Two identical objects collide and bounce off without deformation. If the total momentum before the collision was zero, what is true after the collision?

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Question restatement: Two identical objects collide and bounce off without deformation. If the total momentum before the collision was zero, what is true after the collision?

Option a: Both objects move in the same direction at half speed. This cannot conserve momentum if the total initial momentum was zero, because two objects moving in the same direction would have a net momentum unless their speeds were zero, which contradicts the bounce with no deformation. Additionally, sharing momentum into the same direction would require some external impulse to set both traveling forward with equal halves, which is inconsistent with the initial condition of zero net momentum.

Option b: The objects move in opposite directions with equal speed. This option aligns with both the symmetry of the collision and momentum conservation. Since the objects are identical and there is no deformation, their speeds are equal in magnitude after the impact, but directed oppositely, so their momenta cancel out, keeping the total momentum at zero. This is the standard outcome for a head-on elastic collision between identical masses with zero net initial momentum.

Option c: One object remains at rest while the other moves with doubled speed. If one mass stayed at rest while the other moved, the total momentum would be nonzero after the collision unless there was an external impulse or an initial momentum that canceled out. This would violate the given condition of zero total momentum prior to collision and would require energy transfer mechanisms not described in the scenario.

Option d: The objects are stationary due to energy loss. Energy loss does not imply the system must become stationary; in fact, momentum conservation governs the motion. If there is zero total momentum initially and the collision is elastic (no deformation), the objects should move post-collision rather than both becoming stationary. Also, the phrase energy loss leading to stationarity contradicts the given bounce-without-deformation condition, which implies momentum is redistributed as kinetic energy in the two moving bodies rather than dissipated to zero velocity.

Summary: By momentum conservation and symmetry for two identical, perfectly elastic bodies with zero net initial momentum, the natural post-collision state is equal and opposite momenta, i.e., opposite directions with equal speeds. The other options violate momentum conservation or rely on unsupported assumptions about external forces or energy loss in this idealized scenario.

SPH4U - Physics 12 (2025-26) - A

Two identical objects collide and bounce off without deformation. If the total momentum before the collision was zero, what is true after the collision?

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