Final answer:
The buoyant force on a barge equals the weight of the water it displaces and acts upward. The drag force opposes the barge's motion and can be calculated using Newton's second law by subtracting the applied force from the net force needed to accelerate the barge.
Step-by-step explanation:
Calculating Buoyant Force and Drag Force on a Barge
The question involves calculating two forces acting on a barge: the buoyant force and the drag force. The buoyant force is a physics concept from the principle of buoyancy, which states that any object submerged in a fluid is acted upon by an upward force equal to the weight of the fluid displaced by the object. This force acts in the direction opposite to gravity. In the case of the barge, the buoyant force would equal the weight of the water displaced by the submerged volume of the barge.
To calculate the drag force acting on the barge, we use Newton's second law, F = m × a, where F is the total force applied to the barge, m is the mass of the barge, and a is its acceleration. Since the problem states the mass (5.0 × 10^6 kg) and acceleration (7.5 × 10^-2 m/s²), we can calculate the net force applied to the barge. The drag force is opposite to the direction of the applied force and acceleration. Thus, the magnitude of the drag force can be found by subtracting the applied force from the net force required to accelerate the barge.