Two lumps of putty are moving in opposite directions, each...

Two lumps of putty are moving in opposite directions, each one having a speed of $30.0 \mathrm{~m} / \mathrm{s}$. They collide and stick together. After the collision the combined lumps are at rest. If the mass of each lump was $1.00 \mathrm{~kg}$ before the collision, and no energy is lost to the environment, what is the change in mass of the system due to the collision?

Key Concepts

Mass-Energy Equivalence

Central to Einstein's theory of relativity, the mass-energy equivalence principle (expressed by the equation E = mc²) states that energy and mass are interchangeable. This concept explains how the kinetic energy lost in an inelastic collision can be converted into an increase in the system’s rest mass, even though the additional mass is typically very small in magnitude.

Kinetic Energy Transformation

In collision scenarios, especially in inelastic collisions, the kinetic energy initially present in the moving objects may be transformed into other forms of energy. In cases where no energy is lost to the environment, the energy is conserved via a transformation process, often becoming mass or internal energy according to the relationship between energy and mass.

Inelastic Collision

An inelastic collision is one in which the colliding bodies stick together after impact, meaning that while momentum is conserved, kinetic energy is not necessarily conserved in its original form. Instead, some or all of the kinetic energy is converted to other forms of energy, such as internal energy or binding energy.

Conservation of Momentum

This fundamental principle of physics states that the total momentum of an isolated system remains constant when no external forces act on it. In collision problems, it allows us to track the overall motion before and after impact, ensuring that the vector sum of the momenta of all objects remains unchanged.

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