Work, Energy and Power — NDA Physics

Formulas (3)

• What work means in physics — W = F d cos θ · Work done by a constant force
  $$W = F\,d\cos\theta$$
• The sign of work — positive, zero, or negative by the angle · Sign cases of W = F d cos θ
  $$\cos 0^\circ = 1,\quad \cos 90^\circ = 0,\quad \cos 180^\circ = -1$$
• Work done by gravity depends only on the height change · Work done by gravity over a height change h
  $$W_\text{gravity} = \pm\,mgh$$

Watch out for (4)

• Work needs MOVEMENT in the force's direction — holding a weight is zero work
  → What work means in physics — W = F d cos θ
• Perpendicular force does ZERO work — not maximum
  → The sign of work — positive, zero, or negative by the angle
• Negative work means the force OPPOSES motion
  → The sign of work — positive, zero, or negative by the angle
• Gravity's work does NOT depend on the path
  → Work done by gravity depends only on the height change

Formulas (4)

• Kinetic energy — energy of motion (½mv²) · Kinetic energy
  $$KE = \tfrac{1}{2}mv^2$$
• Potential energy — energy of position (mgh) · Gravitational potential energy
  $$PE = mgh$$
• Conservation of energy — PE converts to KE as a body falls · Energy conservation for a freely falling body
  $$mgh = \tfrac{1}{2}mv^2 \;\Rightarrow\; v = \sqrt{2gh}$$
• Kinetic energy and its change depend on the reference frame · Frame-dependent change in kinetic energy
  $$\Delta K_{S'} = mgh + mu\sqrt{2gh} \;>\; \Delta K_{S} = mgh$$

Reference tables (1)

Watch out for (8)

• Kinetic energy grows with the SQUARE of speed
  → Kinetic energy — energy of motion (½mv²)
• Convert grams to kilograms before substituting
  → Kinetic energy — energy of motion (½mv²)
• Potential energy is about POSITION or SHAPE — not motion
  → Potential energy — energy of position (mgh)
• Energy is conserved for an ISOLATED system
  → Conservation of energy — PE converts to KE as a body falls
• At the bottom of a free fall, KE equals the starting PE
  → Conservation of energy — PE converts to KE as a body falls
• Friction is the standard NON-conservative force
  → Conservative forces and energy transformations
• The falling-apple sequence ends in HEAT, not sound
  → Conservative forces and energy transformations
• Even the CHANGE in kinetic energy is frame-dependent
  → Kinetic energy and its change depend on the reference frame

Formulas (3)

• Work-energy theorem — net work equals change in kinetic energy · Work-energy theorem
  $$W_\text{net} = \Delta KE = \tfrac{1}{2}mv_f^2 - \tfrac{1}{2}mv_i^2$$
• Power — the rate of doing work (P = W/t = Fv) · Power
  $$P = \dfrac{W}{t} = Fv$$
• Potential energy from a force — U = − ∫ F dx · Potential energy from a conservative force
  $$U(x) = -\int F(x)\,dx \quad\Longleftrightarrow\quad F(x) = -\dfrac{dU}{dx}$$

Reference tables (1)

Watch out for (5)

• The theorem uses NET work — not the work of one force
  → Work-energy theorem — net work equals change in kinetic energy
• Power is a RATE — do not confuse it with energy
  → Power — the rate of doing work (P = W/t = Fv)
• P = Fv uses the speed at that instant
  → Power — the rate of doing work (P = W/t = Fv)
• 1 kWh is 3.6 × 10⁶ J — not 1000 or 3600
  → Units of work, energy, and power
• Do not forget the MINUS sign when integrating
  → Potential energy from a force — U = − ∫ F dx

Formulas (1)

• The lever and mechanical advantage · Mechanical advantage of a lever
  $$MA = \dfrac{\text{load}}{\text{effort}} = \dfrac{\text{effort arm}}{\text{load arm}}$$

Reference tables (1)

Watch out for (2)

• Mechanical advantage multiplies FORCE, not work
  → The lever and mechanical advantage
• Second class = LOAD in the middle (not fulcrum)
  → The three orders of levers