PHYS16 – Lecture 26 Ch. 12 Static Equilibrium

Static Equil. Pre-question If ball 2 has twice the mass of ball 1 and the system is in static equilibrium then what is the ratio of L 2 to L 1 ? A) 1:1 B) 2:1 C) 1:2 D) There is not enough information. L1L1 L2L2 m2m2 m1m1

Simple Machines – levers Static Equilibrium – Center of Gravity – Newton’s Second law for torques and forces Stability Requirements Ch. 12 Static Equilibrium

Static Equilibrium Forces should not cause linear acceleration Torques should not cause rotational acceleration Object has no rotational or linear motion

Strategy for solving problems Free Body Diagram – Identify all forces – Draw exactly where forces act – Draw which way forces point Define Axes Apply Force balance Apply Torque balance – Make sure to determine pivot correctly

Walk the plank! If Adrienne (50 kg) stands on left end of plank, can Bo (90 kg) walk all the way to the right end? How far can he go? No, he can only walk 3.3 m from second support… AB 2 m4 m3 m

Will the ladder slip A 3.0m ladder leans against a frictionless wall at angle 60 degrees. What is the minimum value of coeff. of static friction with the ground that prevents ladder from slipping? Coeff. of static friction = 0.29

Sign problem What is the tension in the cable holding the post? Mass of sign is 33.1 kg, mass of post is 19.7 kg, length of post is 2.4 m, distance of sign = 1.95 m, and cable is attached to wall 1.14 m above post.

Stability Mathematically – Potential first deriv. = zero and second deriv. > zero and local min Practically – When center of mass is above the base of support U x FGFG FGFG Base of support FGFG Tipping PointUnstable

Conclusions Static Equilibrium – both forces and torques on an object have to sum to zero Stability – center of gravity must be over base of support