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# PHYSICS – KEY POINTS

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1. For motion on curved path, distance/displacement > 1
2. For motion on straight path, distance/displacement = 1
3. For falling body, distance/displacement = 1
4. For motion on curved path, speed/velocity > 1
5. For motion on straight path, speed/velocity = 1
6. An acclration is said to be uniform if
a. Average accelration = instantaneous accelration
b. Velocity changes uniformly
7. When velocity is constant, then velocity time graph is a horizontal straight line
8. If accelration is constant, then velocity time graph is a straight line which rises same height for equal intervals of time
9. If acclration is variable, then velocity time graph is curved
10. Suppose velocity of a body starts from 0 to v in time t then average velocity will be
Vav = 0 + v/2 = v/2
11. Equations for linear motion with uniform accelration are following
a. vf = vi + at
b. S = Vav × t = (vf + vi/2) × t
c. S = vit + 1/2 g²
d. vf² – vi² = 2aS
e. S = vt = v × underroot 2H/g
12. For vertical upward motion, use negative sign with accelration in these equations. Example: A body is thrown vertically upward with velocity 80m/s. How much height it will cover in 10sec? H= vit-0.5gt² = 80×10-0.5(10)(10)² = 800-500=300m/s
13. To find distance covered in nth sec
S = 5(2tn – 1) Example: A body is fallen from certain height. How much distance it will cover in 4th sec? S = 5(2×4 – 1) = 35m
14. To find distance covered in n sec
S = 5t² Example: A body is fallen from certain height. How much distance it will cover in 4 sec? S = 5(4)² = 80m
15. Two bodies of same masses moving with different velocities are stopped by same force. The relation between their velocities and distances in which they are stopped is
FS = mv²/2
S = v²
S1/S2 = v1²/v2²
16. Newton’s Law of motion are applicable for only low speeds as compared to speed of light
17. For fast moving objects, relativistic mechanics developed by Albert Einstein. It is applicable for atomic particles
18. Newton ist law is also called law of inertia.
19. Inertia of a body is directly proportional to mass of the body
20. The property of inertia is possessed by all bodies in nature
21. Intertial frame of reference , a = 0 (non accelrated) .
22. Newton’ ist law is about non accelrated frame of reference
23. Earth is considered to be an inertial frame of reference
24. Non inertial frame of reference, a > 0 or a < 0
(accelrated)
25. Newton’ 2nd law is also called law of accelration
26. F = ma (a inversly proportional to m) (a directly proportional to F)
Example: A body of mass 2kg is moving with 2m/s² accelration. 2kg mass is added to the body. Now its accelration will be?? m1/m2 = a2/a1 ; 2/2+2 = a2/2 ; a2 = 1m/s²
27. A body is moving with constant acclration, the force acting on it will be constant
28. A body is moving with zero accelration, force acting on it will be zero
29. A body is moving with variable accelration, force acting on it will be variable
30. Newton’ 3rd law says every action has an equal and opposite reaction
31. Action and reaction forces never act on same body
32. The reaction force does not cancel the action force because they act on different bodies
What is the effect on speed of a fighter plane chasing another when it opens fire?
Speed of chasing plane ist decreases then increases according to newton 3rd law while speed of pursued plane increases when it returns the fire
33. Seat belts are useful in driving because these belts change the forces of motion prevent the passengers from moving forward when a moving car stops quickly
34. A motorcycle’s safety helmet is padded so as to extend time of injury of any collision to prevent serious injury
35. Momentum determines how easy or difficult it is to stop a moving body
36. The idea of linear momentum was introduced by Newton
37. P = mv Example: If % increase in velocity or mass of body is 70%, then % increase in momentum will also be 70% because there is direct relation without any square or underroot of v, m or P
38. SI unit is Ns
39. Momentum is not a dot or cross product of mass and velocity. It is just a product of mass and velocity
