Transcript PHYS16 – Lecture 26 Ch. 12 Static Equilibrium Static Equil. Pre-question • If ball 2 has twice the mass of ball 1

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
L
L
ratio of L2 to L1?
2
1
m1
m2
A) 1:1
B) 2:1
C) 1:2
D) There is not enough information.
Ch. 12 Static Equilibrium
• Simple Machines – levers
• Static Equilibrium
– Center of Gravity
– Newton’s Second law for torques and forces
• Stability Requirements
Static Equilibrium
• Forces should not cause linear acceleration


 F  ma  0
• Torques should not cause rotational
acceleration
  I  0
• 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?
A
B
2m
3m
4m
No, he can only walk 3.3 m from second support…
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
U
x
• Practically – When center of mass is above the
base of support
F
F
F
G
Base of support
G
G
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