- Linear Momentum
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- Impulse and Momentum
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- Conservation of Linear momentum
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- Recoil of the Gun
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- Motion of the system with varying mass(Rocket)
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- Linear Momentum Problems with Solutions

- We have already studied about the newton's laws of motion and about their application

- It becomes difficult to use Newton's law of motion as it is while studying complex problems like collision of two objects,motion of the molecules of the gas,rocket propulsion system etc.

- Thus a further study of newton's law is required to find some theorem or principles which are direct consequences of Newton's law

- We have already studied one such principle which is principle of conservation of energy.Here in this chapter we will define momentum and learn about the principle of conservation of momentum .

- Thus we begin this chapter with the concept of impulse and momentum which like work and energy are developed from Newton's law of motion

- From our daily life experiences like during the game of table tennis if the ball hits a player it does not hurt him. On the other hand, when a fast moving cricket ball hits a spectator, it may hurt him.
- This suggests that impact produced by moving objects depends on both their mass and velocity.
- So, there appears to exist some quantity of importance that combines the object's mass and its velocity called momentum and was introduced by Newton.
- Momentum can be defined as "mass in motion". All objects have mass; so if an object is moving, then it has momentum - it has its mass in motion.
- The momentum, p of an object is defined as the product of its mass, $m$ and velocity, $v$. That is, Momentum $p=mv$ (1)
- Momentum has both direction and magnitude so it is a vector quantity. Its direction is the same as that of velocity, $v$.
- The SI unit of momentum is kilogram-meter per second (kg m s
^{-1}). - Since the application of an unbalanced force brings a change in the velocity of the object, it is therefore clear that a force also produces a change of momentum.
- We define the momentum at the start of the time interval is the
*initial momentum*and at the end of the time interval is the*final momentum*. - When the object moves then it gains momentum as the velocity increases. Hence greater the velocity greater is the momentum.
- Newton actually expressed his second law in momentum form

"Force is directly proportional to the rate of change of momentum of a body and it takes place in the direction in which the force acts."

- $F = \frac {dp}{dt}$

or

$F =\frac {d(mv)}{dt}$

for constant mass

$F= m \frac {dv}{dt} =ma$

- So $F = \frac {dp}{dt}$ and $F= ma$ are equivalent
- This can be expressed in vector form as

$f= \frac {d\mathbf{p}}{dt}$

Find the momentum of the object of mass of .5 kg and moving with velocity 10 m/s?

Momentum is given by

$p= mv = .5 \times 10 = 5 kgms^{-1}$

A tennis player hit the ball at the speed 40 m/s . The mass of the ball is .05 kg and it was in contact with racket for 4 ms. Find the force applied by the tennis player?

$F = \frac {dp}{dt}$

Initial momentum =0

Final momentum= .05 x 40 = 2 kgm/s

$F = \frac {2 -0}{4 \times 10^{-3}} = 500 N$

Class 11 Maths Class 11 Physics Class 11 Chemistry