Physics
Instructor: Dr. Tatiana Erukhimova
Lecture 6
Balance of Forces and Torques
Concept of Center of Mass
r
 Fext  0
r r
  r  F
r
or

r
ext
0
  r F
Map of Texas
  r F  0
Because
r  0
F  mg
  r F  0
r
r

F  mg
  r F  0
Because
r  0
F  mg
Brady, TX
Skyhooks
The skyhook alone won’t balance
on your finger, but when you put
a belt on it, it does! This is all
because adding the belt which
curves under as it hangs actually
moves the center of mass right
under your finger!
Newton’s Laws
1st Law: A body acted on by no net force moves with
constant velocity (which may be zero) and zero acceleration
2nd Law: The acceleration of an object is directly
proportional to the net force acting on it and is inversely
proportional to its mass. The direction of the acceleration
is in the direction of the net force acting on the object.
3rd Law: For every action there is an equal, but
opposite reaction
Aristotle: a natural state of
an object is at rest; a force
is necessary to keep an
object in motion. It follows
from common sense.
384-322 B.C.
Galileo: was able to
identify a hidden force of
friction behind commonsense experiments
1564-1642
Galileo: If no force is applied to
a moving object, it will continue
to move with constant speed in
a straight line
Inertial reference frames
Galilean principle of relativity: Laws of
physics (and everything in the Universe)
look the same for all observers who move
with a constant velocity with respect to
each other.
Newton’s
rd
3
Law
For every action there is an
equal, but opposite, reaction
2nd Law
From experiments we know:
1.Force is a vector
2.The direction of acceleration vector is the
same as the direction of the force vector
3.The magnitude of the force and
acceleration are related by a constant
which depends on number of blocks
involved.
Newton’s second law


F  ma
The vector acceleration of an object is in the same
direction as the vector force applied to the object
and the magnitudes are related by a constant called
the mass of the object.
A Recipe for Solving Problems
1. Sketch
Isolate the body (only external forces but not forces
that one part of the object exert on another part)
2. Write down 2nd Newton’s law


F  ma
Choose a coordinate system
Write 2nd Newton’s law in component form:





F  Fx i  Fy j  m ax i  m ay j
Fx  m ax , Fy  m ay
3. Solve for acceleration
Newton’s 2nd Law


F  ma
Fx  max
Fy  may
Newton’s 3rd Law
N
N
Gravitational force


F  mg
Normal force (perpendicular to the surface)
P
P
No friction
m1
m1
m2
Free body diagram
N1
F12
F21
m1
N2
m2
m2g
m1g
F12=F21
No friction:
=0
H

What is the normal force?
Coefficient of friction: 
H
What is the normal force?
Friction
Two types of friction:
1. Kinetic: The friction force
that slows things down
2. Static: The force that
makes it hard to even get
things moving
Kinetic Friction
• For kinetic friction, it turns out that the
larger the Normal Force the larger the
friction. We can write
FFriction = KineticN
Here  is a constant
• Warning:
– THIS IS NOT A VECTOR EQUATION!
Static Friction
• This is more complicated
• For static friction, the friction force can vary
FFriction  StaticN
Example of the refrigerator:
– If I don’t push, what is the static friction
force?
– What if I push a little?
There is some maximum value the friction force can
achieve, and once we apply a force greater than this
maximum there is a net force on the object, so it
accelerates.
The maximum of the force of friction varied linearly
with the amount that the block pushes on the table.


F friction   N

 - coefficient of friction, N is the vertical force exerted by
the block on the table
The friction force only exists when there is another
force trying to move an object
Coefficient of friction: 
Mass m
H
What is the normal force?
What is the acceleration of the block?
Is it better to push or pull a
sled?
You can pull or push a sled with the same force
magnitude, FP, and angle Q, as shown in the figures.
Assuming the sled doesn’t leave the ground and has a
constant coefficient of friction, , which is better?
FP
FP
Pulling Against Friction
A box of mass m is on a surface with coefficient
of kinetic friction . You pull with constant
force FP at angle Q. The box does not leave
the surface and moves to the right.
What is the magnitude of the acceleration?
Q
Hockey Puck
• Which of these three best
represents a hockey puck
in the real world?
a)
b)
c)
A small block, mass 2kg, rests on top of a larger
block, mass 20 kg. The coefficient of friction
between the blocks is 0.25. If the larger block is
on a frictionless table, what is the largest
horizontal force that can be applied to it without
the small block slipping?
F
N1
N2
N1
N1
F
N1
m1 g
m2 g
V0

A block of mass m is given an initial velocity V0 up an
inclined plane with angle of incline θ. Find acceleration
of the block if
a)  = 0
b) non-zero 
A block of mass 20 kg is pushed against a vertical
surface as shown. The coefficient of friction between the
surface and the block is μ = 0.2. If θ = 300, what is the
minimum magnitude of P to hold the block still?
P 

A Problem With First Year Physics Strings
and Pulleys
m1
m1, m2 are given
m2>m1
String is massless
and unstretchable
m2
Find accelerations of m1 and m2 (assume
no friction)
A wedge with mass M rests on a frictionless
horizontal tabletop. A block with mass m is
placed on the wedge and a horizontal force F
is applied to the wedge. What must the
magnitude of F be if the block is to remain
at a constant height above the tabletop?

F
