Answer to Question #91256 in Mechanics | Relativity for Umar

Question

A body of mass 2kg moving with velocity of 6m/s collides with a stationary object of mass 0.5kg. If the two bodies move together after the impact, calculate their common velocity

Answer 1

We can find the common velocity of the two bodies from the law of conservation of momentum:

$$m_1v_{1i} + m_2v_{2i} = (m_1 + m_2) v_{com},$$

here, $m_1 = 2 kg$ is the mass of the body, $m_2 = 0.5 kg$ is the mass of the stationary object, $v_{1i} = 6 m/s$ is the initial velocity of the body, $v_{2i} = 0$ is the initial velocity of the object, $v_{com}$ is the common velocity of the system of two bodies.

Then, from this equation we can calculate the common velocity of the system of two bodies:

$$v_{com} = \dfrac{m_1v_{1i}}{(m_1 + m_2)} = \dfrac{2 kg \cdot 6 \dfrac{m}{s}}{(2 kg + 0.5 kg)} = 4.8 \dfrac{m}{s}.$$

Answer:

$v_{com} = 4.8 \dfrac{m}{s}.$