Question

STT 10.8 A small ball with mass M is at rest. It is then struck by a ball with twice the mass, moving at speed V0. The situation after the collision is shown in the figure. Is this possible?

A yes
B no, because momentum is not conserved
C no, because energy is not conserved
D no, because neither momentum nor energy is conserved.

Answer 1

The correct answer is C. no, because energy is not conserved.

Step-by-step explanation:

The situation described violates the principle of conservation of energy. In an elastic collision, both momentum and kinetic energy are conserved. However, in the scenario depicted, the small ball at rest gains kinetic energy after the collision, which is not possible if only elastic collisions are considered. The correct choice is C, as the violation of energy conservation is the primary reason why this situation is not possible.

In an elastic collision between two objects with masses
`\(m_1\)` and
`\(m_2\)` and velocities
`\(u_1\)` and
`\(u_2\)` before the collision and
`\(v_1\)` and
`\(v_2\)` after the collision, both momentum and kinetic energy are conserved. The conservation of momentum is expressed as
`\(m_1u_1 + m_2u_2 = m_1v_1 + m_2v_2\`), and the conservation of kinetic energy is expressed as
`\((1)/(2)m_1u_1^2 + (1)/(2)m_2u_2^2 = (1)/(2)m_1v_1^2 + (1)/(2)m_2v_2^2\)`.

In the given situation, since the small ball is initially at rest
`(\(u_1 = 0\))`, the kinetic energy before the collision is solely due to the moving ball with twice the mass. After the collision, the small ball gains kinetic energy, which violates the conservation of energy in an elastic collision. Therefore, the correct conclusion is that the situation is not possible due to the non-conservation of energy (Option C).