- 1.1a: Work done by gravity = mgh = mg * d * sin(θ) = 60 kg * 9.8 m/s² * 3 m * sin(40°) ≈ 1132.5 J
- 1.1b: Work done by normal force = 0 J (normal force is perpendicular to displacement)
- 1.2a: Work done by gravity = 0 J (gravity acts vertically, displacement is horizontal)
- 1.2b: Work done by applied force = F * d * cos(θ) = 60 N * 3.25 m * cos(30°) ≈ 168.8 J
- 1.3a: Free body diagram forces: weight (mg) downward, normal force perpendicular to incline, tension (8000 N) up the incline, friction (20 N) down the incline.
- 1.3b: Net work = Work by tension + Work by friction + Work by gravity = (8000 N * 3 m) + (-20 N * 3 m) + (-1200 kg * 9.8 m/s² * sin(30°) * 3 m) = 24000 J - 60 J - 17640 J = 6300 J
- 1.4: Net work = Work by applied force + Work by friction = (50 N * 2.60 m * cos(30°)) + (-4.2 N * 2.60 m) ≈ 112.58 J - 10.92 J = 101.66 J. Using work-energy principle: 101.66 J = 0.5 * 5 kg * v² → v ≈ 6.38 m/s
- 1.5a: Work done by engine = F_engine * d = 200 N * 4.8 m = 960 J
- 1.5b: Net work = Work by engine + Work by friction + Work by gravity = 960 J + (-23 N * 4.8 m) + (720 kg * 9.8 m/s² * sin(42°) * 4.8 m) ≈ 960 J - 110.4 J + 22752.6 J = 23602.2 J. Using work-energy principle: 23602.2 J = 0.5 * 720 kg * v² → v ≈ 8.08 m/s
Parent Tip: Review the logic above to help your child master the concept of work energy and power worksheet answers.
