Net External Force & Work Done: Explained & Justified

[clarkandlarry]

A sailboat is moving at a constant velocity. Is work being done by a net external force acting on the boat? Explain.

The speed of a particle doubles and then doubles again because a net external force acts on it. Does the net force do more work during the first or the second doubling? Justify your answer.

 

[G01]

Welcome to PF Clark and Larry!

This seems like a homework question, so according to the forum rules, you must show your own thoughts on the problems before anyone can help you.

Also, please post future homework problems in the appropriate Homework forums:

https://www.physicsforums.com/forumdisplay.php?f=152

 

[Moetasim]

I can provide a response to the content regarding net external force and work done. In the case of a sailboat moving at a constant velocity, there is no net external force acting on the boat. This means that there is no change in the boat's kinetic energy and therefore, no work is being done on the boat.

In the scenario where the speed of a particle doubles and then doubles again due to a net external force, it can be stated that the net force does more work during the first doubling. This is because during the first doubling, the particle experiences a greater change in velocity, resulting in a larger change in kinetic energy. This means that the net force applied over a certain distance results in a greater amount of work done. In the second doubling, the particle has already gained a significant amount of kinetic energy, and therefore, the same amount of force applied over the same distance will result in a smaller change in kinetic energy and consequently, less work done.

This can be justified by the work-energy theorem, which states that the work done on an object is equal to the change in its kinetic energy. As the particle's speed doubles, its kinetic energy increases by a factor of four, whereas in the second doubling, the kinetic energy only increases by a factor of two. Therefore, the net force does more work during the first doubling due to the larger change in kinetic energy.

In conclusion, the net force does more work during the first doubling because the particle experiences a greater change in velocity and kinetic energy. This is in line with the work-energy theorem and the concept of work being equal to the change in kinetic energy.