Static Equilibrium Problems 1 DISCLAIMER USAGE The content

Static Equilibrium Problems 1

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Class Problem: A chair lift loaded with two passengers weighs 500 lbs. Determine the forces in the cable to the left and right of the lift. FA Force A y Force C 62˚ FC 10˚ x Force W (Weight) 500 lbs 2 x 2 system of equations 3

• Class Problem: The distance measuring wheel, like the one below, is subjected to an angled force (F 1 = 10. 25 lb, θ 1 = 22°). If the angle of the ground is θ 2 = 51° and the measuring wheel is in equilibrium, then what is the magnitude of the normal force Fn and the weight of the wheel. NOTE: A normal force is a force that is perpendicular to the plane of contact, meaning that it forms a 90 -degree angle with the plane as shown in the image below. y F 1 = 10. 25 lb θ 1 = 22˚ x β β = 90˚ - θ 2 β = 90˚ - 51˚ = 39˚ β = 39˚ Wwheel Fn 4

• Class Problem: The distance measuring wheel, like the one below, is subjected to an angled force (F 1 = 10. 25 lb, θ 1 = 22°). If the angle of the ground is θ 2 = 51° and the measuring wheel is in equilibrium, then what is the magnitude of the normal force Fn and the weight of the wheel. y Force 1 10. 25 lb Normal Force Wheel Weight 22˚ x 39˚ Wwheel Fn 5

Class Problem: You have decided to make a workout setup at home. Using two ropes, you tie one end of each to a paint bucket and the other ends together at point A. When you apply a force F at angle φ, the system is in equilibrium. What is the angle φ? How do frictionless pulleys work? The rope around a frictionless pulley will carry the same tension throughout its length. y Force W 1 x Force W 2 F Force F 6

y (Eq 1) (Eq 2) x Plug F from Eq 1 into Eq 2: F Solve Eq 1 for F in terms of φ: 7