TS Inter 1st Year Physics Notes Chapter 5 Laws of Motion

Here students can locate TS Inter 1st Year Physics Notes 5th Lesson Laws of Motion to prepare for their exam.

TS Inter 1st Year Physics Notes 5th Lesson Laws of Motion

→ Force: Force is that which changes or tries to change the state of a body. Force is a vector.
D.F = MLT-2, Unit: Newton (N)

→ Newton’s Laws of Motion :
1st Law : Every body continues to be in its state of rest or of uniform motion in a straight line unless compelled by some external force.

→ Inertia : It is the property of the body to oppose any change in its state.
Simply inertia means resistance to change. Mass of a body m’ is a measure for the inertia of a body.

→ 2nd Law: The rate of change of momentum of a body is directly proportional to the applied force and takes place in the direction in which the force acts.
Note : Internal forces cannot change the momentum of the body or system,
F ∝ \(\frac{\mathrm{d} \overline{\mathrm{p}}}{\mathrm{dt}}, \quad \frac{\mathrm{d} \overline{\mathrm{p}}}{\mathrm{dt}}=\mathrm{m} \frac{\mathrm{dv}}{\mathrm{dt}}\) or F = k.ma

→ Momentum (p) : It is the product of mass (m) and velocity (v) of a body.
Momentum (p) = mass x velocity = m v It is a vector, unit: Kg – m/sec. D.F = MLT-1

→ Impulse : When force acts between two bodies in contact for a very small time then product of force and time is defined as Impulse.

Impulse = Force × time = F.t,
Impulse = change in momentum
Impulse is a vector. Unit: Kg-m/sec,
D.F. = MLT-1

→ Some observations of momentum:
1) If equal force is applied on two bodies of different masses the body with less mass will gain more velocity and body with more mass will gain less velocity. But change in momentum is same for both bodies.

2) To stop a fast moving cricket ball abruptly we require a large force. Whereas if we move our hands along the direction of motion of the ball we require less force to stop it.
I = Ft; F ∝ \(\frac{1}{t}\)
Ex : When a horse pulls a cart, horse applies force on the cart. Whereas cart applies the reaction on the ground so motion is possible.

3) In some cases action and reaction app-lies on the same system then the body is in equilibrium. In this case motion is not possible.
Ex : When you sit on a bench or chair force (F = ma) equal to your weight is applied on the bench or chair called action. At the same time the chair or bench will apply equal amount of force on you as reaction. In this case the person and bench or chair are in equilibrium and motion is not possible.

→ Law of conservation of momentum: Under the absence of external force, “The total momentum of an isolated system of interacting particles is conserved” i.e., total momentum of system is constant.

→ Friction : It is a contact force parallel to the surfaces in contact. Friction will always oppose relative motion between the bodies.

TS Inter 1st Year Physics Notes Chapter 5 Laws of Motion

→ Normal reaction (N): When two bodies are one over the other, force applied by the lower body on the bottom layers of upper body is called normal reaction.
On a horizontal surface normal reaction N = mg weight of upper body.
TS Inter 1st Year Physics Notes Chapter 5 Laws of Motion 1
On an inclined surface normal reaction N = mg cos θ
TS Inter 1st Year Physics Notes Chapter 5 Laws of Motion 2

→ Motion of a car on a horizontal road : On a horizontal road when a car is in circular motion three forces will act on it. They are

  • weight of car (mg)
  • normal reaction (N)
  • Frictional force (f)

In this type of motion friction between road and tyres gives necessary centripetal force.
For safe journey centripetal force must be equal to Frictional force i.e., \(\frac{\mathrm{mv}^2}{\mathrm{R}}\) = µmg
Safe velocity of car v = \(\sqrt{\mu \mathrm{gR}}\)

→ Static friction: Friction between two bodies at rest is called static friction.
Static friction does not exist by itself. It will come into account when a force tries to develop motion between the bodies.

