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Force And Laws Of Motion


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A presentation on all the laws of motion including Law of Conservation Of momentum with applications and mathematical equations.

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Force And Laws Of Motion

  1. 1. Acknowledgement • We would like to give our sincere thanks to Mrs. Swarachita Hazra, our science teacher for giving such an informative project. It was real fun to have learnt through this project instead of routine text books. We gained a lot of knowledge while surfing through internet. We hope we will get such projects in the future also. Thank You once again.
  2. 2. ISAAC NEWTON • Sir Isaac Newton was an English physicist and mathe matician who is widely regarded as one of the most influential scientists of all time and as a key figure in the scientific revolution. Newton also made seminal contributions to optics and shares credit with Gottfried Leibniz for the invention of the infinitesimal calculus. He gave 3 laws of motion. Here, in this presentation we will learn about them.
  3. 3. Force • Force is a push or a pull acting on an object. Its SI unit is Newton i.e: Kg m/sec2 Its Formula is Mass x Acceleration Later in the presentation we will learn how he formula is derived. Forces are of two types 1)Balanced Force 2)Unbalanced Force
  6. 6. INERTIA • Inertia is the property of matter that cause it to resist any change in its motion or state of rest • INERTIA makes the moving object continue to move at a constant speed in the same direction unless some external force changes the object’s motion • Inertia is not physical quantity and thus it does not have units
  7. 7. Introduction to Newton's First Law of Motion • Some of the bodies (or objects) around us are at rest , whereas other are in motion. Newton's first law describes the behavior of such bodies which are in a state of rest or of uniform motion in a straight line.
  8. 8. Newton’s first law of motion • According to Newton's first law... • An object at rest will remain at rest or an object in motion will remain in motion in a straight line at constant speed , unless an external force is applied to it & changes its state of motion.
  9. 9. Activity 1 • Make a pile of similar carom coins on a table as shown in the figure. • Attempt a sharp horizontal hit at the bottom of a pile using a striker. If the hit was strong enough, the bottom coin moves out quickly. Once the lowest coin is removed, the inertia of the other coins make them ‘fall’ vertically on the table.
  10. 10. Activity 2 • Set a 5 rupee coin on a stiff card covering an empty glass tumbler as shown in the figure. • Give the card a sharp horizontal flick with a finger. If we do it fast then the card shoots away, allowing the coin to fall vertically into the glass tumbler due to its inertia. • The inertia of the coin tries to maintain its state of rest even when the card flows off.
  11. 11. Usain Bolt made a world record of running 100m in just 9.58 secs. But why does he and the other athletes run after finishing the race? •
  12. 12. This is because • An athlete keeps on running few meters after finishing line because initially both the upper and the lower part of the body of the athlete are in state of motion. If he reaches the finishing line and stops then his legs come to rest but hut the upper part of the body tends to remain in the state of motion due of inertia of motion and he falls forward so, in order to avoid any injury he keeps on running for few meters after the finishing line..
  13. 13. A bullet is fired from a gun and a hole is made in the object. But why does this happen?
  14. 14. This is because • When we fire a bullet from a gun to stationary objects, a hole is made in them because initially both bullet and the objects are in the state of rest. When bullet is fired, the bullet comes to motion but the object tends to remain in the state of rest due to inertia of rest and hence a hole is made.
  15. 15. MOMENTUM • If an object is to be accelerated, we know that a greater force is required to give a greater velocity. So, there appears to exist some quantity of importance that combines the object’s mass and its velocity. • One such property called momentum was introduced by Newton. The momentum, p of an object is defined as the product of its mass, m and velocity, v. • That is, p = mv
  16. 16. • Momentum has both direction and magnitude. • Its direction is same as that of velocity, v. • The SI unit of momentum is kilogram-metre per second (kg m s-1). • Since the application of an unbalanced force brings a change in the velocity of an object, it is therefore clear that a force also produces a change in momentum. • The change of momentum of the car is not only determined by the magnitude of the force but also by the time during which the force is exerted. • The force necessary to change the momentum of an object depends on the time rate at which the momentum is changed.
  17. 17. Newton’s 2nd Law of Motion • Second law of motion states that rate of change of momentum is directly proportional to the force applied. • For e.g.- During the game of tennis if the ball hits a player it does not hurt him. • On the other hand, when a fast moving cricket ball hits a spectator , it may hurt him.
  18. 18. Mathematical Representation • Change of momentum= mv-mu Rate of change of momentum= mv-mu/t mv-mu/t ∝ F m(v-u/t) ∝ F kma = F Where k stands for constant of proportionality F=MA
  19. 19. Understand the First law of Motion • Let us consider a situation in which a car with a dead battery is to be pushed along a straight road to give it a speed of 1m s- 1, which is sufficient to start its engine. If one or two persons give a sudden push to it, t hardly starts. But a continuous push over sometime results in a gradual acceleration of the car to this speed.
