Physics - Chapter 6

• 6.1 Work - 189
• 6.2 Work and Energy - 197
• 6.3 Conservation of Energy 206
• 6.4 Power 211

6.1 §

Work is done when a force is applied to an object and the object moves in the direction of the applied force

• Work = Force x Distance
  • W = Fd
  • SI Unit: Newton-Meter (N x m) = joule (J)
• 1 Joule = 1 N x m = 1 kg x $\frac{m^2}{s^2}$
• Work is zero if the distance moved is zero
• When lifting something at an angle only the component of the force in the direction of the displacement does work
  • Therefore work = force x distance x (cosine of angle between force and displacement)
  • W = Fd cos $\theta$
  • SI Unit: Joule
• Work can be positive negative or zero

6.2 §

• Doing work on an object means you’re changing it’s energy
  • Pushing a shopping cart = Changing it’s Kinetic Energy
  • Climbing a mountain = Increasing your potential energy
• Acceleration is given by a = $\frac{F}{m}$
  • a = acceleration, F = Force, m = mass
• Kinetic Energy = $\frac{1}{2}$(mass) x (velocity)${}^2$
  • KE = $\frac{1}{2}$mv${}^2$
  • SI Units: kg x $\frac{m^2}{s^2}$ = J
• $△$ KE = $\frac{1}{2}$mv${}_f^2$ - $\frac{1}{2}$mv${}_i^2$
• Kinetic energy of an object is due to its motion, Kinetic energy is measured in joule (same as work)
• A ball resting on a shelf has zero kinetic energy but it has potential energy because the work done to lift the ball hasn’t been lost and if it fell off of the shelf gravity would do the same amount of work on the way down
• Energy that is stored for later is Potential Energy
• Potential Energy of Gravity = mass x (acceleration due to gravity) x height
  • PE${}_{gravity}$ = mgh
  • SI Unit: kg x $\frac{m^2}{s^2}$ = J

6.3 §

• Conservation of Energy - The amount of energy in the universe stays the same
• Mechanical Energy - the sum of potential and kinetic energy
  • Mechanical Energy = Potential Energy + Kinetic Energy
  • E = PE + KE
• In an ideal system the energy is transformed from potential to kinetic but the sum is constant of both

6.4 §

• The faster work is done the greater the power
• Power: Amount of work done in a given amount of time
  • Power = $\frac{work}{time}$
  • P = $\frac{W}{t}$
  • SI Units: J/s = watt (W)
• 1 watt = 1 W = 1 J/s