Answer:
To determine how deep the rectangular barge will sit in the river, we need to consider the concept of buoyancy. Here's a step-by-step explanation:
1. Buoyancy Principle: When an object is placed in a fluid, it experiences an upward force called buoyant force. The magnitude of this force depends on the volume of the object submerged in the fluid and the density of the fluid.
2. Barge Dimensions: The rectangular barge has dimensions of 3.0 m (width) by 22.0 m (length). The depth at which it sits in the harbor is given as 0.90 m.
3. Volume of the Barge: To determine the volume of the barge, we multiply its length, width, and depth: Volume = Length x Width x Depth. In this case, the volume is 3.0 m x 22.0 m x 0.90 m = 59.4 cubic meters.
4. Density of the Fluid: The density of water, which is typically used to represent river water, is approximately 1000 kg/m^3.
5. Buoyant Force: The buoyant force acting on the barge is equal to the weight of the fluid displaced by the submerged portion of the barge. It can be calculated using the formula: Buoyant Force = Density of Fluid x Volume of Displaced Fluid x Acceleration due to Gravity.
6. Calculation: In this case, the volume of displaced fluid is equal to the volume of the barge, which is 59.4 cubic meters. Plugging in the values, the buoyant force can be calculated as Buoyant Force = 1000 kg/m^3 x 59.4 m^3 x 9.8 m/s^2.
7. Final Depth: The barge will sit in the river at a depth where the buoyant force is equal to its weight. This occurs when the weight of the barge is equal to the buoyant force. By equating the two forces, we can determine the depth at which the barge will sit in the river.
It's important to note that the specific depth at which the barge will sit in the river depends on factors such as the weight of the barge, the weight of the cargo (if any), and any additional factors that may affect buoyancy. Without this information, we can't provide an exact depth.