2. Vectors The length of the line represents: the magnitude and, The direction of the line segment represents: the direction of the vector quantity.
3. Kinematic Equations vf = vo + at(no s) vf2 – vo2 = 2as(no t) s = vot + ½ at2 (no vf) s = vtt – ½ at2 (no vo) (no a)
4. Components of Projectile Motion The motion is in two dimensions Horizontal (perpendicular to the gravitational field) Vertical (parallel to thegravitational field)
10. Aiming a banana above a monkeys head and he lets go of the branch
11. Components of Projectile Motion Both the banana and the monkey accelerate at the same rate downwards. Both fall the same amount below their gravity free path. Banana passes over the monkey’s head. Passes over by the same amount as it was originally aimed over the monkey’s head.
16. Determining Characteristics of Projectiles Step 2 Determining Time to Maximum Height Note: Only vertical component affects the height.
17. Determining Characteristics of Projectiles vfv = vov + at a = -9.8ms-2 (i.e. acceleration is in the opposite direction to the motion when the projectile is still climbing) 0 = voV + at vv = 0 (at maximum height)
18. Determining Characteristics of Projectiles Step 3 Determining Maximum Height Note: Only vertical component affects the height sv = voVt + ½at2 a = -9.8ms-2 (i.e. acceleration is in the opposite direction to the motion) Use t from Step 2
19. Determining Characteristics of Projectiles Step 4 Determining range Note: Only horizontal component affects range. If the ground is flat, the time in the air = 2 x time to maximum height sh = voHt + ½ at2 a = 0 in horizontal component sh = voHt t = 2 x value of t in Step 2
23. Determining Characteristics of Projectiles Vertical component: sv = vtVt + ½ at2a = -9.8 ms-2 This gives distance above ground. (i.e. acceleration is in the opposite direction to the motion)
29. Different Launch Height The final height may be different from the initial height. How does this change the characteristics of flight? The object will still follow a parabolic path. It will travel further. It will drop further vertically with each unit of time than if launched at the same height.
33. Effect of Air Resistance Air is a retarding force and so resists the motion. Retardation depends on the size, shape and mass, speed, texture of the object. It also depends on the density of the air A large surface area will result in greater air resistance effects. A streamlined ‘bullet’ shape will minimise the effect of air resistance.
40. Circular Motion An object moving in a circular path will have a constant speed. It is continually changing direction. Therefore it’s velocity is continually changing. A relationship can be determined for the speed of the object.
41. Circular Motion Terms Period Is the time needed to complete one cycle/rev (in secs). The symbol T is used. Frequency Number of cycles/revs completed per unit time. Units are Hertz (Hz) f =
42. Circular Motion Terms In uniform circular motion, the object in one revolution moves 2r in T seconds.
43. Centripetal Acceleration A particle undergoing uniform circular motion is continually changing velocity. acceleration is changing.
44. Centripetal Acceleration v1 = vb - va. v2 = vc - vb and so on. The magnitude of v1 = v2. The direction is always to the centre of the circle.
46. Force Causing the Centripetal Acceleration Any particle undergoing uniform circular motion is acted upon by an unbalanced force which is…. Constant in magnitude. Directed towards the centre of the circle. Causes the Centripetal Acceleration.
47. Force Causing the Centripetal Acceleration Moon revolving around the Earth: Gravitational Force, Directed towards the centre of the Earth, Holds the moon in a near circular orbit.
48. Force Causing the Centripetal Acceleration Electrons revolve around the nucleus: Electric Force, Directed to centre of the nucleus, Holds electrons in circular orbit.
49. Force Causing the Centripetal Acceleration Car rounding a corner: Sideways frictional force, Directed towards centre of turn, Force between car tyre and road. If force not great enough: Car skids.
50. Centripetal Acceleration and Friction The force acts on the passenger in the car if they do not have their seat belt on. Note: it is an European car.
51. Force Causing the Centripetal Acceleration Billy can being swung. Vertically or horizontally The tension force between arm and can causes the can to move in circular motion.
52. Centripetal Acceleration and the Normal Force Car turns on a banked section of curved road: the chances of skidding is reduced.
56. Newton’s Law of Gravitation Newton determined that a 1/d2. d = distance from the centres of the objects and not the surfaces. This is true for spherical objects. Newton’s 2nd law also states that Fa. This means that F 1/d2.
57. Newton’s Law of Gravitation His second law also says F m. As two masses are involved, Newton suggested that the force should be proportional to both masses. This is also consistent with his third law. If one mass applies force on a second object, the second mass should also apply an equal but opposite force on the first.
58.
59. Newton’s Law of Gravitation We can find the value of g at any height above the earth’s surface.
60. Satellites in Circular Orbits Objectswill continue to move at a constant velocity unless acted upon by an unbalanced force. Newton’s first law. As satellites move in a circular path, their direction (and hence velocity) is continually changing.
62. Satellites in Circular Orbits This will give the orbital velocity for a satellite to remain in an orbit of r from the centre of the Earth (ie re + r) irrespective of the mass of the satellite. Can you derive this equation?
