1) The document discusses Newton's laws of motion and provides explanations and formulas for tension in a string when two bodies of unequal mass are connected by a string passing over a pulley. 2) It also discusses concepts like momentum, the law of conservation of momentum, different types of friction, advantages and disadvantages of friction, and methods to reduce friction. 3) Formulas are provided for calculating acceleration, tension, momentum, static and kinetic friction.

1. Class X
By Miss Tehmina Faizan

2. PUSH
PULL
TWIST
BEND
STRETCH
DISTORT
SHAPE FORCE
ROTATE

5. Newton's Laws of Motion
1st Law
Law of Inertia
2nd Law
F = ma
3rd Law
F12 = -F21

6. 1st Law: “A body will remain at rest, or moving at
constant velocity, unless it is acted by an unbalanced
force.”
2nd Law:F = ma.
3rd Law: “For every action there is always an equal and
opposite reaction”
If two bodies exert a force on one another, the forces
are equal in magnitude, but opposite in direction.
F12 = -F21
Newton’s Laws of Motion

14. Tension In The String

15. TENSION IN A STRING
CASE I
a
a
MOTION OF BODIES CONNECTED BY A STRING
When the bodies move vertically
Consider two bodies of unequal masses m1 and
m2 connected by the ends of a string, which
passes over a frictionless pulley as shown in the
diagram.
Net force on Body B: Two forces are acting on B
(i) Weight of A = W₂ = m₂g acting downward
(ii) Tension in string= T acting upward
So, net force F₂ = m₂ a = T - m₂ g (b/c T > W₂)….(ii)

16. CASE I
a
a
• Acceleration: Adding eq. (i) and (ii),
• m₁a + m₂a = m₁g - T + T - m₂g
• m₁a + m₂a = m₁g - m₂g OR
• m₁a + m₂a = (m₁ - m₂) g
• Therefore, a = (m₁ - m₂) g / (m₁ + m₂)
• Tension: Dividing eq. (i) and (ii),
• m₁a / m₂a = (m₁g – T) / (T - m₂g)
• m₁ / m₂ = (m₁g – T) / (T - m₂g)
• By cross multiplying,
• m₁ (T - m₂g) = m₂ (m₁g – T) OR
• m₁T - m₁ m₂ g = m₁ m₂ g - m₂T
• m₁T + m₂T = m₁ m₂ g + m₁ m₂ g
• ( m₁ + m₂)T = 2m₁ m₂ g
• T =2m₁m₂g / (m₁+ m₂)

17. TENSION IN A STRING
CASE 2:
a
a
When one of the bodies moves vertically while the other moves horizontally
Two bodies A & B of masses m1 and m2 are attached to the ends of a string, which passes over
a frictionless pulley as shown in the figure. The body "A" moves vertically downward with
an acceleration equal to "a" and the body "B" moves on a smooth horizontal plane towards the
pulley with the same acceleration.
Situation: Body A= m₁ and Body B= m₂
where m₁ > m₂
Required Data: Acceleration in the string a= ?
Tension in the string T= ?
Net force on Body A: Two forces are acting on A
(i) Weight of A = W₁ = m₁g acting downward
(ii) Tension in string= T acting upward
So, net force F₁ = m₁a = m₁g- T (b/c W₁ > T)………(i)
Net force on Body B:
There are three forces acting on it.
(i) Tension (T) in the string, which acts horizontally
(ii) Weight W2 = m2g acting vertically downward.
(iii) Reaction of the surface (R) on the body which
acts vertically upward. As there is no motion of body "B" in the vertical direction.
Therefore weight and normal reaction cancel each other

18. Thus the net horizontal force acting upon body B is T
T = m2a --------(ii)
Acceleration:
Putting the value of T in equation (i), we get
m1g – m2a = m1a
m1g = m1a + m2a
m1g = a (m1 + m2)
a = m1g / (m1 + m2)
Tension :
Putting the value of "a" in equation (ii), we get
T = m2a --------(ii)
OR T = m2m1g / (m1 + m2)

19. MOMENTUM
Physical quantity that describes the quantity of motion in a body is called
momentum.The momentum of a moving body is defined as
“The product of mass and velocity of a moving body is called linear momentum“
Formula: P = mV
Unit: N.s or kgm/s

20. LAW OF CONSERVATION OF
MOMENTUM
The law of conservation of momentum states that:
"When some bodies constituting an isolated system act upon
one another, the total momentum of the system remains constant."
"Total momentum of an isolated system before and
after collision is constant."
OR

21. FRICTION
“Friction is the force resisting the relative motion of
solid surfaces”
Types of Friction:
1. Static Friction: Static friction is friction between two or
more solid objects that are not moving relative to each
other.
2. Kinetic Friction: Kinetic friction, also known as dynamic
friction or sliding friction, occurs when two objects are
moving relative to each other and rub together (like a sled
on the ground).
Formula: F = µ R = µ W = µ mg
Unit: N

22. ADVANTAGES AND DISADVANTAGES OF
FRICTION
1. The main disadvantage of friction is that it produces heat
in various parts of machines. In this way some useful
energy is wasted as heat energy.
2. 2. Due to friction we have to exert more power in
machines.
3. Friction helps in stopping a vehicle on applying the brakes.
4. It helps in generating heat when we rub our hands together.
5. Asteroids burn in the atmosphere before reaching the earth
due to friction and saves lives on earth.

23. METHODS OF REDUCING FRICTION
1)Friction can be reduced by making the surface
smooth by polishing.
2)Friction can be reduced by applying lubricants
(like oil or grease) to the rubbing surface.
3)Friction can be reduced by using wheels to move
objects.
4)Friction can be reduced by using ball bearing
between the moving parts of machine.