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Center of Mass : Introduction 0/4

Lecture1.1

Lecture1.2

Lecture1.3

Lecture1.4


Momentum Conservation & Collision 0/4

Lecture2.1

Lecture2.2

Lecture2.3

Lecture2.4

Momentum Conservation
If the net external force acting on a system is zero than momentum of system remains conserve.
This is the law of momentum conservation.
Q11.
Initially system was at rest. Now the man starts running with velocity of 10 m/s with respect to the plank. Find out the velocity of plank with respect to ground.
Ans:
Let’s assume that velocity of plank is V m/s with respect to ground. Given that velocity of man is 10 m/s with respect to plank. Hence, velocity of man with respect to ground is (V10) m/s in opposite direction of plank.
Let’s apply momentum conservation on the system,
Q12.
A system of man and vehicle is at rest as shown in above diagram. The man jumps horizontally with velocity u m/s with respect to vehicle. Find out velocity of vehicle with respect to ground after jump.
Ans:
Let’s assume that velocity of vehicle is V m/s with respect to ground. Now velocity of man with respect to ground will be (uv) m/s in opposite direction.
Because initial momentum of the system was zero and there is no external force acting on the system, moment of system will be conserved.
Q13.
Find out maximum height achieved by the block and maximum velocity of wedge. (Hint – at maximum height relative velocity of block with respect to wedge will be zero.)
Ans:
In this case we need to apply two type of conservation. As there is no external force is acting in the horizontal direction so momentum will be conserved in horizontal direction for the system.
In vertical direction only gravitational force is acting on the system which is a conservative force and hence we can apply energy conservation on the system.
By applying momentum conservation we will get velocity of wedge. By applying energy conservation we will get maximum height achieved by the block.
Applying momentum conservation when relative velocity of block is zero, i.e. block and wedge both are moving with velocity V m/s.
Now apply energy conservation,
Q14.
Consider a ring mass system. Spring is in its natural position at initial point. Find out the maximum extension in the spring possible at any moment.
Ans:
When there will be maximum tension in the spring velocity of separation will be equal to 0. It does not mean that both blocks will be at rest. It means that both blocks will move with equal velocity.
Apply momentum conservation,
Apply energy conservation,
Reference frame of Center of mass
In the reference frame of Center of mass, velocity of Center of mass is always zero with respect to Center of mass. That means momentum of a system is always zero in the reference frame of Center of mass.
Acceleration of Centre of mass with respect to Centre of mass is always zero. That means net external force which includes pseudoforce also is always zero on the system in the reference frame of Centre of mass.
That means momentum of the system is always conserved in the reference frame of Center of mass.