Re: elastic string question
Use conservation of energy. Neglecting the mass of
the string, the total energy comes from three sources:
kinetic energy of particle, gravitational potential
of particle, and elastic energy of string. By
symmetry, the particle will move on a vertical line
passing through the midpoint of A and B. Both when
the particle is released from rest and when it comes
back to rest at the lowest point of its travel, its
kinetic energy is zero. Hence, the sum of the
gravitational and elastic energies must be the same
at both points.
the string, the total energy comes from three sources:
kinetic energy of particle, gravitational potential
of particle, and elastic energy of string. By
symmetry, the particle will move on a vertical line
passing through the midpoint of A and B. Both when
the particle is released from rest and when it comes
back to rest at the lowest point of its travel, its
kinetic energy is zero. Hence, the sum of the
gravitational and elastic energies must be the same
at both points.