# Law of Motion VII

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Physical Application
i) When we push any block in the forward direction then block pushes us in the backward direction with an equal and opposite force.
ii) Horse pulls the rod attached to the cart in the forward direction and the tension of the rod pulls the cart in the backward direction
iii) Earth pulls the body on its surface in vertically downward direction and the body pulls the earth with the same force in vertically upward direction.
iv) While walking we push the ground in the backward direction using static frictional force and the ground pushes us in the forward direction using static frictional force.
v) When a person sitting on the horse whips the horse and horse suddenly accelerates, the saddle on the back of the horse pushes the person in the forward direction using static frictional force and the person pushes the saddle in the backward direction using static frictional force.

Linear Momentum

It is defined as the quantity of motion contained in the body. Mathematically it is given by the product of mass and velocity. It is a vector quantity represented by p.
Principle Of Conservation Of Linear Momentum
It states that in the absence of any external applied force total momentum of a system remains conserved.

Physical Application
i) Recoil of gun – when bullet is fired in the forward direction gun recoils in the backward direction.
ii) When a person jumps on the boat from the shore of river, boat along with the person on it moves in the forward direction.
iii) When a person on the boat jumps forward on the shore of river, boat starts moving in the backward direction.
iv) In rocket propulsion fuel is ejected out in the downward direction due to which rocket is propelled up in vertically upward direction.

Different Cases of Conservation of Linear Momentum

Recoil of gun
Let mass of gun be mg and that of bullet be mb
Initially both are at rest, hence their initial momentum is zero.
Finally when bullet rushes out with velocity vg, gun recoils with velocity vb, hence their final momentum is
Since there is no external applied force, from the principal of conservation of linear momentum

From above expression it must be clear that
1. Gun recoils opposite to the direction of motion of bullet.
2. Greater is the mass of mullet mor velocity of bullet vgreater is the recoil of the gun.
3. Greater is the mass of gun mg, smaller is the recoil of gun.

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