Momentum

Two particles $P$ and $Q$, of masses $0.2\text{kg}$ and $0.1\text{kg}$ respectively, are free to move in a straight line on a smooth horizontal plane. $P$ is projected towards $Q$ with speed $5\text{ms}^{-1}$. At the same instant, $Q$ is projected away from $P$ with speed $2\text{ms}^{-1}$. When $P$ collides with $Q$, the particles coalesce.

Find the kinetic energy lost during the collision.

A particle $A$ of mass $2.5\text{ kg}$ is released from rest from the top of a smooth plane, which makes an angle of $\sin^{-1} 0.2$ with the horizontal. The particle $A$ collides $2$ seconds later with a particle $B$, of mass $3\text{ kg}$, which is moving up a line of greatest slope of the plane. The speed of $B$ immediately before the collision is $3.5\text{ m s}^{-1}$. Immediately after the collision, $B$ has a velocity of $0.5\text{ m s}^{-1}$ down the plane.

Find the distance $A$ moves up the plane after the collision.

Two particles $A$ and $B$ of masses $km$ and $m$ respectively, where $k$ and $m$ are constants, are free to move in a straight line on a smooth horizontal plane. Particle $A$ is projected towards $B$ with speed $2u$ and at the same instant $B$ is projected towards $A$ with speed $u$.

The particles collide. After the collision the speed of $A$ is $u$ and both particles move in the same direction as $A$’s original motion.

It is given that $35\%$ of the total kinetic energy is lost in the collision. Find, in terms of $u$, the speed of $B$ after the collision.

Two particles $P$ and $Q$ of masses $0.2\text{ kg}$ and $0.5\text{ kg}$ respectively are at rest on a smooth horizontal plane. Particle $P$ is projected with a speed $6\text{ m s}^{-1}$ directly towards $Q$. After $P$ and $Q$ collide, $P$ moves with a speed of $1\text{ m s}^{-1}$.

Find the two possible speeds of $Q$ after the collision.

Two particles, $A$ and $B$, of masses $3\text{ kg}$ and $6\text{ kg}$ respectively, lie on a smooth horizontal plane. Initially, $B$ is at rest and $A$ is moving towards $B$ with speed $8\text{ m s}^{-1}$. After $A$ and $B$ collide, $A$ moves with speed $2\text{ m s}^{-1}$.

Find the greater of the two possible total losses of kinetic energy due to the collision.

Two particles $P$ and $Q$, of masses $0.1\text{ kg}$ and $0.4\text{ kg}$ respectively, are free to move on a smooth horizontal plane. Particle $P$ is projected with speed $4\text{ m s}^{-1}$ towards $Q$ which is stationary. After $P$ and $Q$ collide, the speeds of $P$ and $Q$ are equal.

Find the two possible values of the speed of $P$ after the collision.