40. The rate of change of momentum(P/t) is equal to applied force
Example: if velocity of a moving body of mass 2kg changes from 5m/s to 10m/s in 2sec, find force? Momentum =mvf-mvi = 20-10=10Ns ; F = P/t = 10/2 = 5N
41. Change of momentum takes place in direction of applied force
42. Second law in terms of linear momentum, “” force applied on body is equal to rate of change of momentum”””
43. K.E = mv²/2 = Pv/2
44. P = 2×K.E/v
45. K.E and momentum are equal if v=2m/s
K.E = Pv/2 = P×2/2 = P
46. Product of force and time is called impulse
47. I = Ft = mv/t × t = mv
48. SI unit of impulse is Ns
49. Elastic collosion : total energy, k.e and linear momentum are conserved
50. Inelastic collision : total energy and linear momentum are conserved but k.e is not conserved
51. If two balls at same temperature collide, then momentum is conserved
52. When two objects of equal masses collide they inter change their velocities
53. When a ball of mass m moving with velocity v collides with exactly similar ball of mass m which is at rest, then after collision they inter change their velocities
54. If m2 >>> m1 and v2=0 then after collision m1 bounce back with same velocity while m2 remains stationary
55. If m1>>>m2 and v2=0 then after collision, there is no change in velocity of m1 while m2 begins to move with approximately twice of the velocity of m1
56. F = P/t = mv/t
Example: Suppose Gases burn in rocket at 1000kg/s. Rocket eject gases at the rate of 2000km/s. Find force? F = v×m/t = 2×106 × 106 = 2×10¹²N
57. Suppose water flows out from pipe at 3kg/s and its velocity changes from 5m/s to zero on striking ball.
Force = v × m/t = 5×3 = 15N
58. Propulsion of jet aircrafts, rocket and missile type weapons depends on application of momentum principles and law of action and reaction
59. Rocket equation is a = mv/M
Here M is mass of rocket. When fuel is burned and ejected, mass of rocket decreases and hence accelration increases
60. A hose pipe ejects water at speed of 0.3m/s through a hole of area 50cm-2. If water strikes a wall normally, calculate force on wall, assuming velocity of water after striking wall is zero?
F = Area × density × velocity² = 5×10-³×10³×0.3² = 0.45N
61. Projectile motion is 2 dimensional motion under constant accelration due to gravity
62. a = 0 in horizontal direction
63. F = 0 in horziontal direction
64. v remains unchanged in horizontal direction
65. S = Vx × t is horizontal distance
66. a = g in vertical direction
67. Y = vit + 1/2 gt² = (0)t + 1/2 gt² = 1/2 gt²
68. This vertical motion is same as for a freely falling body (vi=0)
69. Velocity along horizontal direction is Vfx = Vix = viCos theta
70. Velocity along vertical direction is Viy = viSin theta
71. Vfy = Viy- at = viSin theta – at
72. Tan theta = Vfy/Vfx = viSin theta – at/vix
73. At highest point of trajectory, velocity is minimum not zero
74. Height of projectile = vi² Sin² theta/2g
75. Time of flight = 2viSin theta/g
76. Time to reach maxi. height = viSin theta/g
77. Range of projectile = vi² Sin2 theta/g
78. For maximum range, theta = 45°
79. For maximum range, R = 4H
80. R = 4H when theta = 45°
81. For maximum height, R = 2H
82. R = 2H when theta = 63°
83. For Range = Height, theta = 76°
84. For determing ratio of range to height for any given angle, R/H = 4 [cos theta/sin theta]
85. If sum of two angles is 90°, these angles are said to be complementory angles
86. For complementory angles, ranges are equal
For example at 60° and 30°, ranges are equal
At 50° and 40°, ranges are equal
87. Horizontal range and maximum range of projectile are related as R = Rmax Sin2theta
88. Un-powered and un-guided missile is called ballistic missile
89. For short ranges and flat earth, trajectory is parabolic
90. For long ranges and curved(spherical) earth, trajectory is elliptical
91. The graph of displacement of a vertically thrown ball varrying with time is parabolic
92. If body is moving with uniform velocity then there will be no impulse
93. If body is moving with variable motion then there will be impulse

### One Comment

1. Waqas Anjum says:

Nice

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