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# Physics - 11 Complete Syllabus Notes

### Chapter 4 - Laws of Motion

Newton's Law of Motion:
"Everybody continues in its state of rest or uniform motion on a straight line unless external force is acted upon it to change its state."
Newton's first law of motion is also called as law of inertia. The resistance of a body to change its state is called inertia.

• Inertia of rest
• Inertia of motion
• Inertia of Direction
Newtons first law of motion gives qualitative defination of force. According to first law of motion, force is the external agency that tends to change its state of body.

Momentum (Linear Momentum)
The motion contain in a body is called momentum.
The linear momentum of a body is a product of its mass and velocityb.
It is denoted by p and given by
p = mv
In vector form,
$\overrightarrow{p}=m\overrightarrow{v}$
* it is vector quantity
* its S.I unit is kgms-1
* its dimensional formula is [MLT-1]

Newton's Second Law of Motion:
"The rate of change of linear momentum of a body is doirectly proportional to the applied force and changes takes places in the directional of force."

$i.e.&space;F&space;\alpha&space;\frac{dp}{dt}$
$or,&space;F&space;=k&space;\frac{dp}{dt}$
Where k is proportionality constant whose value is equal to 1.
$\therefore&space;F&space;=&space;\frac{dp}{dt}$
Newton second law of motion gives quantilavedefinition of force . according to second law of motion force is the rate of change of linear momentum of a body.
also,
Newton's second law of motion can be expressed as
F = ma
or, F = m{(v - u) / t}
or, F = (mv -mu) / t
or, F = (final momentum - Initial Momentum) / time taken
or, F = (change in momentum) / time taken
Therefore, Force = Rate of change of momentum

F = dp / dt
F = d(mv)/dt
F = mdv/dt + vdm/dt
F = ma + 0
F = ma

Newton's Third Law of Motion:
In every action there is an equal and opposite reaction.

Q. Newton second law of motion is called real law of motion:
→ Newton second law of motion is called real law of motion because both first law of motion and third law of motion are contained in second law of motion. Newton second law of motion is called real law of motion:

i) Newton's first law of motion from second law:
According to second law of motion,
F = ma
If there is absance of external force (f=0)
then, 0=ma
or, ma = 0
since, m ≠ 0
Therefore, a = 0
Here, zero acceleration means either the body is at rest or moving with uniform speed. Thus, in absance of external force object cannot change its state which is first law of motion.

ii) Newton third law of motion from second law:

Consider an isolated system considering of two object A and B of masses M 1 and M2 moving in a st. line with velocity u 1 and u2( u1 > u2) respectively. As shown in above figure , Suppose they collide and after collision let their velocities become v1 v2 respectively.

From Newton's second law of motion
Force exerted on A = (change in momentum of A) / Time of impact
$F_{a}=&space;\frac{\Delta&space;P_{a}}{t}$
$\Delta&space;P_{a}=&space;f_{a}&space;\times&space;t$
and force exerted on B = (change in momentum of B) / Time of impact
$F_{a}=&space;\frac{\Delta&space;P_{B}}{t}$
$\Delta&space;P_{B}=&space;f_{B}&space;\times&space;t$

Now,
Total change in momentum,
$\Delta&space;P=&space;\Delta&space;P_{A}&space;+&space;\Delta&space;P_{B}$
$\Delta&space;P=&space;F_{A}&space;\times&space;t&space;+&space;F_{B}&space;\times&space;t$
$\0=&space;F_{A}&space;\times&space;t&space;+&space;F_{B}&space;\times&space;t$
F A = -FB
Which is third law of motion //

Principle of Conservation of Linear Momentum:
→If the system is isolated then the total linear momentum of the system remains conserve or constant.
i.e. total initial momentum = total final momentum

Proof: From above figure fig(i) , consider an isolated system consisting of two object A and B of masses m1 and m 2 moving in a st line with velocity u1 and u 2 (u1 > u2) respectively. as shown in above figure, Suppose they collide and after collision let, their velociities become v1 and v2 respectively.

From Newton's second law of motion,
Force exerted on A = (change in momentum of A) / time of impact
F A = (m1v1 - m1u1) / t

Force exerted on B = (change in momentum of B) / time of impact
F B =( M2V2 - M2U2) / t
Now, from newton third law of motion
F A = -FB
$\frac{M_{1}V_{1}-M_{1}U_{1}}{t}$ = $-\left&space;(&space;\frac{M_{2}V_{2}-M_{2}U_{2}}{t}&space;\right&space;)$
$M_{1}V_{1}-M_{1}U_{1}&space;=&space;-M_{2}V_{2}+&space;M_{2}U_{2}$
$M_{1}V_{1}+M_{2}V_{2}&space;=&space;M_{1}U_{1}+&space;M_{2}U_{2}$
$M_{1}U_{1}+M_{2}U_{2}&space;=&space;M_{1}V_{1}+&space;M_{2}V_{2}$
i.e total iitial momentum = total final momentum

Application of Law of Motion:

1) Apparent weight of man lift Answer the weight measured by the weighing machine in the lift is called apparent weight . A man of mass m handing in the lift and g be the acceleration due to gravity

a) When lift at rest:
R+(-mg)=net force
R-mg=ma
R-mg=0
R=mg
Therefore,
apparement weight = real weight

b) When lift moving upward and downward with uniform speed :
R+(-mg)=net force
R-mg=ma
R-mg=0
R=mg
Therefore,
apparement weight = real weight

c) When lift moving upward with uniform acceleration'a' :
R+(-mg)=net force
R-mg=ma
R=mg+ma
R=m(a+g)
Therefore,
apparement weight is greater then real weight

d) When lift moving downward with uniform acceleration'a' :
mg+(-R)=net force
mg-R=ma
-R=ma-mg
-R=m(g-a)
R=m(g-a)
Therefore,
apparement weight is smaller real weight

e) If a=g(when lift is moving downward, freefall)
R=m(g-g)
R=m*0
R=0
Therefore,
This is the condition of weightlessness.

f) If a>g
R will be negative
Negative R means the person appears to stick on the ceiling of lift.

Impulse:

Impulse is a physical quality which measures effect of force. If the force is constant impulse is expressed as a product of force and time.
i.e. Impulse = force × time
If the force is variable then impulse is expressed as product of average force and time up to which force act.
i.e. Impulse = Average Force × time

* It is a vector quantity
* Its S.I unit is Kg ms-1 and dimensional formula is [MLT -1]

From Newton's Second Law of motion
Force = (change in momentum) / time
Force × time = change in momentum
Impulse = change in momentum

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