Acceleration due to Gravity:
"The acceleration produced by the motion of a body due to the effect of gravity is known as acceleration due to gravity."
➡It is denoted by g.
➡The value of g near the surface of the Earth is 9.8 metre per second square.
➡The value of acceleration due to gravity g does not depend on the mass of the object.
➡Consider a body of mass m moving with acceleration due to gravity g then the gravitational force on the body is mg, which is called as weight of the body.
➡The force acting on the body due to gravitational pull of the Earth is given by
F = mg
➡According to Newton's universal law of gravitation,
➡Gravitational force F = GMm/R2
Therefore,
mg = GMm/R2
g = GM/R2
Where,
➡G is gravitational constant
➡M is mass of the earth
➡R is radius of the earth
From the above equation we can say that acceleration due to gravity does not depend on mass of the object shape of the object and size of the object but only depends on mass and radius of the earth or planet.
➡Acceleration due to gravity in terms of radius(R) and mean density:
➡Acceleration due to gravity in terms of mass(M) and mean density:
Apparent weight:
" When a body moves or accelerate in the opposite direction of gravity or along the direction of gravity then the body weight appears to change, this resulted weight of the body is known as Apparent weight. "
➡The gravitational force nothing but the force of attraction exerted by the Earth on the body of mass m.
➡Weight of the body is referred as the gravitational force acting on a body.
➡ W = mg
Apparent weight of a body in lift:
➡3 conditions are considered for the Apparent weight of a body in lift.
➡1. When the lift is at rest( acceleration is zero/ uniform velocity)
➡2. When the lift accelerates upwards
➡3. When the lift accelerates downwards
1. When the lift is at rest:
➡Consider an object in a lift which is at rest or moving upwards and downwards with uniform velocity.
➡Since the lift is at rest or at uniform velocity, its acceleration will be zero.
➡Therefore the Apparent weight of an object is equal to its actual weight.
➡W1 = R = mg
2. When the lift accelerates upwards:
➡Consider an object of mass m in a lift which is moving upwards with uniform acceleration a
➡Since it is moving upwards it's floor pushes the object with the same acceleration.
➡Therefore excess force appears to occur on the object which is not the floor.
➡The Apparent weight will be greater than the actual weight.
➡ W1 = m(g + a)
3. When did lift accelerates downwards:
➡a. When the lift move downwards with acceleration a which is less than the acceleration due to gravity g then the object accelerates downloads by taking a part of force of gravity as its acceleration to move downwards.
➡Therefore Apparent weight will be less than that of the actual weight.
➡W1 = m(g - a)
➡b. When the lift moves downward with an acceleration greater than that of acceleration due to gravity.
➡Then the Apparent weight of the object will be negative.
➡The object will be staying at the ceiling of the lift.
➡W1 = m(g - a) = negative.
➡c. When the lift is free falling, then the acceleration of the lift is equal to acceleration due to gravity (a = g).
➡At free falling, the object will be experiencing a state of weightlessness.
➡W1 = m(g -a) = m(g - g) = 0
Motion:
" When the body position changes with respect to its surrounding and time, then the body is said to be in Motion. "
Kinds Of Motion:
There are 8 different kinds of motion.
1. Translatory motion
2. Circular motion
3. Oscillatory motion
4. Vibratory motion
5. Repetitive motion
6. Periodic motion
7. Multiple motion
8. Random motion
➡1. Translatory motion:
When all the particles of a body moves in the direction of motion, then that motion is known as Translatory motion.
➡Translatory motions are of two types.
a. Rectilinear motion
b. Curvilinear motion
➡a. Rectilinear motion:
When an object moves along a straight line then its motion is known as rectilinear motion.
Example- free falling bodies.
➡b. Curvilinear motion:
When an object moves along a curved path then its motion is known as curvilinear motion.
Example- vehicles moving along a curved path.
➡2. Circular motion:
When an object moves in a circle then its motion is known as circular motion.
Circular motion is of two types
➡a. Rotatory motion
➡b. Revolutionary motion
➡a. Rotatory motion:
When an object without changing its position moves in a circular path then that motion is known as rotatory motion.
➡b. Revolutionary motion:
When a body changes its position while moving in a circular path then that motion is known as Revolutionary motion.
➡3. Oscillatory motion:
When an object
moves to and fro or back and forth along the same path then the motion is known as oscillatory motion.
➡4. Vibratory motion:
Vibratory motion is similar to oscillatory motion. Here the object moves either in to and fro motion or in back and forth along with that the moving object undergoes change in shape or size is known as vibratory motion.
➡5. Repetitive motion:
When the object which is in motion repeats itself after certain interval of time then such motion is known as repetitive motion.
➡6. Periodic motion:
A repetitive motion, where the motion repeats itself after a fixed interval of time is known as periodic motion.
➡7. Multiple motion:
When an object processes two or more motion at the same time such motion is known as multiple motion.
➡8. Random motion:
When the motion of a body suddenly changes from one kind to another kind then such motion of a body is known as random motion.
Momentum:
"Momentum is simply defined as mass in motion or when a force is applied on an object of mass M then the object changes its position in the direction of force."
➡Momentum = mass X velocity
Newton's second law of motion:
" Newton's second law of motion is defined as the rate of change of momentum is directly proportional to the net force acting on an object and takes place in the direction of net force. "
➡Derivation of F = ma
Consider an object of mass m having an initial velocity u.
Therefore its initial momentum is p1 = mu
Let the final velocity of an object is v
Therefore its final Momentum is p2 = mv
Change in momentum = p2 - p1
Rate of change of momentum
= p2 - p1/Δt
= mv - mu /Δ t
= m(v - u)/Δ t
= mΔv / Δ t
From Newton's second law of motion,
F ∝ mΔv/Δt
Since acceleration a = Δv/Δt
F ∝ ma
F = k ma
When unit of force is considered acting on a unit mass then concept of proportionality K is equals to 1
F = ma
