STATIC EQUILIBRIUM AND ELASTICITY

PHYSICS 1 WITH CALCULUS

CONDITIONS FOR EQUILIBRIUM

τ∑ = 0

F∑ = 0

EXAMPLE-YOGI

YOGI HAS A MASS OF 90 KG, THE BASKET HAS A MASS OF 15 KG. THE ROPE WILL BREAK IF THE TENSION EXCEEDS 876 N.

HOW FAR CAN YOGI WALK OUT ON THE 4 M POLE?

WHAT IS THE FORCE OF THE WALL WHEN YOGI IS AS FAR OUT AS HE CAN GO?

EXAMPLE

THE COEFFICIENT OF FRICTION BETWEEN THE LADDER AND THE GROUND IS 0.1. IT IS THE SAME AT THE WALL. THE MONKEY HAS A MASS OF 40 KG, AND THE LADDER’S IS 15 KG.

IF THE MONKEY IS 2/3 OF THE WAY UP THE 6 M LONG LADDER, WHAT IS THE TENSION IN THE ROPE?

HOOKE’S LAW REVISITED

σ = Yε

Where: σ =FA

, ε =Δllo

,

and Y = Modulus of Elasticity

EXAMPLE

THE GOLDEN GATE BRIDGE WEIGHS 419,800 TONS (M = 3.808X108 KG) IS SUSPENDED BY 500 VERTICAL CABLES. AFTER THE BRIDGE WAS SUSPENDED, THE LONGEST OF THOSE CABLES WAS 500 FT LONG (152.4 M). THE CABLES ARE MADE OF STEEL (Y = 200.0X109 PA) AND HAVE A DIAMETER OF 68.26 MM. WHAT WAS THE LENGTH OF THE LONGEST CABLE BEFORE THE BRIDGE WAS HUNG ON IT?