What are Force and Inertia?
Force
Force can be defined as a push or pull that changes or tries to change the state of rest or motion. The force is a vector quantity.
Inertia
Inertia can be characterized as the property of a body because of which a body opposes the progressions in itself and its state. We can quantify the inertia of a body by estimating its mass of the body. If a body is a weighty, more noteworthy force will be expected to have an impact on the state of the body.
Newton's Laws of Motion
Newton proposed three laws of motion they are:
Newton’s First Law of Motion: Newton’s first law of motion states that if the net external force on a body is zero, then that body will remain at rest or it will move with a constant velocity. This law defines inertia therefore it is also called the law of inertia.
Newton’s Second Law of Motion: Newton’s second law of motion provides us with the definition of force. According to Newton’s second law of motion, the acceleration of an object is directly proportional to the total force applied or acting on it and is inversely proportional to the mass.
Newton’s Third Law of Motion: Newton’s third law of motion states that to every action there is an equal and opposite reaction.
What are Momentum and Impulse?
Momentum
Momentum is represented by p
p=mv; where m is equal to the mass of the body or object and v is equal to the velocity of the body. Therefore momentum can be defined as the product of mass and velocity.
Impulse
When a large amount of force is applied or acts for an extremely short period then the total effect of the force is called Impulse.
Linear Momentum
The total amount of motion present in a body is called its momentum. The linear momentum of a body is equal to the product of its mass and velocity. It is denoted by p.
Linear momentum p = mu.
Its S1 unit is kg-m/s and the dimensional formula is [MLT-1].
It is a vector quantity whose direction is in the direction of the body's velocity.
Law of Conservation of Linear Momentum
If no external force acts on a system, then its total linear momentum remains conserved.
Linear momentum depends on the frame of reference but the law of conservation of linear momentum is independent of the frame of reference.
Newton’s laws of motion are valid only in an inertial frame of reference.
Weight (w)
It is a field force, the force with which a body is pulled toward the center of the earth due to gravity. It has the magnitude mg, where m is the mass of the body and g is the acceleration due to gravity.
w = mg
Apparent Weight in a Lift
(i) When a lift is at rest or moving with a constant speed, then
R = mg
The weighing machine will read the actual weight.
(ii) When a lift is accelerating upward, then the apparent weight
R1 = m(g + a)
The weighing machine will read the apparent weight, which is more than the actual weight.
(iii) When a lift is accelerating downward, then the apparent weight
R2 = m (g – a)
The weighing machine will read the apparent weight, which is less than the actual weight.
(iv) When the lift is falling freely under gravity, then
R2 = m(g – g)= 0
The apparent weight of the body becomes zero.
(v) If the lift is accelerating downward with an acceleration greater than g, then the body will lift from the floor to the ceiling of the lift.
Rocket
Rocket is an example of variable mass following the law of conservation of momentum.
Thrust on the rocket at any instant F = – u (dM / dt)
where u = exhaust speed of the burnt and dM / dt = rate 0f gases combustion of fuel.
The velocity of the rocket at any instant is given by u = vo + u loge (Mo / M )
where, vo = initial velocity of the rocket,
Mo = initial mass of the rocket and
M = present mass of the rocket.
If the effect of gravity is taken into account then the speed of the rocket
u = vo + u loge (Mo / M) – gt
Friction
A force acting on the point of contact of the objects, which opposes the relative motion is called friction.
It acts parallel to the contact surfaces.
Frictional forces are produced due to intermolecular interactions acting between the molecules of the bodies in contact.
Friction is of three types:
1. Static Friction
It is an opposing force that comes into play when one body tends to move over the surface of the other body but the actual motion is not taking place.
Static friction is a self-adjusting force that increases as the applied force is increased,
2. Limiting Friction
It is the maximum value of static friction when the body is on the verge of starting motion.
Limiting friction (fs) = μsR
where μs, = coefficient of limiting friction and R = normal reaction.
Limiting friction does not depend on the contact surface area but on their nature, i.e., smoothness or roughness.
If the angle of friction is θ, then the coefficient of limiting friction
μs = tan θ
3. Kinetic Friction
If the body begins to slide on the surface, the magnitude of the frictional force rapidly decreases to a constant value of fk kinetic friction.
Kinetic friction, fk = μk N
where μ k = coefficient of kinetic friction and N = normal force.
Kinetic friction is of two types:
(a) Sliding friction
(b) Rolling friction
As, rolling friction < sliding friction, therefore it is easier to roll a body than to slide.
Kinetic friction (fk) = μk R
where μk = coefficient of kinetic friction and R = normal reaction.
The angle of repose or angle of sliding It is the minimum angle of inclination of a plane with the horizontal, such that a body placed on it, just begins to slide down.
If the angle of repose is a. and the coefficient of limiting friction is μ, then
μs = tan α
Motion on an Inclined Plane
When an object moves along an inclined plane, different forces act on it like the normal plane reaction, friction force acting in the opposite direction of motion, etc. Different relations for the motion are given below.
The normal reaction of plane
R = mg cos θ
and the net force acting downward on the block.
F = mg sin θ – f
Acceleration on an inclined plane a = g (sin θ – μ cos θ)
When the angle of inclination of the plane from the horizontal is less than the angle of repose (α), then
(i) minimum force required to move the body up the inclined plane
f1 = mg (sin θ + μ cos θ)
(ii) minimum force required to push the body down the inclined plane
f2 = mg (μ cos θ – sin θ) J
Tension
Tension force always pulls a body.
Tension is a reactive force. It is not an active force.
Tension across a massless pulley or frictionless pulley remains constant.
The rope becomes slack when the tension force becomes zero.
Upcoming Topics:
The motion of bodies in contact.
Pulley mass System.
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