A mass m=1 kg moving horizontally with velocity v0=2 m / s collides in elastically with a pend

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A mass m=1 kg moving horizontally with velocity v0=2 m / s...

A mass $m=1 \mathrm{~kg}$ moving horizontally with velocity $v_{0}=2 \mathrm{~m} / \mathrm{s}$ collides in elastically with a pendulum of same mass. Find the maximum change in potential energy (in Joule) of combined mass.

Key Concepts

Elastic Collision

An elastic collision is one in which both kinetic energy and momentum are conserved. This means that no energy is lost to deformation, heat, or sound during the collision. The conservation principles allow for the analysis of individual velocities of the colliding objects post-impact.

Conservation of Linear Momentum

In any collision, the total linear momentum of the system is conserved if there are no external forces acting on it. This concept is crucial as it provides an equation relating the velocities of the objects involved before and after the collision, regardless of the energy exchanges or transformations that may occur.

Conservation of Energy

The conservation of energy principle states that the total energy in an isolated system remains constant. In the context of elastic collisions, the kinetic energy before the collision equals the kinetic energy after the collision. This provides an additional constraint that, together with momentum conservation, helps to determine the outcomes of the collision.

Conversion of Energy in Pendulum Motion

In pendulum motion, the kinetic energy acquired by the pendulum is gradually converted into gravitational potential energy as it swings upward. The maximum potential energy occurs at the peak of the swing when the pendulum's velocity momentarily drops to zero. This conversion is key to understanding how energy is redistributed after the collision and determining the maximum change in potential energy.

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