Newton's Laws of Motion and Friction PDF

PHYSICS BY Er.VINAY KUMAR 9905428278 CHAPTER : ( 4) NEWTON,S LAWS OF MOTION AND FRICTION FORCE :- Force is a push or pull which tries to change the state of rest or motion of a body. INERTIA :- inherent property o...

PHYSICS BY Er.VINAY KUMAR 9905428278 CHAPTER : ( 4) NEWTON,S LAWS OF MOTION AND FRICTION FORCE :- Force is a push or pull which tries to change the state of rest or motion of a body. INERTIA :- inherent property of object to remain at rest or uniform motion unless acted upon by a force is called inertia. It depends upon mass of the object - Greater mass greater inertia greater the force required to change the state. NEWTON,S LAWS OF MOTION :- First law :- Everybody continues in its state of rest or of uniform motion in a straight line unless it is compelled to change that state by the forces acting on it (i) This law is also called law of inertia. (ii) Another form of the law can be as follows : For a body ⃗ = 0 if and only if ⃗ = 0 Linear momentum :- If a body of mass m is moving with velocity ⃗⃗ then its linear momentum ⃗ is given by ⃗ = m ⃗⃗ Second law : - the time rate of change of momentum of a body is directly proportional to the external force and the change takes place in the direction of force. ⃗ ⃗ ⃗ or ⃗ = K If K = 1 ⃗ ⃗⃗⃗⃗⃗ ⃗⃗ ⃗= = =m = m⃗ Third law :- To every action there is always an equal and opposite reaction. NOTE: (I) Forces always occur in pair (ii) Action and reaction never act on same body but always on different bodies. OBJECTIVE QUESTIONS (1) A force vector applied on a mass is represented by ⃗ = 6 ̂ -8 ̂ + 10 ̂ and accelerates with 1 m/s2. what is the mass of the body (a) 10 kg (b)10√ (c) 2√ kg (d) 20kg (2) A particle is moving with a constant speed along a straight line path. A force is not required to (a) increase its speed (b) decrease the momentum (c) change the direction (d) keep it moving with uniform velocity (3) A lift of mass 1000 kg is moving with an acceleration of 1m/s2 in upward direction tension developed in the string , which is connected to the lift is (a) 9800 N (b) 1000 N Page 15 PHYSICS BY Er.VINAY KUMAR 9905428278 (c) 10800N (d) 11000N (4) If rope of lift breaks suddenly , the tension exerted by the surface of lift (a) mg (b) m(g+a) (c) m(g – a) (d) 0 (5) A man is hanging on a spring balance which is kept in a lift. the lift ascends. the spring balance will show in its reading (a) Increase (b) decrease (c) no change (d) change depend upon velocity (6) A man weighs 80kg. he stands on a weighing scale in a lift which is moving upwards with acceleration 5 m/s. what would be the reading on the scale (g = 10m/s2) (a) 400 N (b) 800 N (c) 1200N (d) 0 (7) An automobile traveling with a speed of 60km/h , can brake to stop within a distance of 20 m. if the car is going twice as fast , i.e. 120km/h , the stopping distance will be (a) 20m (b) 40m (c) 60 m (d) 80 m (8) A body , whose momentum is constant , must have constant (a) force (b) velocity (c) acceleration (d) all (9) The motion of a rocket is based on the principle of conservation of (a) mass (b) kinetic energy (c) linear momentum (d) angular momentum (10) A bullet of mass 5g is shot from a gun of mass 5kg. the muzzle velocity of the bullet is 500m/s. the recoil velocity of the gun is (a) 0.5 m/s (b) 0.25 m/s (c) 1 m/s (d) data is insufficient (11) Two bodies of mass 3kg and 4kg are suspended at the ends of massless string passing over a frictionless pulley. the acceleration of the system is (g = 9.8 m/s2) (a) 4.9 m/s2 (b) 2.45m/s2 (c) 1.4 m/s2 (d) 9.5 m/s2 (12) Two masses 5 kg and 4.8 kg tied to a string are hanging over a light frictionless pulley. what is the acceleration of the masses when they are