Question

if 2 objects collide and stick together, what will happen to their velocities?
a. none of the above
b. velocities will increase
c. velocities will decrease
d. velocities will stay the same

Explanation:

Step1: Apply conservation of momentum

According to the law of conservation of momentum \(m_1v_1 + m_2v_2=(m_1 + m_2)v\).

Step2: Analyze velocity change

Let \(m_1\) and \(m_2\) be the masses of the two objects, \(v_1\) and \(v_2\) be their initial velocities, and \(v\) be the final velocity. If we assume \(v_1\) and \(v_2\) are in the same direction (for simplicity, without loss of generality), then \(v=\frac{m_1v_1 + m_2v_2}{m_1 + m_2}\). Since \(m_1 + m_2>m_1\) and \(m_1 + m_2>m_2\) (assuming \(m_1>0\) and \(m_2>0\)), if \(v_1\) and \(v_2\) are non - zero, the final velocity \(v\) will be a weighted average of \(v_1\) and \(v_2\). In a perfectly inelastic collision (objects stick together), the kinetic energy is not conserved (some is lost as heat, sound etc.). If we consider a case where one object is initially at rest (\(v_2 = 0\)), then \(v=\frac{m_1v_1}{m_1 + m_2}

Answer:

C. velocities will decrease