FORMULA CHAPTER
Chapter 03 – Laws of Motion
Linear Magnification Using Heights
Worked example
Given: hi = -6 cm, ho = 2 cm Calculation: m = -6/2 Answer: m = -3
Change in Momentum
Worked example
Given: m = 2 kg; u = 3 m/s; v = 8 m/s Calculation: Δp = 2(8 − 3) Answer: Δp = 10 kg·m/s
Newton’s Second Law
Worked example
Given: m = 5 kg, a = 2 m/s² Calculation: F = 5×2 Answer: F = 10 N
Universal Law of Gravitation
Worked example
Given: m1 = 2 kg, m2 = 3 kg, r = 2 m Calculation: F = G×2×3/2² Answer: F = 1.5G N
Acceleration Due to Gravity
Worked example
Given: Planet mass = M; radius = R Calculation: g = GM/R² Answer: Surface gravitational acceleration = GM/R²
Downward Free-Fall Velocity
Worked example
Given: u = 0; g = 9.8 m/s²; t = 2 s Calculation: v = 0 + 9.8 × 2 Answer: v = 19.6 m/s downward
Downward Free-Fall Distance
Worked example
Given: u = 0; g = 9.8 m/s²; t = 2 s Calculation: h = 0 + ½ × 9.8 × 2² Answer: h = 19.6 m
Downward Free-Fall Velocity–Distance Relation
Worked example
Given: u = 0, g = 10 m/s², h = 20 m Calculation: v² = 2×10×20 Answer: v = 20 m/s
Upward Vertical Motion Velocity
Worked example
Given: u = 20 m/s; g = 9.8 m/s²; t = 1 s Calculation: v = 20 − 9.8 × 1 Answer: v = 10.2 m/s upward
Upward Vertical Motion Height
Worked example
Given: u = 20 m/s; g = 9.8 m/s²; t = 1 s Calculation: h = 20 × 1 − ½ × 9.8 × 1² Answer: h = 15.1 m
Upward Vertical Motion Velocity–Height Relation
Worked example
Given: u = 20 m/s; g = 10 m/s²; h = 15 m Calculation: v² = 20² − 2 × 10 × 15 = 100 Answer: v = 10 m/s
Weight
Worked example
Given: m = 5 kg, g = 9.8 m/s² Calculation: W = 5×9.8 Answer: W = 49 N