A small submarine of mass 5,000 kg sinks in water with a uniform speed of 10 m/s. What is the size (magnitude) of the resultant force acting on the submarine?

To solve this problem, we need to understand that if the submarine is sinking at a uniform speed, it means the net force acting on it is zero. This is due to Newton's first law of motion, which states that an object will remain at rest or move in a straight line at a constant speed unless acted upon by an external force.

In this case, the forces acting on the submarine are gravity (downwards) and buoyancy (upwards). The force of gravity (weight) can be calculated using the formula:

Weight = mass x gravity Weight = 5000 kg x 9.8 m/s² = 49,000 N (downwards)

The buoyancy force is equal to the weight of the water displaced by the submarine, which in this case must be equal to the weight of the submarine for the forces to balance out and for the submarine to sink at a constant speed.

So, the buoyancy force is also 49,000 N, but acting upwards.

The resultant force is therefore:

Resultant force = Weight - Buoyancy force Resultant force = 49,000 N - 49,000 N = 0 N

So, the size (magnitude) of the resultant force acting on the submarine is 0 N.