FORCE NEWTON’S LAWS OF MOTION
Subtopic of Newton’s Laws of motion & Forces
1. The Concepts of Force and Mass, 2. Newton’s First Law of Motion, 3. Newton’s Second Law of Motion, 4. The Vector Nature of Newton’s Second Law of Motion, 5. Newton’s Third Law of Motion, 6. Types of Forces : An Overview, 7. The Gravitational Force, 8. The Normal Force, 9. Static and Kinetic Frictional Forces, 10. The Tension Force, 11. Equilibrium Applications of Newton’s Laws of Motion, 12. Non-equilibrium Applications of Newton’s Laws of Motion, 13. Concepts & Calculations.
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Newton’s Laws of Motions Applications
Newton’s First Law ( law of Inertia ): Every body continues its state of rest or uniform motion in a straight line unless it is acted upon by a net external force
It defines inertia,force and equilibrium.
If the net external force on an object is zero , the acceleration of object is zero.
Types of inertia: There are three types of inertia. (i) Inertia of rest, motion and direction.
Ex. When a bus is at rest and starts suddenly moving forward the passengers inside fall back.
Inertia of Motion: The inability of a body to change its state of motion by itself is called inertia of motion.
Inertia of direction: The inability of a body to change its direction of motion by itself is called inertia of direction.
Linear momentum :
Linear momentum is a measure of quantity of motion possessed by a moving body.
Units of linear momentum:
In SI, it is expressed in
kg m s-1 or N s and in CGS it is expressed in g cm s-1 or dyne second.
Dimensional formula of linear momentum is [M L T-1]
Newton’s second laws:
The rate of change of momentum of a body is directly proportional to the resultant or net external force acting on the body and takes place in the direction in which the force acts
Newton’s third laws:
To every action there is always an equal and opposite reaction
Action and reaction do not occur on the same body they act on different bodies at same instant of time
Newton’s third law is not applicable to pseudo forces.
Newtons’s third law defines nature of force and gives the law of conservation of linear momentum.
A bird is in a wire cage hanging from a spring balance. When the bird starts flying in the cage, the reading of the balance decreases.
If the bird is in a closed cage (or) air tight cage and it howers in the cage the reading of the spring balance does not change.
Free Body Diagram :
When several bodies are connected by strings, springs, surfaces of contact, then all the forces acting on a body are considered and sketched on the body under consideration by just isolating it . Then the diagram so formed is called Free Body Diagram (FBD). The following points are kept in mind.
Frames of Reference:
Any co-ordinate system relative to which the motion, position of a body can be described is called a frame of refernce.
There are two types of frames of refernce
a) inertial or unaccelerated frames of reference b) non-inertial or accelerated frames of reference
Inertial frames of reference :
a) Frames of reference in which Newton Laws of motion are applicable are called inertial frame.
b) Inertial frames of reference are either at rest or move with uniform velocity with respect to a fixed imaginary axis.
c) In inertial frame, acceleration of a body is caused by real forces.
Real Force :
Force acting on an object due to its interaction with another object is called a real force.
d) All fundamental forces of nature are real.
e) Real forces form action, reaction pair.
Pseudo force :
In non-inertial frame Newton’s second law is as such not applicable. In order to make Newton’s second law applicable in non-inertial frame a Pseudo force is introduced.
Application of Impulse :
a) shock absorbers are used in vechicles to reduce the magnitude of impulsive force
b) A cricketer lowers his hands, while catching the ball to reduce the impulsive force
Laws of conservation of momentum:
When the resultant external force acting on a system is zero, the total momentum (vector sum) of the system remains constant. This is called the “law of conservation of linear momentum”.
Newton’s third law of motion leads to the law of conservation of linear momentum.
Walking, running, swimming, jet propulsion, motion of rockets, rowing of a boat, recoil of a gun etc., can be explained by Newton’s third law of motion.
Explosions, disintegration of nuclei, recoil of gun, collisions etc., can be explained on the basis of the law of conservation of linear momentum.
