Download normal force

Forces
and
Free-Body Diagrams
Text Reference
Section 2.1

Fa
FORCE
is an applied
push or pull on
an object causing
acceleration,
compression,
stretching,
twisting, and/or
stabilization
Force of Gravity (Weight)
is the force of attraction between all
objects acting downwards toward the
centre of the Earth


Fg  mg

Fg  weight force of gravity N 




m  mass amount of matter kg 

g  gravitation field cons tan t 9.8 N / kg down 

a  acceleration due to gravity 9.8 m / s 2 down 





FN
NORMAL FORCE
is the force the
acts
perpendicular to
the surfaces that
are in contact
with the object

FT
TENSION FORCE
• is the force exerted by
•
•
stretchable materials like
ropes, fibers, springs,
cables, etc.
is always directed away
from the body being
pulled and has the same
magnitude throughout the
length of the material
force increases when the
material’s stretch-ability
increases

Ff
FRICTIONAL FORCE
• is the force that resists motion
•
•
•
between objects in contact
always acts in the opposite
direction to the direction of
motion of the object
is a function of the nature and
weight of the two surfaces in
contact (and not on speed or
surface area of contact)
there are 3 types
STATIC FRICTION


Fs  s FN
• is the force that prevents stationary objects
from starting to move
• measured in Newton
• is the product of the normal force measured
in Newton and the static coefficient of friction
which has no units
• Note that the static coefficient is greater than
the kinetic coefficient of friction.
KINETIC FRICTION


Fk  k FN
• is the force that resists the motion of moving
objects
• measured in Newton
• is the product of the normal force measured
in Newton and the kinetic coefficient of
friction which has no units
• Note that once the object is moving, kinetic
and not static coefficient must be used.
AIR RESISTANCE
• is the force that resists the motion of flying or
•
•
•
•
falling objects in the air
measured in Newton
is noticeable at high speeds
is opposite to the direction of motion
is a function of the object’s velocity squared
Free Fall and Terminal Velocity
1. Accelerating – speeding up when parachute is closed
2.
3.
(force of gravity is greater than force of air resistance).
Terminal Velocity occurs when object falls at a constant
speed when both forces are in balance. Note that every
object has a different terminal velocity.
Decelerating – slowing down when parachute is opened
(force of gravity is less than force of air resistance).
Diagrams:
SYSTEM DIAGRAM:
• A sketch that includes all
items and objects in the
scenario.
FREE-BODY DIAGRAM:
• A picture comprised of a
circle or square with a dot
in the centre to represent
ONE of the objects in the
system.
• All forces acting on that
particular object are
drawn outward from the
dot.
Example of a FBD:
OBJECT on a FLAT SURFACE:

FN

Ff

FN

Ff
OBJECT on a RAMP:

FT

Fg

Fg

Fg cos 

Fg sin
 
 






FNET  FTOTAL  FRESULTANT FR  FSUM  F
1.
2.
3.
4.
5.
Find the resultant force for an object with the following forces acting
on it: 197 N [up], 198 N [down], 25 N [right] and 24 N [left].
Two students are trying to pull a 20 kg toboggan out of a deep snow
drift that provides an opposing force of 8.0 N. They are using ropes
attached to the toboggan that are parallel to the ground. The forces
exerted by the students and the directions in which they pull on the
ropes are 20 N at 30° and 15 N at 20° from the forward horizontal
direction. What is the acceleration of the toboggan?
The driver of a 2000 kg car applies the brakes on a dry concrete
roadway. Calculate the force of friction between the tires and the
road surface.
A 20 kg box is dragged across a level floor with a force of 100 N.
The force is applied at an angle of 40° above the horizontal. If the
coefficient of kinetic friction is 0.32, then what is the acceleration of
the box?
A student on a toboggan is sliding down a snow-covered hillside.
The student and toboggan together have a mass of 50 kg and the
slope is at an angle of 30° to the horizontal. Find the student’s
acceleration:
a) Assuming that there is no friction.
b) Assuming that the coefficient of kinetic friction is 0.15.
Newton’s First Law of Motion:
The Law of Inertia
• INERTIA is the ability of an
•
•
object to resist changes to its
motion. The greater the
mass, the greater the inertia
of an object.
If the net force acting on an
object is zero, then that
object maintains its state of
rest (static equilibrium) or
motion at constant velocity
(dynamic equilibrium).
There is NO acceleration
because the forces are in
BALANCE.

2
a  0 m / s F 

 Fx  0

 Fy  0
Newton’s Second Law of Motion:
FNET=ma
• If the external net force
•
•
acting on an object is NOT
zero, then the object
accelerates in the direction of
the net force.
The acceleration is directly
proportional to the net force
and inversely proportional to
the object’s mass.
The system has an
ACCELERATION because the
forces are UNBALANCED.

2
a  0 m / s F 

 Fx  0

 Fy  0
m
1 N  1 kg  2 
s 
Example #1: Static Equilibrium
A clothes-line is attached to high
poles 10.0 m apart. A pulley
allowed to roll freely on the line
has a 30 kg mass hanging from it.
Find the tension in each half of
the clothes-line if the sag at the
centre is 0.40 m.
Example #2: Dynamic Equilibrium
and Acceleration of the System
a)
b)
c)
A baby carriage with a mass of 50 kg is pushed
along a rough sidewalk with an applied
horizontal force of 200 N and is moving at a
constant velocity of 3.0 m/s.
What is the force of friction?
What is the applied horizontal force required to
accelerate it from rest to 7.0 m/s in 2.0 s?
What is the applied force required to accelerate
it from rest to 7.0 m/s in 2.0 s if the force was
applied at an angle of 30° from the horizontal?
Newton’s Third Law of Motion:
The Law of Action-Reaction
• For every action force, there
•
•
is a simultaneous reaction
force that is equal in
magnitude, but opposite in
direction.
Sometimes this force may be
fictitious, for example,
centripetal force and
centrifugal force.
These law deals with solving
tension problems!!!


FACTION  FREACTION
Example #3:
Pulley Systems
1. A toy train consists of 3 carts joined together by 2 short
2.
3.
strings and with a longer string for pulling which is attached
to cart 1. If a child pulls the toy with a horizontal force of
6.0 N, then what force must each of the short strings be able
to withstand? The total mass is 3.0 kg where cart 3 is 1.0
kg, cart 2 is 1.5 kg, and cart 1 is 0.5 kg.
A pulley has a mass of 6.0 kg on one end and a mass of 8.0
kg on the other end. What is the acceleration of the 6.0 kg
mass? What is the tension in the string?
A mass of 6.0 kg is on a table and is pulled by 8.0 kg mass
hanging at the end of the table on a pulley. What is the
acceleration of the 6.0 kg mass? What is the tension in the
string?
Examples continued:
Pulley and Ramps with Friction
1. A mass of 5.0 kg is on a table and is pulled by 2.0 kg mass
2.
hanging at the end of the table on a pulley.
a) What is the static coefficient of friction such that the
system is just about to move?
b) What is the acceleration of the system if the coefficient of
kinetic friction is 0.20? What is the tension in the rope?
A mass of 5.0 kg is on a ramp and is pulled by 4.0 kg mass
hanging at the end of the ramp on a pulley. The ramp has
an incline of 25°.
a) What is the acceleration of the system if the coefficient of
kinetic friction is 0.2?
b) What is the coefficient of static friction that will just
prevent the block from sliding up?