Forces and Laws of Motion:
Force: It is the force that enables us to do any work. To do anything, either we
pull or push the object. Therefore, pull or push is called force.
Example, to open a door, either we push or pull it. A drawer is pulled to open
and pushed to close.
Effects of Force:
(i) Force can move a stationary body or object. For example, a football can be
set to move by kicking it, i.e., by applying a force.
(ii) Force can stop a moving body. For example, by applying brakes, a running
cycle or a running vehicle can be stopped.
(iii) Force can change the direction of a moving object. For example, by
applying force, i.e., by moving handle, the direction of a running bicycle can
be changed. Similarly by moving steering, the direction of a running vehicle is
changed.
• Forces are mainly of two types:
(A) Balanced forces
(B) Unbalanced forces
(A) Balanced Forces
If the resultant of applied forces is equal to zero, it is called balanced forces.
Example, in the tug of war if both the team apply similar magnitude of
forces in opposite directions, rope does not move in either side. This happens
because of balanced forces in which resultant of applied forces become zero.
• Balanced forces do not cause any change of state of an object. Balanced
forces are equal in magnitude and opposite in direction.
(B) Unbalanced Forces
If the resultant of applied forces are greater than zero, the forces are
called unbalanced forces. An object in rest can be moved because of
applying balanced forces.
Unbalanced forces can do the following:
~ Move a stationary object
~ Increase the speed of a moving object
~ Decrease the speed of a moving object
~ Stop a moving object
~ Change the shape and size of an object
Laws of Motion:
Galileo Galilei:
Galileo first of all said that object move with a constant speed when no faces
act on them. This means if an object is moving on a frictionless path and no
other force is acting upon it, the object would be moving forever. That is,
there is no unbalanced force working on the object.
Newton’s Laws of Motion:
Newton studied the ideas of Galileo and gave the three laws of motion.
These laws are known as Newton's laws of motion.
Newton's First Law of Motion (Law of Inertia):
Any object remains in the state of rest or in uniform motion along a straight line, until
it is compelled to change the state by applying external force.
Mass and Inertia
* The property of an object because of which it resists to get disturb its state is called
inertia. Inertia of an object is measured by its mass. Inertia is directly proportional to
the mass. This means inertia increases with increase in mass and decreases with
decrease in mass. A heavy object will have more inertia than the lighter one.
* In other words, the natural tendency of an object that resists the change in state of
motion or rest of the object is called inertia.
Momentum
• Momentum is the power of motion of an object.
• The product of velocity and mass is called the
momentum. Momentum is denoted by 'p’.
Therefore, Momentum of the object = Mass x Velocity
Momentum and Mass and Velocity
• Since momentum is the product of mass and velocity (p = m x v) of an object. This
means momentum is directly proportional to mass and velocity. Momentum
increases with increase of either mass or velocity of an object.
• This means if a lighter and a heavier object is moving with same velocity, then
heavier object will have more momentum than the lighter one.
• Usually, road accidents prove more fatal because of high speed than in slower
speed. This happens because vehicles running with high speed have greater
momentum compared to a vehicle running with slower speed.
Momentum of an object which is in the state of rest :
Let an object with mass 'm' is in the rest. Since, object is in rest,
therefore, its velocity, v = 0
Now, we know that,
Momentum = mass x velocity
Unit of momentum :
SI unit of mass = kg
SI unit of velocity = meter per second i.e., m/s
We know that
Momentum (p) = m x v
Therefore, p = kg x m/s
Numerical Problems Based on Momentum
Type I. Calculation of Momentum
Qus.1. What will be the momentum of a stone having mass of 10 kg when it
is thrown with a velocity of 2 m/s ?
Qus.2. A car having mass of 1000 kg is moving with a velocity of 0.5
m/s. What will be its momentum ?
Statement of Second Law
Rate of change of momentum of an object is proportional to
applied unbalanced force in the direction of force.
Mathematical expression
Suppose, Mass of an object = m kg
Initial velocity of an object = u m/s
Final velocity of an object = v m/s
So, Initial momentum, p₁ = mu, Final momentum, p₂ = mv
CHANGE IN MOMENTUM
= Final momentum - Initial momentum
= my-mu
= m(v-u)
RATE OF CHANGE OF MOMENTUM
= Change in momentum / Time taken
= m(v - u) / t
According to IInd law, this rate of change is momentum is directly
proportional to force.
F ∝ m(v - u) / t
We know that,
(v - u) / t = a
So, F = kma
Where k is a constant.
Its value = 1.
• F = 1 x m x a = ma
SI unit = kg m/s² or Newton
Proof of Newton's First Law of Motion from Second Law First law
states that if external force F = 0 , then a moving body keeps
moving with the same velocity, or a body at rest continues to be
at rest.
So, F = 0
We know, F = m(v-u) / t
Third Law of Motion
To every action there is an equal and opposite reaction.
Applications:
(i) Walking is enabled by IIIrd law.
(ii) A boat moves back when we deboard it.
(iii) A gun recoils.
(iv) Rowing of a boat.
Law of Conservation of Momentum
When two (or more) bodies act upon one another, their total
momentum remains constant (or conserved) provided no external
forces are acting.
Initial momentum = Final momentum
Suppose, two objects A and B each of mass m¹, and mass m², are moving
initially with velocities u¹, and u₂, strike each other after time t and start
moving with velocities v¹, and v², respectively.
Now,
Initial momentum of object A = m¹u¹
Initial momentum of object B = m²u²
Final momentum of object A = m₁v¹
Final momentum of object B = m²v²
Rate of change of momentum in
A, F1 = (m¹v² - m¹u¹) / t
= m¹(v¹-u¹) / t
Qus.1. A bullet of mass 20 g is fired horizontally with a velocity
of 150 m/s from a pistol of mass 2 kg. Find the recoil velocity of
the pistol.
Q.2. Two hockey players viz A of mass 50 kg is moving with a velocity
of 4 m/s and another one B belonging to opposite team with mass 60
kg is moving with 3 m/s, get entangled while chasing and fall down.
Find the velocity with which they fall down and in which direction?
THANK YOU
