A sailboat is moving at a constant velocity. Is work being done by a net external force acting on the boat?
The answer key is "No" according to the work energy theorem about work is done when there is a change in final and initial velocity. But if I use Work = Force x displacement, even though the velocity is constant there is still some displacement done by the (constant) force acting on it. So I figured that the answer is "Yes". Which one is true?
Best Answer
The wind is certainly doing work, because it applies a force and the point where the force is applied is displaced. However it isn't doing any work on the boat, it's doing the work on the water.
The key point is that the net force on the boat is zero. We know the net force on the boat is zero because the boat is moving at constant velocity - if the net force were non-zero the boat would be accelerating. Since the net force on the boat is zero no work is being done on the boat.
The velocity of the boat is constant because the drag of the water is balancing out the force applied by the wind. So overall the wind is applying a force to the water - the boat is just the instrument through which the force from the wind is communicated to the water. So the wind is doing work on the water, but not on the boat.