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5. More Application of Newton’s Laws

Static. Kinetic. 5. More Application of Newton’s Laws. 5-1 Force of Friction. , m s : coefficient of static friction. f s  m s n. , m k : coefficient of kinetic friction. f k = m k n. Assume m : Constant. Example 5-1. +). Example 5-2. Initial vel. v 0 = 20 m/sec.

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5. More Application of Newton’s Laws

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  1. Static Kinetic 5. More Application of Newton’s Laws 5-1 Force of Friction , ms : coefficient of static friction fs msn , mk : coefficient of kinetic friction fk= mkn Assume m : Constant

  2. Example 5-1 +) Example 5-2 Initial vel. v0 = 20 m/sec. friction : mk l = 115 m F1 = T - mkm1g = m1a F2 = m2g - T = m2a m2g - mkm1g = m1a +m2a =mkm1g

  3. y v q x 5-2 Uniform Circular Motion Angular velocity T = mrw2 Centripetal & Centrifugal forces Newton’s 2nd Law

  4. Tcosq q Tsinq Example 5-5 Example 5-3 : vincrease with fixed r T increase For a certain Tmax :(string breaks if T > Tmax ) Example 5-4

  5. Example 5-3 At Bottom: At Top: At A-point:

  6. 5-3 Non-uniform Circular Motion Example 5-4 At Bottom At Top Minimum velocity at Top : TT = 0 cf Potential Energy  Kinetic Energy: Energy Conservation

  7. 5-4 Motion in presence of velocity-dependent resistive forces : Assumption Terminal Velocity Assume v = 0 at t = 0 Define , , ,

  8. Air Drag at High Speed Drag Coefficient Air density Cross section cf Momentum transfer : For terminal velocity

  9. ~10-13 G = 6.6710-11 N·m2/kg2 ke = 8.99109 N·m2/C2 1 Radioactive particles Bound of Quark ~102 ~1012 5-5 Numerical Calculation for a differential Equation 5-6 Fundamental forces of Nature 1. Gravitational Force: 2. Electromagnetic Force: 3. Strong Force: Short range forces (~ 10-15 m) 4. Weak Force:

  10. 5-7 Gravitational Field , Earth Gravitation force per unit mass cf) Electric Field Electric force per unit charge

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