A rectangular barge 6 m long and 3 m wide float in fresh water. Water density is 1000 kg/m^3 horse?
Answer in units of m.
If the barge can only be pushed 5.34722 cm deeper into the water before water overflows to sink it, how many 350 kg horses can it carry?
To find out how many 350 kg horses the barge can carry, we need to determine the change in buoyant force when the barge is pushed 5.34722 cm deeper into the water.
First, let's calculate the volume of the barge. The volume of a rectangular box is given by the formula:
Volume = length x width x height
In this case, the barge's length is 6 m, width is 3 m, and the change in height (the depth pushed into the water) is 5.34722 cm or 0.0534722 m.
Volume = 6 m x 3 m x 0.0534722 m = 0.9645 m^3
Next, we can calculate the initial buoyant force acting on the barge before it sinks. The buoyant force is given by the formula:
Buoyant force = density of water x volume of the displaced water x gravitational acceleration
In this case, the density of water is 1000 kg/m^3 and the volume of the displaced water is equal to the volume of the barge, which is 0.9645 m^3. The gravitational acceleration is approximately 9.8 m/s^2.
Buoyant force = 1000 kg/m^3 x 0.9645 m^3 x 9.8 m/s^2 = 9421.41 N
Now, let's calculate the final buoyant force when the barge is pushed 5.34722 cm deeper into the water. Since the change in height is relatively small, we can assume that the volume of the displaced water remains the same.
Final buoyant force = density of water x volume of the displaced water x gravitational acceleration
Final buoyant force = 1000 kg/m^3 x 0.9645 m^3 x 9.8 m/s^2 = 9421.41 N
Since the final buoyant force is the same as the initial buoyant force, it means that the barge remains afloat even when pushed 5.34722 cm deeper into the water. Therefore, the barge can carry any number of 350 kg horses without sinking.