Question

two objects (m_1) and (m_2) approach each other along a straight line with speeds (v_1) and (v_2) as shown. the objects collide and stick together. what is the total change of linear momentum of the objects as a result of the collision? a. (m_1v_1 + m_2v_2) b. (m_1v_1 - m_2v_2) c. (m_2v_2 - m_1v_1) d. zero

Explanation:

Step1: Recall law of conservation of momentum

In an isolated - system (no external forces acting on the two - object system during the collision), the total linear momentum before the collision is equal to the total linear momentum after the collision.
Let the initial momentum of object 1 be $p_1 = m_1v_1$ (taking the right - hand direction as positive) and the initial momentum of object 2 be $p_2=-m_2v_2$ (since it is moving in the opposite direction). The total initial momentum $P_i=m_1v_1 - m_2v_2$. After the collision, the two objects stick together with mass $m = m_1 + m_2$ and move with a common velocity $v$. By the law of conservation of momentum $P_i = P_f$, where $P_f=(m_1 + m_2)v$.

Step2: Calculate change in momentum

The change in total linear momentum $\Delta P=P_f - P_i$. Since $P_i = P_f$ according to the law of conservation of momentum, $\Delta P=(m_1v_1 - m_2v_2)-(m_1v_1 - m_2v_2)=0$.

Answer:

D. zero