Consider two situations, given figures. Case

(I), the springmass system is constrained; in case

(II), the spring-mass system is free to move in the smooth horizontal surface. If ${\mathrm{m}}_1$ is projected with a velocity $v_0,$ can you conserve the momentum of the system in each case? Explain.

 

Two blocks of masses ${\mathrm{m}}_1$ and $m_2,$ interconnected with a spring of stiffness $K,$ are kept on a smooth horizontal surface. Find out the ratio of velocity, displacement, kinetic energy and acceleration of block with mass $m_1$ to block with mass $m_2.$

A bomb, initially at rest, explodes into several pieces.

(a) Is linear momentum of the system conserved? 

(b) Is kinetic energy of the system conserved? Explain.

You are standing perfectly still and then you take a step forward. Before the step your momentum was zero, but afterward you have some momentum. Is the principle of conservation of momentum violated in this case?

Discuss the possibility of conservation of linear momentum of a block moving on a rough inclined plane if $\mu =\tan \theta .$

A mud ball at rest explodes into three fragments of masses in the ratio $1: 2: 1.$ The two equal masses move with velocities $2\hat{i}+5\hat{j}-6\hat{k}$ and $-4\hat{i}+3\hat{j}+2\hat{k}.$ Find the velocity of the third mass.

(a) A rail road car of mass $M$ is moving without friction on a straight horizontal track with a velocity $u.$ A man of mass $\mathrm{m}$ lands on it normally from a helicopter. What will be the new velocity of the car?

(b) If now the man begins to run on it with speed $v_{\text{rel }}$ with respect to car in a direction opposite to motion of the car, what will be the new velocity of the car?