When a shot is fired from a gun, while the shot moves forwards, the gun moves backwards. This motion of gun is called recoil of the gun. When a gun of mass ‘M’ fires a bullet of mass ‘m’ with a muzzle velocity ‘v’, the gun recoils with a velocity ‘V’ given by V = mv/M.
Advantage of Friction:
Friction plays an important role in our daily life. While walking friction between the ground and shoes prevent us from slipping
Without friction motion cannot be conveyed by belts from motor to machine
Vehicles will not come to rest even if the brakes are applied when there is no friction between tyres and the road.
When there is no friction knots cannot be tied.
The frictional force, which is effective before motion starts between two surfaces in contact with each other, is known as static friction
Dynamic or Kinetic Friction:
The frictional force, which is effective when two surfaces in contact with each other are in relative motion with respect to each other, is known as dynamic friction. It is independent of velocity of the body.
SOME PRACTICE PROBLEMS ON NEWTONS LAWS OF MOTION, FRICTION & UNIFORM CIRCULAR MOTION
Ques-1. A man sits on a chair supported by a rope passing over a frictionless fixed pulley. The man who weights 1,000 N exerts a force of 450 N on the chair downwards while pulling the rope on the other side. If the chair weights 250N, then the acceleration of the chair is
(A) 0.45 m/s2 (B) 0 (C) 2 m/s2 (D) 9/25 m/s2
Answer : 3
Ques-2. Two persons are holding a rope of negligible weight tightly at its ends so that it is horizontal. A 15 kg weight in attached to rope at the mid point which now no more remains horizontal. The minimum tension required to completely straighten the rope is
(A) 150 N (B) 75 N (C) 50 N (D) Infinitely large
Answer : 2
Ques-3. A 40 N block is supported by two ropes. One rope is horizontal and the other makes an angle of 30° with the ceiling. The tension in the rope attached to the ceiling is approximately :
(A) 80 N (B) 40 N (C) 34.6 N (D) 46.2 N
Answer : 1
Ques-4. A man of 60 kg is standing on the floor of a room. A light rope is rigidly fixed to the floor and is held vertically by the man who starts pulling the rope upwards with a force of 200 N. The reaction force on the feet of the man will be (Take g = 10/22)
(A) 400 N (B) 600 N (C) 200 N (D) 800 N
Answer : 4
Ques-5. A 500 kg horse pulls a cart of mass 1500 kg along a level road with an acc. of 1 m/s2. If coefficient of sliding friction is 0.2, then force exerted by earth on horse is
(A) 3000 N (B) 4000 N (C) 5000 N (D) 6000 N
Answer : 4
Ques-6. A force of 150N produces an acceleration of 2ms–2 in a body and a force of 200N produces an acceleration of 3ms–2. The mass of the body and the coefficient of kinetic friction are
(A) 50kg, 0.1 (B) 25kg, 0.1 (C) 50kg, 0.5 (D) 50kg, 0.2
Answer : 1
Ques-7. An eraser weighing 2N is pressed against the black board with a force of 5N. If the coefficient of friction is 0.4, the force parallel to the black board is required to slide the eraser upwards with uniform velocity is
(A) 2N (B) 2.8N (C) 4N (D) 4.8N
Answer : 3
Ques-8. A block weighing 10kg is at rest on a horizontal table. The coefficient of static friction between the block and the table is 0.5. If a force acts down at 60º from the horizontal, how large can it be without causing the block to move? (g = 10 ms–2)
(A) 346 N (B) 446 N (C) 746 N (D) 846 N
Answer : 3
Ques-9. Starting from rest, the time taken by a body sliding down on a rough inclined plane 45° at with the horizontal is, twice the time taken to travel on a smooth plane of same inclination and same distance. Then the coefficient of kinetic friction is
(A) 25 (B) 0.33 (C) 50 (D) 0.75
Answer : 4
Ques-10. A man slides down on a telegraphic pole with an acceleration equal to one-fourth of acceleration due to gravity. The frictional force between man and pole is equal to(in terms of man’s weight w)
(A) W/4 (B) 3W/4 (C) W/2 (D) W
Answer : 2
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