Question 340: Work, Energy and Power & Circular Motion

Question

Three objects A, B and C are kept in a straight line on a frictionless horizontal surface. These have masses m, 2m and m, respectively. The object A moves towards B with a speed 9 m/s and makes an elastic collision with it. Thereafter, B makes completely inelastic collision with C. All motions occur on the same straight line. Find the final speed (in m/s) of the object C.

Accepted Answer

Let $$V_1$$ and $$V_2$$ be the velocities of blocks A and B immediately after the elastic collision:
$${v_1} = \left( {{{{m_1} - {m_2}} \over {{m_1} + {m_2}}}} ight)m = \left( {{{m - 2m} \over {m + 2m}}} ight) 	imes 9 =  - 3$$ m/s
$${v_2} = \left( {{{2{m_1}} \over {{m_1} + {m_2}}}} ight)m = \left( {{{2m} \over {m + 2m}}} ight) 	imes 9 = 6$$ m/s
After the perfectly inelastic collision between blocks B and C, let $$v$$ be the common velocity. Applying centre of mass concept, we get
$$2m{v_2} = (2m + m)v$$
$$ \Rightarrow v = {2 \over 3} 	imes 6 = 4$$ m/s

Work, Energy and Power & Circular Motion

Integer / Numeric Answer Type