Physics

• Work


  In Physics, it is a scalar product of distance and force defined as the energy transferred to or from an object by means of force acting on the object. Energy transferred to the object is positive work, and energy transferred from the object is negative work.
• Work (W)


  • Often associated whenever there is an exertion of effort
  • The use of force to move an object over a distance
• Mathematically, work


  W = Fx, where F is the amount of force exerted, and x is the displacement the object in question has taken. UNIT: Nm or Joule (J)
• Calculate the dot product of vector A with vector B by hand

  1. A = [1,3,5]

  2. B = [6,4,2]

  3. A-B = (A.) (Bx) + (A)(B) + (A₂)(Bz)

  4. A-B = 28
• Work is derived from dot product multiplication, where vectors are multiplied to attain a scalar product. The positive or negative signs of work do not indicate direction unlike in force and displacement.
• Negative work indicates something else, and this will be tackled on the topic on energy.
• When a force is exerted on an object which does not move, no work is done on the object.
• When an object is carried at constant velocity by a force which acts at right angles to the motion, no work is done on the object.
• Work is calculated as the product of force and displacement whose direction is parallel to the direction of the force. If the direction of the force is perpendicular from the direction of movement, then work is not observed.
• Seb, a 90-kg parkour practitioner, did three (3) back handsprings, which garnered him a distance of two (2) meters. If his body exerted 180 J worth of work, how much acceleration did his body have?


  Solving for a = 0, W = Fx, F = ma, a = W/mx, Seb's acceleration a = 1 m/s².
• Given Happy Lou lifting a 3 lbs kettle bell one (1) meter above the ground, determine the amount of work she did if the height lowers by 5 cm every time she exerts 1.5 N more.


  Happy Lou exerts an applied force equal to the weight force of the bell. Solving for the kettle bell's weight force Fw = mg = 3 lbs x 1 kg (g) = 13.33 N. Solving for Happy Lou's work given her applied force Fapp = Fw, W = Fwy, Fwy = {13.33 + 1.5 (0.05 m)} dy, W = 13.33y + 1.5 (0.05 m) y|_0^1 = 28.33 J.
• Energy


  The ability to do work. No work can be done without energy because energy gives the strength for applying force to get the work done.
• Mechanical Energy


  The energy possessed by a physical object based on its current state. It is a form of energy possessed by the object as "one whole object".
• Kinetic Energy (KE or K)


  The energy associated with motion. It is the capacity of the moving object to do work. It depends on its mass as well as its velocity v.
• Potential Energy (PE or U)

  The energy due to the state of the object - it could either mean the position of the object or the extent of its elasticity. It is the energy that has the potential to do work.
• Gravitational Potential Energy (U₁)


  The potential energy associated with the position of the object relative to the Earth or some other gravitational source. It is proportional to the height y the object has reached due to the work exerted on it.
• Elastic Potential Energy (U₂)


  The potential energy of an object experiencing compression or expansion. It may be stored in elastic materials.
• Elastic materials are those that can be stretched or compressed under the action of a distorting force but which can return back to their original shape once that force is removed.
• Springs are a special instance of a device which can store elastic potential energy due to either compression or stretching.
• Hooke's Law


  The amount of force applied is directly proportional to the amount of stretch or compression.
• Potential energy (U₂)


  The potential energy of an object experiencing compression or expansion, which may be stored in elastic materials
• Elastic materials


  • Can be stretched or compressed under the action of a distorting force but can return back to their original shape once that force is removed
  • Examples: rubber bands, bungee cords, trampolines, springs, a drawn bow
• Springs


  • A special instance of a device which can store elastic potential energy due to either compression or stretching
  • A force is required to compress a spring, and the greater the compression, the more force is required to compress it further
  • For certain springs, the amount of force applied is directly proportional to the amount of stretch or compression
• Hooke's Law


  F = kx, where F is the distortion force, k is the spring constant of the material, and x is the distortion's displacement
• Elastic potential energy


  • The amount of energy stored in an object is related to the amount of distortion in it
  • The more the object is stretched or compressed, the more energy is stored
  • If the object is not distorted in any way, it is said to be in its equilibrium position
• Equilibrium position


  • The position that an object naturally assumes when there is no force applied to it
  • The zero-potential energy position
• Potential energy (U)


  Mathematically represented as U = 1/2 kx^2
• Potential energy (U)


  • Dependent on force, much like kinetic energy
  • More evident in U due to its relationship with the acceleration constant g
• Potential energy (U) = mgy
• Energy is always positive, and both kinetic and potential energies are always attuned (comply) with one another as dictated by the law of conservation of energy
• Energy can be transformed from one form to another, but the total amount of energy never changes
• Work-Energy Theorem


  The total work (Wtot) done on the system is equal to the change in kinetic energy
• Work (Wtot)


  Potential energy decreases as work is being done
• Wtot + ΔU = 0, therefore Wtot = -ΔU
• Wtot = ΔK, therefore -ΔU = ΔK
• Conservative force


  • A force that offers a two-way conversion between kinetic and potential energy
  • The total work done is reversible, the work value remains the same despite being independent of the path of the body, and if the initial and final displacements are the same, then Wtot = 0
• Nonconservative force


  • A force that is dependent on the direction of the work done by the system, or if potential energy is absent in the force itself
  • The total work done is irreversible, the work value changes due to the interference of such force, and Wtot ≠ 0 despite the initial and final displacements being the same
• Power


  The rate at which work is done, or how fast a force is delivered on an object
• Power (P) = W/t = Fx/t = Fv
• Units of Power


  • Joule/s, Watt (W), Imperial horsepower (hp), Metric horsepower (hpm)