Physics 105A
Give me a lever
long enough and
a fulcrum on
which to place it,
and I shall move
the world.
Analytical Mechanics
Statics:
Balancing Forces and Balancing Torques
14 April 2020
Manuel Calderón de la Barca Sánchez

“Bare minimum” use of Newton’s Law…
but it can get tricky!
Need a thorough understanding to build a strong base

Key point:
By Newton’s 2nd Law: total external force on static objects
must be zero.

Static:
v = 0 , no net force
w = 0, no net torque

Name of the game: Find conditions so that vector
sum of all forces and torques on an object are zero.
14 April 2020
MCBS
Statics
Balancing Forces
 Forces we’ll encounter
Tension
– Force from object, typically a rope or string, exerted when pulled
– Can be the same throughout rope
– ...but not always!
Normal Forces
– Force perpendicular to object’s surface
– Applied by object as it is compressed
http://xkcd.com/81
Friction
– Force parallel to object’s surface
– Typically depends on the Normal force,
– and on properties of material (m).
 Static friction condition: inequality.
Gravity
14 April 2020
MCBS
Rope wrapped around a pole

A rope wraps an angle q
around a pole. You grab one
end and pull with a tension T0.
The other end is attached to a
boat.
T+dT
Normal
dq

If the coefficient of static friction
btw. rope and pole is m, what is
the largest force the rope can
exert on the boat if the rope is
not to slip around the pole?
14 April 2020
MCBS
Friction
T
Balancing Torques
a
14 April 2020
b
MCBS
Leaning ladder
 A ladder leans against a frictionless wall.
If the coefficient
of friction with the ground is m, what is the smallest angle
the ladder can make with the ground and not slip?
14 April 2020
MCBS
Statics: Block on a plane

A block of mass M rests on a fixed plane inclined at an angle q.
You apply a horizontal force Mg on the block. Assume that the
friction force between the block and the plane is large enough to
keep the block at rest.
What are the normal and friction forces N, Ff that the plane exerts on the
block?
If the coefficient of static friction is m, for what range of angles q will the
block in fact remain at rest?
M
Mg
q
14 April 2020
MCBS