An object of mass m moving at speed v0 strikes an object of mass 2m which had been at rest. The first object bounces backward along its initial path at speed v0. Is this collision elastic, and if not, what is the change in kinetic energy of the system?Select one:a.The collision is elastic.b.The kinetic energy decreases by mv2.c.The kinetic energy decreases by mv2.d.The kinetic energy increases by mv2.
Question
An object of mass m moving at speed v0 strikes an object of mass 2m which had been at rest. The first object bounces backward along its initial path at speed v0. Is this collision elastic, and if not, what is the change in kinetic energy of the system?Select one:a.The collision is elastic.b.The kinetic energy decreases by mv2.c.The kinetic energy decreases by mv2.d.The kinetic energy increases by mv2.
Solution
The collision is not elastic. In an elastic collision, both momentum and kinetic energy are conserved. Here, while the momentum is conserved, the kinetic energy is not.
Before the collision, the kinetic energy of the system is 1/2 * m * v0^2 (since the second object is at rest). After the collision, the kinetic energy of the system is 1/2 * m * v0^2 (for the first object moving backwards) + 1/2 * 2m * v0^2 (for the second object moving forwards) = 1.5 * m * v0^2.
The change in kinetic energy of the system is therefore 1.5 * m * v0^2 - 0.5 * m * v0^2 = m * v0^2. So, the kinetic energy increases by m * v0^2. Therefore, the correct answer is d. The kinetic energy increases by mv0^2.
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