free to move (g= 9.8m/s 2) (a) 0.2 (b) 9.8 (c) 5 (d) 4.8 (13) On a planet x a man throws a 500 gm mass with a speed of 20ms-1 and catches it as it comes down 20 second later. The weight of the mass is (a) 1N (b) 104 N (c) 10N (d) none of these Page 16 PHYSICS BY Er.VINAY KUMAR 9905428278 (14) If an inclined plane is made slowly horizontal by reducing its inclination with horizontal, the component of weight parallel to the plane of block resting on the inclined plane (a) remains same (b) increase (c) decreases (d) first increase and then decreases (15) If the tension in the cable of 1000 kg elevator is 1000 kg weight , the elevator (a) is accelerating upwards (b) is accelerating downwards (c) may be at rest or accelerating (d) may be at rest or in uniform motion (16) A monkey of mass 30 kg climbs a rope which can withstand a maximum tension of 360N. The maximum acceleration which this rope can tolerate for the climbing of monkey is (g=10ms-2) (a) 2ms-2 (b) 3ms-2 (c) 4ms-2 (d) 5ms-2 (17) Apparent weight of a body in an elevator is more than rest weight if elevator is (a) going up and slowing down (b) going up and speeding up (c) going down and slowing down(d) going down and speeding up (18) The momentum is most closely related to (a) Force (b) Impulse (c) Power (d) K.E. (19) Two forces are such that the sum of their magnitudes is 18 N and their resultant is perpendicular of the smaller force and magnitude of resultant is 12N. Then the magnitudes of the forces are (a) 12 N , 6 N (b) 13N , 5N (c) 10N , 8N (d) 16N , 2N Page 17 PHYSICS BY Er.VINAY KUMAR 9905428278 (20) If two forces of 5 N each are acting along x and y axes , then the magnitude and direction of resultant is (a) 5√ , /3 (b) 5√ , /4 (c) -5√ /3 (d) -5√ /4 (21) The vector sum of two forces is perpendicular to their vector differences in that case , the force (a) Are equal to each other in magnitude (b) Are not equal to each other in magnitude (c) Cannot be predicted (d) Are equal to each other (22) A particle moves in the x-y plane under the influence of a force such that its linear momentum is p(t)=A icos(kt)-jsin(kt)] , where A and K are constants. The angle between the force and the momentum is (a) 00 (b) 300 (c) 450 (d) 900 SHORT ANSWER QUESTIONS 1. Two forces F1 and F2 act on a 2 kg mass at 120o with each other. If F1 = 10 N and F2=5N find the acceleration ANS: 2.5√ m/s2 2. A light string passing over a smooth light pulley connects two blocks of masses m 1 and m2 ( vertically ). If the acceleration of the system is g/8 , then find the ratio of the masses. ANS: 9:7 3. Three identical blocks of masses m = 2 kg each are drawn by a force F = 10.2 N with an acceleration of 0.6 m/s2 on a surface. then what is the tension in the string between first two blocks. If there is no friction between the surface and the blocks. ANS: 3.4 N 4. Two blocks of masses 5 kg and 2 kg are connected by a massless string.A vertical force F is applied on the 5 kg block. Find the value of F if tension in the string is 40 N ANS: 140 N 5. Two bodies of masses m1 and m2 are connected by a light string passing over a smooth light fixed pulley. The acceleration of the system is g/7. Then find the ratio of their masses. ANS: 4:3 6. A 5 kg block slides down a plane inclined at 30o to the horizontal. Find Page 18 PHYSICS BY Er.VINAY KUMAR 9905428278 (a) the acceleration of the block if the plane is frictionless. (b) the acceleration if the coefficient of kinetic friction is 0.2 ANS: 4.9 m/s2 , 3.2 m/s2 7. Find the time required by a block to come to rest from a speed of 10 m/s moving on a horizontal surface where 0.2. What is the distance covered before stopping ? ANS: 25.5 m 8. A block lying on a horizontal surface is pulled