The rubber band in a slingshot is an elastic band which
when pulled to extend it beyond its equilibrium length returns to the original length
when released.
The behavior of the rubber band can be
considered to be like that of a spring. When a spring is stretched or compressed from
its equilibrium length it requires a certain amount of work to do so. The force that has
to be applied is related to the distortion by the Hooke's Law as F = -kx. The work done
is stored in the spring as potential energy which is released when there is no force
acting on the spring.
In the case of the rubber band in the
slingshot, stretching it by an extra distance requires energy which is stored as
potential energy in the band. When the band is released, this energy is converted to
kinetic energy of the stone. The kinetic energy KE = (1/2)mv^2, as the mass of the stone
remains the same, any extra kinetic energy results in an increase in the velocity. If
the stone has a greater kinetic energy, it will go
faster.
This explains the stone going faster if the rubber
band in the slingshot is stretched an extra distance.
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