PROBLEMS (EASY TYPE)
1) A wooden plank of mass m_{0} is resting on a smooth horizontal floor. A man of mass am_{0} starts moving from one end of plank to other. The length of plank is l_{0}. Find the displacement of plank over the floor when man reaches other end of plank?
Solution:
The center of mass remains stationary as no external force. Hence,
_{ }
_{ }
2) A particle of mass 5kg is initially at rest. A force starts acting on it one direction whose magnitude changes with time. The force time graph is as shown in figure. Find the velocity of particle after 10 sec?
Solution:
Impulse = DMomentum
= Area under Ft graph.
_{ }
3) Three identical balls, ball A, ball B, ball C are placed on a smooth floor on a straight line at the separation of 20m between balls as shown in figure. Initially balls are stationary. Ball A is given a velocity of 5m/s towards Ball B. Collision between A+B has coefficient of restitution as ½. But collision between B+C has coefficient of restitution as 1. What is the time interval between 2 consecutive collision between ball A and ball B?
Solution:
(1) Collision of A and B:
If velocities of ball A and ball B are V_{1} and V_{2} after collision then,
Then
_{ }
And _{ }
_{ }
(2) Collision between B and C:
Velocities get interchanged and so B is at rest after collision.
So time interval = _{ }
= 16 sec
4) A light spring of spring constant K_{0} is kept compressed with compression = _{ }
between two masses of mass ‘m’ and ‘am’. When released the blocks acquire a velocity in opposite directions. The spring loses contact with both blocks when it comes in natural length! Find the final velocities of the two blocks?
Solution:
Since no external force is acting, hence
_{ } But initial momentum = 0. Hence if final velocities of m and am are V_{1} and V_{2} then,
mV_{1}  amV_{2} = 0
V_{1} = aV_{2}  (1)
Now energy remains conserved so,
E_{i} = E_{f}.
_{ }
5) A bullet of mass m_{0} strikes a block of mass ‘hm_{0}’ with a speed of V_{0} and gets embedded into the mass ‘hm_{0}’. The block is attached to a spring of stiffness ‘K’. Find the loss of K.E. of system after impact?
Solution:
As the spring force is a non impulsive force, so we can conserve momentum as:
_{ }
6) A stationary body explodes into four identical fragments such that three of them fly off mutually perpendicular to each other with same K.E =E_{0} Find energy of explosion?
Solution:
Let the three fragments move along x, y, z direction with velocities_{ } .
Now _{ }
_{ }
