Science

• Projectile Motion


  The motion of an object launched or thrown horizontally or at any other angle other than 90 degrees with respect to the horizontal, following a parabolic path called trajectory
• Projectile Motion


  • Combination of horizontal and vertical motions in which each motion is completely independent of each other
  • A uniform motion - The object travels in a straight line with uniform speed
  • The vertical motion is a free fall - Moving under only the influence of gravity
• Types of Projectile Motion


  • Horizontal Motion
  • Vertical Motion
  • Parabolic Motion
• Horizontal Motion


  • Motion of a ball rolling freely along a level surface
  • Will keep moving forward with an equal distance and time interval
  • No horizontal forces acting on the object
  • NOT affected by gravitational force
• Vertical Motion


  • Motion of a freely falling object
  • Affected by gravitational force
  • Velocity changes by 9.8 m/s each second
  • There is vertical acceleration
• Parabolic Motion


  • Path traced by an object accelerating only in the vertical direction while moving at constant horizontal velocity
  • The vertical velocity of a projectile is equal to zero at the highest point of its trajectory, known as the apex
• Vector


  • A quantity that has both magnitude and direction
  • Magnitude is defined as "distance or quantity"
  • Typically represented by an arrow whose direction is the same as that of the quantity and whose length is proportional to the quantity's magnitude
• PRH (Projectile Launched Horizontally)

  • A projectile launched horizontally that has no initial vertical velocity
  • Its vertical velocity is identical to that of a dropped object
  • The downward velocity increases due to gravity as shown by the vector arrows of increasing lengths
  • The horizontal velocity is uniform as shown by the identical horizontal vector arrows
• Projectile Motion: At an Angle


  • Velocity has 2 components: A constant horizontal velocity that moves in the same direction as the launch, the acceleration of which is 0
  • An upward positive vertical velocity component that is decreasing in magnitude until it becomes 0 at the top of the trajectory
• Factors Affecting Projectile Motion


  • Angle
  • Initial Velocity
• Momentum (p)


  • Affected by velocity, follows the direction of the velocity thus momentum is a vector quantity
  • Tendency to resist any change in its state of motion or rest
  • Inertia in motion (Law of Inertia)
  • Product of mass (m) and velocity (v)
  • Unit is kg – m/s
• Impulse (i)


  • Change in momentum
  • Affected by the force exerted on the object and the time the force was exerted
  • Formula – i = Ft, where F = force exerted, t = time the force was exerted
• Factors that affect the change in momentum


  • △p = m (V_f – V_i) - change in momentum
  • Ft = m (V_f – V_i) - impulse
• Impulse – Change in Momentum Relationship

  • F△t - If the impact time is ↓ then the impact force is ↑
  • F△t - If the impact time is ↑ then the impact force is ↓
• Newton's 3rd Law – for every action there is an opposite reaction
• Deriving Conservation of Linear Momentum

  1. F_A and F_B are action-reaction pair from Newton's Third law are equal and opposite

  2. i_A = - i_B = can also be derived as dis

  3. M_AU_A + M_BU_B = M_AV_A + M_BV_B (LCM) - Law of Conservation Momentum
• Collision Classifications


  • Elastic – total kinetic energy of the system is the same before and after the collision
  • Perfectly Inelastic – TKE is still conserved but 2 objects stick together and move with the same velocity. Some KE is converted to heat
• Mechanical Energy


  • Acquired by objects upon which work is done
  • Closely relates to the definition of energy (capacity to do work)
• Types of Mechanical Energy

  • Potential Energy
  • Kinetic Energy
• Potential Energy


  • Energy possessed by objects at rest
  • Gravitational Potential Energy – energy possessed by an object because of its location or position
  • Elastic Potential Energy – stored in a stretched environment
• Kinetic Energy


  Possessed by an object by virtue of its motion
• Law of Conservation of Mechanical Energy - Energy can neither be created nor destroyed. Can be transformed from 1 form to another
• General Forms of Energy


  • Kinetic Energy - moving energy
  • Potential Energy - possessed by object at rest
• Gravitational Potential Energy (GPE)


  GPE = ½ mgh, where m is the mass of the object, g is the acceleration due to gravity (9.8 m/s^2), and h is the height or elevation of the object
• Kinetic Energy (KE)


  KE = ½ mv^2, where m is the mass of the object and v is its velocity
• Momentum Conservation - No net/unbalanced external force acts on the boy-girl system, thus, the total momentum of the system does not change. The momentum gained by the girl is of equal magnitude but opposite direction to the momentum gained by the boy. In this system, no momentum is gained or lost
• Internal Energy


  Molecular kinetic energy + molecular potential energy
• Heat and Work


  • △u = Q – W, where Q = amount of heat flowing into the system, W = net work done by the system, and △u = change in the system's internal energy
  • Q = W + △u
• Joule (J) as SI unit for energy
• The first law tells us that a system's internal energy can be changed by transferring energy by either work, heat, or a combo
• Combustion Engine


  • Type of heat engine
  • Heat is produced using a combustion process, which in turn makes use an oxidizer for that fuel like air
• Classes of Combustion Engine


  • External Combustion Engine - Burning of fuel takes place outside the engine
  • Internal Combustion Engine - Burning of fuel takes place inside
• 4 Stroke Cycle


  1. Intake Stroke - The intake valve opens, allowing the cylinder to receive the fuel-air mixture as the piston moves downward

  2. Compression Stroke - The piston moves up compressing the fuel-air mixture

  3. Power Stroke - The spark plug at the top of the cylinder causes the mixture to ignite and combust making its temperature high. With its increase in temp, the pressure inside increases causing the piston to go down and perform mechanical work

  4. Exhaust Stroke - The final stroke and occurs when the exhaust valve is open and the intake valve is closed. Piston movement evacuates exhaust gasses go to the atmosphere
• First Law of Thermodynamics - Change in internal energy of a system equals the difference between the heat taken by the system and the work done by the system
• Engine


  • Allows us to produce mechanical work from a type of energy
  • If the energy that was used to perform work was thermal energy, then the engine is called heat engine
  • To perform work, heat is taken in by the engine from a heat source, also called the high temperature reservoir
  • Heat that is lost due to other interactions = friction
  • Lost heat = waste heat
  • The waste heat goes to the low temperature reservoir or the heat sink of the heat engine
• Work


  Work = Heat Input – Heat Output
• Heat Engine


  • Converts thermal energy
  • 3 things that happen in a full cycle: Heat is added, Some of that energy from that input heat is used to do work, The rest of the heat is removed at a relatively cold temperature
• Heat Pump


  • A device that allows heat to transfer from a cold reservoir to a warm one
  • Work is needed and provided by the motor
• Second Law of Thermodynamics - Heat will never of itself flow from a cold temperature to a hot temperature object. Heat naturally flows from hot objects to cold ones. In simpler terms, it means that things tend to balance out; hot things cool down, and cold things warm up, until they reach an equilibrium
• Third Law of Thermodynamics - As you keep cooling something down, it gets harder and harder to do so until, theoretically, you reach a point called absolute zero, where it's impossible to cool something down any further. This law helps explain why we can't reach absolute zero temperature, no matter how hard we try