Understanding the Relationship Between Net Work and Particle Speed"

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If the net work done on a particle is zero, its speed remains constant, indicating that no external forces are acting on it to change its energy. The work-energy principle states that the work done is equal to the change in kinetic energy; thus, zero work implies no change in kinetic energy. In scenarios where a particle moves in a circular path, its speed at the beginning and end of the path remains the same, despite potential variations in kinetic energy during the motion. This highlights that while the particle's speed can fluctuate temporarily, the overall effect of zero net work results in a constant speed over time. Therefore, the relationship between net work and particle speed is crucial in understanding motion dynamics.
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Homework Statement


If the net work done on a particle is zero, what can be said about its speed. And why?



The Attempt at a Solution


is the speed also zero?
 
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actually i think its speed be constant? cause no work is being applied.
 
The work done in a system is the sum of the kinetic and potential energy of the system. In the case of a particle in a field, we'll consider the particle as the system and the work done by a field as an external influence on the particle.

As such, if the work done by the field is zero, the final kinetic energy of the particle is constant. That means, if over the course of time, the particle is made to follow a circular path, at the beginning and the end of that path, the kinetic energy and thus the speed will be the same. However, during the course of the path, i.e. in the middle of the circle, the kinetic energy may vary.
 

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