# MECHANICS PROJECTILE MOTION

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1 1 MECHANICS PROJECTILE MOTION When an object is in free fall, the object is at an acceleration of 10m/s down Displacement is the straight line from start to finish in that direction Projectile: An object that is launched into the air by throwing, kicking, hitting or firing from a weapon. Projectile motion: When an object is dropped or thrown up into the air. An object is experiencing free fall when the only force acting on it is the force of gravity (that means that there is also no air resistance. If you throw and object up and catch it: = =10. =0. = If you drop something: =0 =10. = WORKED EXAMPLE: A girl standing near the edge of a high cliff throws a stone vertically upwards. The stone leaves her hand at 20 m/s. It falls to the rocks below which are 160m down. Calculate how long it takes for the stone to reach the bottom of the cliff. =20. = =10. =160 =? = + 160= = = = 8 +4 =8 = 4 =8

2 2 PROJECTILE MOTION IN TWO DIMENSIONS The path of a projectile is called a trajectory. A trajectory is always parabolic. To identical objects, one dropped and one flicked, will hit the ground at the same time. When bodies are in free fall, their horizontal motion does not affect their vertical motion The vertical motion does not affect the horizontal motion The vertical and horizontal motions are independent of each other. HORIZONTAL PROJECTION The actual velocity can be expressed as a combination of Acceleration in the horizontal direction is zero (0) Acceleration in the vertical direction is the acceleration due to gravity The horizontal velocity remains constant. The vertical velocity increases at 10. every second The displacement is the resultant of the horizontal displacement and the vertical displacement. Horizontal displacement is called the Range.

3 3 WORKED EXAMPLE: John flicks a ball of paper with a horizontal velocity of 2 m/s from the lab bench which is 1.2m high. Calculate how long it will take for the paper to reach the ground and how far away from the base of the lab bench the paper will land. =0. = + = 1.2= = =5 =1 2 =0.24 =? =0.4 =2. =2. =0. =? =0.4 = + = = =0. 8 = = 0.4 = =0. 8 PROJECTION AT AN ANGLE When you project an object at an angle, both 0 = = WORKED EXAMPLE: A cricketer fielding on the boundary throws the ball with a velocity of 20 m/s at an angle of 30 degrees to the ground. Calculate how far away the ball will be when it is caught in order to stump the batsman.

4 4 MOMENTUM = Mass in kg Velocity in. Momentum in.. If motion is only in one plane, one direction will be negative while the other positive. LAW OF CONSERVATION OF MOMENTUM When bodies in a system interact, their total momentum remains constant in both magnitude and direction (provided that no external forces act on the system) + = + IMPULSE It is the change in momentum. Measured in... Δ = WORK Work is done on an object when a force applied to the object causes it to move in the direction of the force If you push a car and it moves, work is being done. If you push a car and it does not move, work is not being done. If you hit the ball while playing tennis, work is only being done while the racket is in contact with the ball. Force in N Displacement in m Work in. = ENERGY = + = + = = = Whenever work is done, energy is transferred or transformed. Energy is the ability to do work. It is a scalar quantity. GRAVITATIONAL The energy an object has due to its position above the ground. = h = acceleration due to gravity =10. Derivation:

5 5 =. = h = h CHEMICAL The energy stored in fuels and food stuffs ELASTIC The energy stored inside a cable/elastic/rope KINETIC The energy an object has because of its motion. = 1 2 LAW OF CONSERVATION OF ENERGY Energy cannot be created or destroyed, merely changed from one form to another. MECHANICAL ENERGY For an object in free fall, projected up, on a swing or a rollercoaster, the mechanical energy is equal to + and it is conserved. WORKED EXAMPLE A 2kg object is dropped from a height of 10m. Ignoring air resistance, calculate the velocity when it is 3m above the ground. = h+ = h = =60+ = WORK-ENERGY THEORY The net work done on an object is calculated using = Fres implies the object is accelerating which means its velocity is changing. Therefore the kinetic energy is also changing. =. =

