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 L2 to L1?

A) 1:1B) 2:1C) 1:2D) There is not enough information.

L1L2

m2

m1

• 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

0 I

0 amF

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…

A B

2 m 4 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

Base of support

FG

Tipping Point Unstable

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