solution:
the spring force applied by a spring with spring constant k can be expressed as
where k acts as the spring constant
and x indicates the spring's deformation
to determine the work completed by the spring
the amount of work done by the spring when moving from x=0 to x=L
substituting the limits x=0 and x=L
we derive the work done in terms of k and L
The alteration in kinetic energy is
Clarification:
According to the work-energy principle, the task performed on an object corresponds to the alteration in its kinetic energy. In mathematical terms:
where:
W signifies the work performed on the object
denotes the kinetic energy at the end
indicates the kinetic energy at the start
Furthermore, when the force is exerted in line with the object’s motion, the work done is expressed as:
Here,
F represents the force’s magnitude
denotes the object’s displacement
In this scenario, the force impacting the object is
F
While the distance moved is the horizontal length traveled, hence
Consequently, the work accomplished is
Thus, the alteration in kinetic energy amounts to
Learn more about work and kinetic energy: