FORMULA CHAPTER
Chapter 03 – Machines
Mechanical Advantage
Worked example
Given: L = 200 N, E = 50 N Calculation: MA = 200 / 50 Answer: MA = 4
Velocity Ratio from Speeds
Worked example
Given: vE = 4 m/s, vL = 1 m/s Calculation: VR = 4 / 1 Answer: VR = 4
Velocity Ratio from Distances
Worked example
Given: dE = 6 m, dL = 2 m Calculation: VR = 6 / 2 Answer: VR = 3
Ideal Machine Work Relation
Worked example
Given: Work input = 500 J Calculation: Work output = Work input Answer: Work output = 500 J
Real Machine Work Relation
Worked example
Given: Work input = 500 J, Work output = 400 J Calculation: 500 J > 400 J Answer: The machine is not ideal.
Efficiency of a Machine
Worked example
Given: MA = 3, VR = 4 Calculation: η = 3 / 4 Answer: η = 0.75 or 75%
Mechanical Advantage from Velocity Ratio and Efficiency
Worked example
Given: VR = 5, η = 0.8 Calculation: MA = 5 × 0.8 Answer: MA = 4
Principle of Levers
Worked example
Given: L = 100 N, load arm = 0.2 m, effort arm = 0.5 m Calculation: 100 × 0.2 = E × 0.5 Answer: E = 40 N
Mechanical Advantage of a Lever
Worked example
Given: effort arm = 60 cm, load arm = 20 cm Calculation: MA = 60 / 20 Answer: MA = 3
Single Movable Pulley
Worked example
Given: E = 50 N Calculation: L = MA × E = 2 × 50 Answer: L = 100 N
Block and Tackle Velocity Ratio
Worked example
Given: n = 4 Calculation: VR = n Answer: VR = 4
Single Fixed Pulley
Worked example
Given: E = 100 N Calculation: L = MA × E = 1 × 100 Answer: L = 100 N
Multiple Movable Pulley System
Worked example
Given: n = 3 Calculation: MA = VR = 2³ Answer: MA = VR = 8
Block and Tackle Mechanical Advantage
Worked example
Given: n = 5 Calculation: MA = n Answer: MA = 5
Mechanical Advantage Including Pulley Weight
Worked example
Given: n = 4, w = 20 N, E = 10 N Calculation: MA = 4 − 20/10 Answer: MA = 2
Pulley Efficiency Including Pulley Weight
Worked example
Given: n = 4, w = 20 N, E = 20 N Calculation: η = 1 − 20/(4 × 20) Answer: η = 0.75 or 75%