Question

4 if two bodies of equal mass collide with each other with equal velocity in an elastic collision, their velocities after the collision will be - a zero. b equal in magnitude and opposite in direction. c half of what they were before the collision. d twice what they were before the collision. 5 who was the first to state the law of conservation of momentum? a aristotle b descartes c huygens d newton

Explanation:

Question 4

In an elastic collision between two bodies of equal mass (\(m_1 = m_2=m\)) with velocities \(u_1 = v\) and \(u_2=-v\) (opposite - direction). Using the conservation of momentum \(m_1u_1 + m_2u_2=m_1v_1 + m_2v_2\) (where \(v_1\) and \(v_2\) are post - collision velocities) and conservation of kinetic energy \(\frac{1}{2}m_1u_1^{2}+\frac{1}{2}m_2u_2^{2}=\frac{1}{2}m_1v_1^{2}+\frac{1}{2}m_2v_2^{2}\). Substituting \(m_1 = m_2=m\), \(u_1 = v\), \(u_2=-v\) into the momentum equation: \(mv - mv=mv_1+mv_2\Rightarrow v_1 + v_2 = 0\Rightarrow v_1=-v_2\). Substituting into the kinetic - energy equation (after canceling out \(\frac{1}{2}m\) terms): \(v^{2}+v^{2}=v_1^{2}+v_2^{2}\). Since \(v_1=-v_2\), we get \(2v^{2}=2v_1^{2}\Rightarrow|v_1| = |v_2|=v\). So velocities are equal in magnitude and opposite in direction.

René Descartes was the first to state the principle related to the conservation of momentum. Aristotle had incorrect ideas about motion (e.g., objects need a force to keep moving). Huygens made contributions to the understanding of collisions (a consequence of momentum conservation). Newton's laws (e.g., \(F = ma\) and the third law \(F_{12}=-F_{21}\)) can be used to derive the conservation of momentum, but Descartes was the first to state the concept in a form related to modern momentum conservation (he used the term 'quantity of motion' \(mv\)).

Answer:

B. equal in magnitude and opposite in direction.

Question 5