A rectangular barge, 5.6 m long and 3.0 m wide, floats in fresh water. Suppose that a 370-kg crate of auto parts is loaded onto the barge.

and the question is???

200

To determine what happens to the barge when the crate of auto parts is loaded onto it, we need to consider the principles of buoyancy.

The buoyant force acting on an object submerged in a fluid is equal to the weight of the fluid displaced by the object. In this case, the barge is floating in fresh water, so the weight of the water displaced by the barge is equal to the buoyant force acting on it.

The weight of an object can be calculated using the formula:

Weight = Mass × Gravity

where Mass is the mass of the object and Gravity is the acceleration due to gravity, which is approximately 9.8 m/s^2 on Earth.

In this case, the mass of the crate is given as 370 kg. To find the weight of the crate, we can use the formula:

Weight = Mass × Gravity
Weight = 370 kg × 9.8 m/s^2
Weight ≈ 3626 Newtons (N)

Now, let's calculate the weight of the water displaced by the barge. The volume of water displaced can be found by multiplying the length, width, and height of the submerged part of the barge. Since we are given the length and width of the barge, we need to determine the height of the submerged part.

When the crate is loaded onto the barge, it will sink down slightly, causing the water level to rise. The height of the submerged part can be determined by subtracting the original waterline level from the new waterline level.

Assuming the height of the crate is small compared to the height of the barge, we can consider the water level rise to be the same as the crate's height.

Now, let's calculate the submerged height:
Submerged Height = 370 kg / (density of water × g)

The density of fresh water is approximately 1000 kg/m^3.
Submerged Height = 370 kg / (1000 kg/m^3 × 9.8 m/s^2)
Submerged Height ≈ 0.038 m (or 3.8 cm)

Now we have all the information we need to calculate the volume of water displaced:
Volume = Length × Width × Submerged Height
Volume = 5.6 m × 3.0 m × 0.038 m
Volume ≈ 0.6384 cubic meters (m^3)

Finally, we can calculate the weight of water displaced using the formula:
Weight = Density × Volume × Gravity

Weight of water displaced = 1000 kg/m^3 × 0.6384 m^3 × 9.8 m/s^2
Weight of water displaced ≈ 6279.36 Newtons (N)

Since the weight of the crate (3626 N) is less than the weight of the water displaced (6279.36 N), the barge will continue to float when the crate of auto parts is loaded onto it.