Kerala Plus One Physics Notes Chapter 5 Law of Motion
A cart moves because a man is pushing it. In each of these cases, an external force pushes the body that moves. Such forces are called contact forces. But forces can be non-contact too. Gravity pulls all objects down to earth, magnets push and pull other magnetic and pieces of iron without touching them. These are non contact forces. So, a force is needed to make a body move from rest and a force is needed to stop a moving body. Let’s learn more about these forces.
Aristotle’s Fallacy (Mistake):
Aristotelian law of motion. An external force is required to keep a body in motion.
The mistake in it: According to Aristotelian law, a force is required to keep a body in uniform motion. But actually, no force is required to move a body in uniform motion.
‘The Law of Inertia (ജഡത്വ നിയമം)
Galileo studied motion of objects on
(a) Inclined plane.
(b) Double inclined plane.
Conclusion of experiment:
If the net external force is zero, a body at rest continues to remain at rest and a body in uniform motion continues to move with uniform velocity.
Inertia (ജഡത്വം )
The property of a body due to which it cannot change it’s state of rest or uniform motion along a straight line by itself is called inertia.
- When a fast moving bus is suddenly stopped, a standing passenger tends to fall in the forward direction. This is because he/she has the tendency to remain in uniform motion.
- When a bus takes a sharp turn, a person sitting in the bus experiences a force acting away from the centre of the curved path. This makes us hold the handle when the bus turns fast.
Linear momentum (നേർ രേഖാ ആക്കം )
The linear momentum of a body is the quantity of motion possessed by the body. It is equal to the product of mass and velocity of the body.
SI unit is kgms-1
Dimensional formula is [MLT-1].
Linear momentum explains why even though two stones are thrown with same velocity, the heavier stone has more impact. Also when they have same mass, the one thrown with more velocity has more impact.
Newton’s First Law of Motion:
“Every body continues in its state of rest or uniform motion in a straight line unless some external unbalanced force acts on it”.From this we note that a body cannot move by itself, and, if it is moving uniformly, cannot stop by itself.
Force is that which changes or tends to change the state of rest or of uniform motion of a body in a straight line.
Why are passengers thrown forward from their seats when a speeding bus stops suddenly?
This is due to inertia of motion. When the speeding bus stops suddenly, lower part of the body in contact with the seat stops. The upper part of the body of the passengers tends to maintain its uniform motion. Hence the passengers are thrown forward.
Newton’s Second Law of Motion (ന്യൂട്ടന്റെ രണ്ടാം ചലന നിയമം)
“The rate of change of linear momentum of a body is directly proportional to the applied force and takes place in the direction in which the force acts”. Mathematically this written as,
The value of k is found to be 1. So,
- SI unit of force is newton.
- 1 N = 1 kgms-2
- CGS unit of force is dyne. 1 dyne = 1g cms-2
- Dimensional formula is [MLT2].
One newton is the force required to produce an acceleration of 1 ms-2 on a body of mass 1 kg.
This is the result of very large force, acting for a very short time. It is the measure of the total effect of the force.
Impulse = force x time
Thus, impulse is measured as the total change in linear momentum produced during the impact.
Why we are hurt less when we jump on a muddy floor in comparison to a hard floor?
When we jump on a muddy floor, the floor is carried in the direction of the jump and the time interval At for which force acts is increased. This decreases rate of change of momentum and hence the force of reaction. Therefore we are hurt less
Newton’s Third Law of Motion (ന്യൂട്ടന്റെ മുന്നാം ചലന നിയമം)
“It states that to every action, there is always an equal and opposite reaction”.
A force acting on a body will immediately cause that body to react with a equal force in the opposite direction.
1 You pull a spring, the spring pulls you back. You push a spring, the spring pushes you back.
2. While waking, we press the ground (action) with our feet slanted, the ground exerts an equal and opposite force on us which helps us walk forward.
A person sitting In the compartment of train moving with uniform speed throws ball h, the upward direction
i. What path cl the bell will appear to him?
ii. What to a person standing outside?
i. vertically downwards
ii. Parabolic to the person standing outside
Apparent weight in lift (elevator):
Let a man having mass ‘m’ stand on a weighting machine on an elevator, The actual weight of the man is mg which acts vertically downwards on the weighing machine which will offer a reaction force R. This R is displayed on the weighing machine. So R is the apparent weight of the man.
1. When lift moves upward with acceleration a. The net upward force on the man is
R – mg = ma
Apparent weight, R = m (g + a)
2. When the lift moves downward with acceleration a. The net downward force on the man is mg – R = ma
Apparent weight, R = m (g – a)
3. If the lift is at rest or moving with uniform velocity upward or downward, the acceleration is 0. So net force on the man
R – mg = m×0 = 0
R = mg
Apparent weight = actual weight
4. When the lift falls freely. It will fall with an acceleration g (acceleration due to gravity). The net downward force on the man,
R – mg = mg R = 0
Apparent weight = 0 Newton
Hence, we will experience weightlessness as seen in chapter 8.
A lift Is going up with an acceleration 2g. A man is inside the lift and his mass is m. What will be the reaction of the floor on the man?