  20. 20. Activity 3 • Take a rubber balloon & inflate it fully. Tie its neck using a thread & fix a straw on its surface. • Pass the thread through the straw & fix one end on a wall. • Fix the other end on a wall at some distance as shown below. • Now remove the thread tied on the balloon & let the air escape. • Observe the direction in which the straw moves.
  21. 21. Activity 4 • Take a test tube & put a small amount of water on it. Place a stop cork at the mouth of it. • Now suspend the test tube horizontally by two strings or wires as shown in the figure. • Heat the test tube with a burner until water vaporises and the cork blows out. • Observe that the test tube recoils in the direction opposite to the direction of the cork.
  22. 22. Why the fielder lowers his hand to take the catch?
  23. 23. This is because • A fielder lowers his hands while taking a catch. He does so to increase the time of momentum in which the momentum is reduced to zero. Hence the player feels less force on his hands according to Newton’s 2nd Law.
  24. 24. Why does they wear boxing gloves while boxing?
  25. 25. This is because • Boxers wear boxing gloves to increase the time of impulse in which the momentum is reduced to 0 according to Newton’s 2nd law and the boxer gets less hurt when the other one punches him.
  26. 26. The third law of motion says that for every action there is an equal and opposite reaction. This must be remembered that action and reaction always act on two different objects. Newton’s 3rd Law of Motion
  27. 27. Understand the 3rd Law of motion
  28. 28. Action-Reaction Pair • Action: the tires on a car push on the road… Reaction: the road pushes on the tires. • Action: while swimming, we push the water backwards... Reaction: the water pushes us forward. • Action: a rocket pushes out exhaust… Reaction: the exhaust pushes the rocket forward.
  29. 29. Activity 5 • Request two children to stand on two separate carts as shown in the figure. • Give them a bag full of sand and ask them to play a game of catch with the bag. • Does each of them receive an instantaneous reaction as a result of throwing the sand bag ? • You can paint a white line on cartwheels to observe the motion of the two carts when the children throw the bag towards each other.
  30. 30. This is because A swimmer is able to swim due to Newton’s 3rd Law of Motion. He pushes the water backward with his hands and water in turn pushes him with equal and opposite force in forward direction.
  31. 31. The A4 (Aggregat 4) rocket was the first rocket to be launched. It was developed in Germany during the second World War. But how does a rocket works?
  32. 32. This is because • Rockets work on Newton’s 3rd law. When fuel in the rocket burns, the gases rush down. These gases exert a force on the ground and ground exerts equal and opposite force on the rocket and the rocket propels.
  33. 33. LAW OF CONSERVATION OF MOMENTUM • The Law of Conservation of Momentum states that if two bodies collide with each other, the total momentum before and after collision remains conserved.
  34. 34. Mathematical Representation Total Momenta before collision = Total Momenta after collision m1u1+ m2u2 = m1v1 = m2v2
  35. 35. Solution: We have been given that u= 3 m s-1 and v= 7 m s-1 , t= 2 s and m= 5 kg. From Eq. we have, F = m(v-u) t Substitution of values in this relation gives F = 5 kg (7 m s-1 – 3 m s-1 )/ 2s= 10N Now, if this force is applied for a duration of 5 s( t= 5 s), then the final velocity can be calculated by rewriting Eq. (9.5) as v = u + Ft m
  36. 36. On substituting the values of u, F, m and t, we get the final velocity, v = 13 m s-1
  37. 37. 5 10 15 20 25 1 2 3 4 5 6 7 8 9 10 11 12
  38. 38. Solution: The initial velocity of the ball is 20 cm s-1 . Due to the friction force exerted by the table, the velocity of the ball decreases down to zero in 10 s. Thus, u= 20 cm s-1 ; v= 0 cm s-1 and t= 10 s. Since the velocity- time graph is a straight line, it is clear that the ball moves with a constant acceleration. The acceleration a is a = v-u t = (0 cm s-1 – 20 cm s-1 )/ 10 s = -2 cm s-2 = -0.02 m s-2
  39. 39. Solution: We have the mass of bullet, m1 = 20 g (= 0.02 kg) and the mass of the pistol, m2 = 2 kg; initial velocities of the bullet (u1 ) and pistol (u2 ) = 0, respectively. The final velocity of the bullet, v1 = 150 m s-1 . The direction of bullet is taken from left to right ( positive, by convention, Fig. 9.17). Let v be the recoil velocity of the pistol. Total momenta of the pistol and bullet before the fire, when the gun is at rest = (2+ 0.02) kg X 0 m s-1 = 0 kg ms-1 Total momenta of the pistol and bullet after it is fired = 0.02 kg X (+ 150 m s-1 ) + 2 kg X v m s-1 = (3 + 2v) kg m s-1 . Cont. in the next slide.
  40. 40. According to the law of conversation of momentum Total momenta after the fire = Total momenta before the fire 3 + 2v = 0  v = -1.5 m s-1 . Negative sign indicates that the direction in which the pistol would recoil is opposite to that of bullet, that is, right to left.
  41. 41. Summary• First law of motion : An object continues to be in a state of rest or of uniform motion along a straight line unless acted upon by an unbalanced force . • The natural tendency of objects to resist a change in their state of rest or uniform motion is called inertia . • The mass of an object is a measure of its inertia . Its SI unit is kg . • Force of friction always opposes motion of objects . • Second law of motion : The rate of change of momentum of an object is proportional to the applied unbalanced force in the direction of the force . • The SI unit of force is kg m/s2 . This is also known as Newton and represented by the symbol N . A force of 1 Newton produces an acceleration of 1m/s2 on an object of mass 1 kg . • The momentum of an object is the product of its mass and velocity and has the same direction as that of the velocity . Its SI unit is kg m/s • Third law of motion : To every action , there is an equal and opposite reaction and they act on 2 different bodies . • In an isolated system (where there is no external force ) , the total momentum remains conserved . s2
  42. 42. Made by :Group 2(Roll No. 11-20) Group Leader: Samyak Jain