→ Laws of static friction :

  • Static Friction does not exist indepen-dently i.e. when external force is zero static friction is zero.
  • The magnitude of static friction gradually increases with applied force to a maximum value called limiting static friction (fs)max
  • Static friction opposes impending motion.
  • Static friction is independent of area of contact.
  • Static friction is proportional to normal reaction.
    (fs)maxµN (or) (fs)max = µsN

→ Kinetic friction (fk) : Frictional force that opposes relative motion between moving bodies is called kinetic friction.

→ Laws of kinetic friction: When a body begins to slide on the other surface static friction abruptly decreases and reaches to a constant value called kinetic friction.

  • Kinetic friction is independent of area of contact.
  • Kinetic friction is independent of velocities of moving bodies.
  • Kinetic friction is proportional to normal v reaction N.
    fk µN (or) fk = µkN

→ Rolling friction (fr): When a body is rolling on a plane without slip then contact forces between the bodies is called rolling friction.
It opposes rolling motion between the surfaces.

TS Inter 1st Year Physics Notes Chapter 5 Laws of Motion

→ Laws of rolling friction :

  • Rolling friction will develop a point contact between the surface and the rolling sphere. For objects like wheels line of contact will develop.
  • Rolling friction (fr) has least value for given normal reaction when compared with static friction (fs) or kinetic friction
  • Rolling friction is directly proportional to normal reaction, fr = µN.
  • In rolling friction the surfaces in contact will get momentarily deformed a little.
  • Rolling friction depends on area of contact. Due to this reason friction increases when air pressure is less in tyres (Flattened tyres).

→ Advantages of friction :

  • We are able to walk because of friction.
  • It is impossible for a car to move on a slippery road.
  • Breaking system of vehicles works with the help of friction.
  • Friction between roads and tyres provides the necessary external force to accelerate the car. Transmission of power to various parts of a machine through belts is possible by friction.

→ Disadvantages of friction :

  • In many cases we will try to reduce friction because it dissipates energy into heat.
  • It causes wear and tear to machine parts.

→ Methods to reduce friction :

  • Lubricants are used to reduce friction.
  • Ball bearings are used between moving parts of machine to reduce friction.
  • A thin cushion of air maintained between solid surfaces reduces friction.
    Ex: Air pressure in tyres.

→ Ball bearings : Ball bearings will convert sliding motion into rolling motion due to their special construction. So sliding friction is converted into rolling friction. Hence friction decreases.

→ Banking of roads : In a curved path the outer edge of road is elevated with some angle ‘θ’ to the horizontal. Due to this arrangement centripetal force necessary for circular motion is provided by gravitational force on vehicle.
Angle of banking θ = tan-1\(\left(\frac{\mathrm{v}^2}{\mathrm{rg}}\right)\)
Safe velocity on a banked road
Vmax = \(\sqrt{g R \tan \theta}\)

→ Motion of a car on a banked road: When a road is banked driving will become safe and safe velocity of vehicles will also increase. Safe velocity of vehicle o,n a banked road
v = \(\sqrt{\mathrm{gR} \tan \theta}\)
Due to baking wear and tear of tyres will decrease. Driving is also easy.

→ Momentum, P = mass × velocity

→ From Newton’s second law,
F ∝ \(\frac{\mathrm{dP}}{\mathrm{dt}}=\mathrm{m} \frac{\mathrm{dv}}{\mathrm{dt}}\) ⇒ F = ma = m\(\frac{(\mathrm{v}-\mathrm{u})}{\mathrm{t}}\)

→ When a body of mass m’ is taken in a lift move with acceleration a’
Moving in upwards apparent weight, W1 = m (g + a) ⇒ W1 = W\(\)

TS Inter 1st Year Physics Notes Chapter 5 Laws of Motion

→ Motion of lawn roller:
(i) When pulling the lawn roller of mass m with a force F
(a) Horizontal component useful for motion, Fx = F cos θ
(b) Normal reaction, N = mg – F sin θ.

(ii) When lawn roller is pushed with a force F
(c) Horizontal component of force,
Fx = F cos θ
(d) Normal reaction, N = mg + F sin θ

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