6 6 POWER Power is the rate at which work is done or the rate at which energy is transferred or transformed. = Measured in. = FRAMES OF REFERENCE Relative Velocity is the velocity of an object measured in a specific frame of reference (a set of reference points that enables the position of an object to be defined at any time) = + WAVES, SOUND AND LIGHT ELECTROMAGNETIC RADIATION The electromagnetic wave is a transverse wave consisting of both an electric field and a magnetic field component. The two fields oscillate at 90 to each other and the direction of motion. This wave is formed by charges continuingly changing velocity (accelerating) A changing magnetic field produces an electric field and a changing electric field produces a magnetic field. This wave can travel through a vacuum because it relies on oscillating fields for movement and not particles. CHARACTERISTICS OF ELECTROMAGNETIC WAVES Travel at the speed of light: (symbol: C) Transfer energy from one plane to another When they strike material that absorbs them, they give energy to that material causing the temperature to increase. These waves can be reflected, refracted, diffracted and undergo interference They don t need a medium to travel through

7 7 ELECTROMAGNETIC SPECTRUM Trend Type of radiation Wavelength (M) Frequency (Hz) Uses Greatest frequency Gamma Electricity Generation X rays Medical (scans) Ultraviolet Medical (disinfection) Visible Spectrum Visibility Infrared TV remotes; heaters Microwaves Telecommunication; cooking Lowest Frequency Radio waves Radio communication The energy of a wave is directly proportional to the frequency of the wave =h h: Plank s constant = The greater the frequency (and hence energy) of a wave, the grater its ability to penetrate various materials. 2D AND 3D WAVES Mechanical wave: need a medium to travel in. Particles of the wave vibrate at 90 to the movement of the wave. Eg: air and water (Suncity wavepool barrier goes up and down in water) Electromagnetic wave: Do not need a medium. Vibrations are increasing and decreasing intensities of magnetic and electric fields. Longitudinal wave: need a medium. Particles vibrate parallel to the direction in which the wave moves. Creates areas of high pressure (compressions) and low pressure (rarefactions). Eg: sound; some earthquakes. Transverse wave: needs a medium. Particles vibrate at 90 to which the wave moves. Eg: slinky TERMINOLOGY Amplitude: distance from equilibrium position to the crest or the trough Wavelength: Distance between two consecutive points in phase Frequency: Number of waves per second Period: Time taken for a complete wave to move past a point Speed: = Superposition: When two pulses cross, their combined displacement it equal to the sum of their individual displacements Nodal Line: And area where destructive interference has occurred and results in a region of zero disturbance Antinodal Line: forms as a result of constructive interference. Photon: a packet of light Intensity of light: the brightness. The more intense a light, the more photons it has. Work Function: The minimum amount of energy needed to emit an electron from the surface of a metal.

8 8 INTERACTION OF ELECTROMAGNETIC RADIATION AND MATTER THE PHOTOELECTRIC EFFECT Light of sufficient energy knocks out electrons from the surface of a metal. Each metal has a threshold frequency the frequency of the photon of light which is needed to eject an electron from the surface of a metal. The greater the frequency of the light, the more energy the ejected electrons will have. The greater the intensity of the light, the more electrons there will be that are ejected. = + h =h SPECTRUMS Absorption Spectrum: 1. Electrons in gas absorb photons of light 2. Which are of particular frequencies relative to the gas 3. The energy releases when they fall is released in all directions 4. Hence this energy is unseen (the black areas) 5. As the colour areas are the frequencies which are not absorbed. Line Emission Spectrum: 1. When electrons gain energy: 2. They become excited and unstable 3. They jump up the energy levels 4. And fall back to a different place 5. Releasing energy 6. And then return to their original position and start again 7. =h hence the different colours

9 9 SOUND THE DOPPLER EFFECT It is the apparent change in frequency of a wave when there is relative motion between the source of the wave and an observer. When the source is moving towards you, it is a higher pitch. When it passes you, it is the true pitch only at that moment. When it moves away, it has a lower pitch. Source moving towards you: = Source moving away from you: = = original frequency = observed frequency = speed of sound (340 m/s) = speed of source WORKED EXAMPLE An ambulance approaches an intersection at 120 km/h emitting a frequency of 256 Hz. What frequency will be heard by a stopped driver as the ambulance approaches? =256 = =? =340 =120.h =33.5. =. 256 =

10 10 APPLICATIONS OF THE DOPPLER EFFECT Medical Measure the rate of blood flow (cells reflect waves from transmitted, received by a receiver) Used to measure babies heartbeat Sport Measure the speed of a ball uses a radar gun (radio waves) Astronomy Distance of stars (by the gasses they are made up of and their movement away from us) SHOCKWAVES It is a cone shaped wave produced when the speed of the source is greater than the speed of the wave. Sonic boom: The sound heard by an observer as a shockwave passes. Eg: Shockwaves in water from a speed boat Thunder air expands and compresses fast.

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