by a force of 0.1 N but the block does not move. Find frictional force on the block. ANS: 0.1N 9. A block of weight 100 N lying on a horizontal surface just begins to move when a horizontal force of 25 N act on it. Determine the coefficient of static friction. ANS: 0.25 10. A block lying on an inclined plane has a weight of 50 N. It just begins to slide down when inclination of the plane with the horizontal is 30 o. Find 11. A block of weight 100 N lying on a horizontal surface is pushed by a force F acting at an angle 30o with horizontal. For what value of F will the block begin to move if = 0.25 ANS: 33.74 N 12. A body of mass 45 kg is moving with a constant velocity of 10 m/s. A constant force acts on the body for 4 sec , and the speed of the body becomes 2 m/s , in opposite direction calculate the acceleration produced. ANS: -3 m/s2 13. A constant retarding force of 50 N is applied to a body of mass 20 kg moving initially with a speed of 15 m/s. How long does the body take to stop ? ANS: 6 sec 14. A man of mass 70 kg stands on a weighing scale in a lift which is moving (i) upwards with a uniform speed of 10 m/s (ii) downwards with a uniform acceleration of 5 m/s2 (iii) upwards with uniform acceleration of 5 m/s2. what would be the readings on the scale in each case ? (iv) what would be the reading if the lift mechanism failed and it falls down freely under gravity ? ANS: 70 kg , 35 kg , 105 kg , zero 15. Two masses m1 and m2 are connected by a massless string. Find the value of tension in the string if a force of 200 N is applied on (I) m1 (ii) m2 ANS. 125 N,75N 16. A 10 N force is applied on a body to produce in it an acceleration of 1 m/s2.Find the mass of the body. ANS. 10 kg Page 19 PHYSICS BY Er.VINAY KUMAR 9905428278 17. A force of 6N acts on a body at rest and of mass 1kg. During this time , the body attains a velocity of 30m/s.Find the time for which force act on the body. ANS. 5sec 18. Calculate the impulse necessary to stop a 1500 kg car travelling at 90 km/h. ANS. -37500Ns 19. A ball moving with momentum of 15 kgm/s strikes against the wall at an angle of 300 and is reflected with the same momentum at the same angle. calculate momentum. ANS. -15√ kgm/s 20. A 75 kg man stands in a lift. what force does the floor exert on him when the elevator starts moving upwards with an acceleration 2m/s2 ANS. 900 N 21. An elevator weighing 5000 kg is moving upward and tension in the supporting cable is 50000N.Find the upward acceleration. How far does it rise in a time of 10 sec starting from rest ? ANS. 0.2 m/s2,10m 22. Two masses 5kg and 4.8kg tied to a string are hanging over a light frictionless pulley. What is the acceleration of masses ANS. 0.2 m/s2 23. A block is kept on a frictionless inclined surface with angle of inclination. If the incline is given an acceleration a to keep the block stationary. Find acceleration. ANS. gtanα 24. A force of 49N is just sufficient to pull a block of wood weighing 10 kg on a rough horizontal surface.calculate the coefficient of friction and angle of friction ANS. 0.5 ,tan-1(5) 25. A block of mass 10 kg is placed on rough horizontal surface having µ=0.5 if a horizontal force of 100N is acting on it.Find acceleration. ANS. 5m/s2 26. The cefficient of friction between the ground and the wheels of a car moving on a horizontal road is 0.5.If the car starts from rest ,what is the minimum distance in which it can acquire a speed of 72km/h ANS. 40m 27. A cubical block rest on an inclined plane of µ=. find angle when the block just slides √ down the inclined plane. ANS. 300 28. A block of mass 2kg rests on a plane at 300 with horizontal if µ= 0.7 ,what will be the frictional force on the block. ANS. 11.9 N Page 20