Let R be the reaction, then
R- mg = 2 mg
R = 3 mg
Conservation of Momentum (ആക്ക സംരക്ഷണം )
The law says the total momentum of an isolated system of interacting particles, is conserved. Total initial momentum equals total final momentum. This is true for all types of collisions. For elastic collisions there is an additional condition apart from the conservation of momentum.
ie., total initial kinetic energy=total final kinetic energy.
Recoil of gun:
When a bullet of mass mb is fired with a velocity , the gun of mass mg will acquire a velocity which is given by
The negative sign shows that direction of is opposite to the direction of , i.e., the gun recoils.
Why does a rifle give a backward kick on firing a bullet?
Before firing, both the bullet and the rifle are at rest and their total momentum is zero. After firing, the bullet gains a large momentum in the forward direction. To conserve momentum, the rifle gains an equal momentum in the opposite direction. So the rifle gives a backward kick.
Equilibrium of a Particle:
This is when the total external forces on the particle is zero. From first law of motion, this means either the particle is at rest or in uniform motion.
When forces act on a particle, equilibrium happens, when they cancel,
It can be any number of forces, but the total should be zero, for equilibrium.
Friction (ഘർഷണം )
Friction is the force that develops at the surfaces of contact of two bodies and impedes (opposes) their relative motion.
Friction is due to the strong atomic or molecular forces of attraction between the two surfaces at the point of contact.
There are different types of friction.
1. Static friction:
The opposing force that comes into play when one body tends to move over the surface of another, but the actual motion has yet not started is static friction.
Limiting static friction:
Consider two surfaces in contact. When a force is applied on one of the surfaces, the force of friction between them will also increase. The maximum value of frictional force before the body just slides over the surface of another body is called limiting friction.
Laws of static friction:
- The force of static friction depends only on the nature of surfaces in contact.
- The magnitude of limiting friction is independent of area, as long as the normal reaction (ft) between the surfaces remains the same.
- The limiting static friction is directly proportional to the normal reaction (R).
where is a constant called coefficient of static friction.
2. Kinetic friction (ഗതി ഘർഷണം )
Kinetic friction or dynamic friction is the opposing force that comes into play when one body is actually moving over the surface of another body.
Laws of kinetic friction:
- Kinetic friction has a constant value depending on the nature of the two surfaces in contact.
- The kinetic friction is proportional to normal reaction (R) where is the coefficient of kinetic friction.
- Kinetic friction between two surfaces is independent of the relative velocities bet-ween the surfaces.
During experiments it has been seen that kinetic friction is always slightly less than the liming friction.
A horse has to apply more force to start a cart than to keep it moving. Why?
During the first few steps of his motion, the horse has to work against the limiting friction ; and once the cart starts moving, the horse has to work against kinetic friction which is less than limiting friction.
Two types of Kinetic friction:
(a) Sliding friction :
The opposing force that comes into play when one body is actually sliding over the surface of the other body is called sliding friction.
(b) Rolingfriction (ഉരുളൽ ഘർഷണം),
The opposing force that comes into play when one- j body is actually rolling over the surface of the other body is called rolling friction.
Definition of :
Coefficient of static friction is the ratio of the force of i the maximum static friction to the normal reaction.
Definition of :
Coefficient of kinetic friction is the ratio of the force of kinetic friction to the normal reaction.
Angle of Friction:
It is the angle which the resultant of the force of limiting friction and the normal reaction makes with the direction of the normal reaction. If is the angle of friction, we have.
Angle of repose:
It is defined as the minimum angle of inclination of a plane with horizontal, such that a body placed on the plane just starts to slide down it.
From above equations we see that angle of friction is equal to angle of repose.
A block of mass 2 kg is kept on the floor. The coefficient of static friction is 0.4. if a force F of 2.5 N is applied on the block as shown in the figure, the frictional force t between the block and the floor will be
Applied force =2.5 N
Limiting friction μmg = 0.4 × 2 × 9.8 = 7.84 N
For the given condition applied force is very smaller than limiting friction.
:. Static friction on a body=Applied force=2.5 N
Uniform circular motion is when an object moves at a constant speed along a circular path.
Centripetal force (അഭികേന്ദബലം)
It is the force required to make a body move along a circular path with uniform speed. It always acts along the radius and towards the centre of the circular path. We know, in uniform circular motion.
where v = linear speed and ω = angular speed, r = radius of the circular path.
Using Newton’s second law, F = ma
It is the force that arises when a body is moving along a circular path, due to the tendency of the body to regain its natural straight line path.
Magnitude of centrifugal force is same as that of centripetal force, but direction is opposite.Car moving along a level circular road
The forces on the car are:
- Weight mg of the car acting vertically down-wards.
- Normal reaction R of the road on the car, vertically upwards.
- The force of static friction F exerted inwards by the ground on the car’s tyres.
As the car does not move upwards or downwards
R = mg …………..(1)
The force of friction provides the necessary centripetal force. The maximum force of friction (limiting static friction) is
This is the maximum velocity with which a vehicle can go round a level curve without skidding.
Banking of Roads:
To avoid skidding and damage to tyres of vehicles, the outer part of a road is slightly raised than the inner part. This is known as banking of roads.
The forces on the car are:
- Weight of the car vertically downwards.
- Normal reaction R acting normal to the road.
- Frictional force acting parallel to the road. Since there is no vertical acceleration,
or R cosθ – F sinθ = mg …(l)
Now for maximum speed,
The centripetal force is provided by horizontal components of R and F as shown in the figure.