Conservation Of Momentum

As shown in the figure, a cart of mass $M$ has a smooth, quarter-circular track of radius $R$. A small block of mass $m$ slides down from the top of the track. The block and the cart are initially at rest. The friction on the wheels is negligible.

A $6.0 \text{ kg}$ object is moving in the positive x-direction at $50 \text{ m/s}$. An internal explosion breaks it into three pieces. A $2.0 \text{ kg}$ piece moves in the positive y-direction at $500 \text{ m/s}$. A $1.0 \text{ kg}$ piece moves in the negative x-direction at $400 \text{ m/s}$.

Two children, A and B, are on sleds on frictionless ice. The mass of A plus sled is $M=30$ kg, and the mass of B plus sled is also $M=30$ kg. Child A, initially holding a box of mass $m=15$ kg, moves at $v_0=2.0$ m/s towards B, who is moving at the same speed $v_0$ towards A. To avoid a collision, A pushes the box towards B, and B catches it.

As shown in the diagram, a light spring with spring constant $k$ connects objects A and B. The mass of object B is $m_B = m$, and the mass of object A is $m_A = 2m$. Another object C, with mass $m_C = m$, is placed in contact with object B. The entire system rests on a smooth horizontal surface. Initially, the system is held at rest with the spring compressed by 6 cm. The external forces are then removed.