63. Satellites in Circular Orbits Speed is also given by the equation: In one revolution, Orbiting satellite moves a distance equivalent to the circumference of the circular path it is following. 2r The time it takes for this revolution: Period (T). Hence;
64. Artificial Earth Satellites Some orbits that are preferred over others. Meteorological and communication purposes. Polar orbit is useful as well.
65. Geostationary Orbits They must satisfy the following conditions: They must be equatorial. Only orbit in which the satellite moves in plane perpendicular to earth’s axis of rotation. The orbit must be circular. Must have a constant speed to match the earth’s rotation.
66. Geostationary Orbits The radius must match a period of 23 hrs 56 min. The radius, speed and centripetal acceleration can be calculated from the period. The direction of orbit must be the same as the earth’s rotation. west to east.
67. Low Altitude Satellites 200 - 3000 km above earth’s surface. Used for meteorology and surveillance. Smaller radius means smaller period.
68. Low Altitude Satellites The orbit is chosen so that: It passes over the same location twice each day at 12 hour intervals. 6am and 6pm. Once in each direction. As seen from the ground.
70. Newton’s Second Law In vector form: F = ma Indicates a relationship between force and acceleration. The acceleration is in the same direction as the net force. Implies the force on an object determines the change in velocity (aF)and
71. Momentum Is a property of a body that is moving. Vector quantity. If no net force is acting on the body/bodies, momentum is defined as the product of mass and velocity.
72. Momentum p = mv Units are given as kgms-1 or sN. Direction is the same as the velocity of the object.
76. Application of Newton II Units are the same as those for momentum Kgms-1 or sN. Defined as the product of the force and the time over which the force acts. During collisions, t is often very small. Fav is often very large.
77. Conservation of Momentum The total momentum of all particles in an isolated system remains constant despite internal interactions between the particles.
79. Energy The total energy in an isolated system is conserved. Energy can be transferred from one object to another. Energy can be converted from one form to another. The units are Joules (J). Is a scalar quantity. Does not have a direction. In collisions, total energy is always conserved.
80. Energy The kinetic energy will not always remain constant. May be converted to other forms. Could be: Rotational kinetic energy Sound Heat.
81. Types of Collisions Elastic collisions Inelastic collisions. Momentum is conserved. No kinetic energy is lost. Occurs on the microscopic scale. Between nuclei. Momentum is conserved. Kinetic energy is lost. All macroscopic collisions are inelastic. Some collisions are almost elastic. Billiard balls. Air track/table gliders.
82. Flash Photography 1. Distance between successive images is a measure of speed. 2.Direction determined from multiple-imagephotograph. 3. Line joining two successive images representmagnitude and direction of velocity vector.
83. Flash Photography To calculate distance - measure distance between successive images and adjust by the scale. To calculate time - time between flashes =
84. Flash Photography Momentum: - Use velocity vector and let m1 = 1 unit and m2 is scaled accordingly. - This doesn’t change the validity of the process, only the scale for the momentum vector. 7. Use vector diagrams for addition.
86. Spacecraft Propulsion All vehicles move forward by pushing back on its surroundings. They obey Newton’s Third Law: For every action, there is a reaction.
87. Spacecraft Propulsion Before a rocket is launched, it is stationary. No momentum. Total momentum after the rocket is fired: must also be zero.
88. Spacecraft Propulsion After the rocket is fired Gases are ejected at high speed and, As the gas has mass, There is momentum acting in a direction directly opposite that in which the rocket is intended to move. To conserve momentum, there must be an equal momentum acting in the direction in which the rocket moves.
89. Spacecraft Propulsion Mass of the rocket is large compared to the gas ejected, the velocity must be….. much lower. As gas is ejected, mass of the rocket…. becomes less. and the velocity…. becomes greater.
91. Spacecraft Propulsion Ion Thrusters Geostationary Satellites Used for station keeping since 1980s LEO Such as Iridium mobile communications cluster Deep space position control Can fire ions in opposite direction to motion
92. Spacecraft Propulsion Ion propulsion is a technique which involves Ionising gas rather than using chemical propulsion Gas such as Xenon Heavy to provide more momentum Is ionised and accelerated
93. Spacecraft Propulsion Solar Sails Converts light energy from the sun into Source of propulsion for spacecraft Giant mirror that reflects sunlight to Transfer momentum from photons to spacecraft
94. Spacecraft Propulsion Solar Sails have light As propellant Sun As engine Force of sunlight at the Earth Is approx 4.70 N m-2
95. Spacecraft Propulsion Photons bounce off (or absorbed) by sail During collision momentum conserved Small mass provides small velocity change
96. Spacecraft Propulsion However, over time Large number of photons Continuous force Large net force eventually Cannot be used to launch spacecraft Still need chemical rocket
97. Spacecraft Propulsion Reflected photons cause greater acceleration than absorbed photons Consider for a given mass p = mv As velocity can change direction by 180o v can double p can double
98. Spacecraft Propulsion If photon is absorbed Momentum of spacecraft pis = pip = Final momentum of system
99. Spacecraft Propulsion If photon reflected Initial momentum of spacecraft ps = pfp = As momentum must be conserved, p of system psys = pfs =
100. Spacecraft Propulsion As a = v/t For reflected photon v can double t is constant Therefore a can double
