mass ≈ 2500 kg
Therefore, the maximum mass that can be loaded into the box before it sinks in the freshwater lake is approximately 2500 kilograms.