Miscellaneous Forces
Weight
• Weight is the force of gravity upon an
object. This force is represented by the
symbol Fg (units of Newtons)
• Acceleration of gravity on the earth is
always -9.81 m/s/s, so weight can be
calculated by multiplying the mass and 9.81 m/s/s
Normal Force
• Normal Force is the
force of a surface on
an object, and acts
against the force of
gravity (weight). It is
always perpendicular
to the contact surface.
It is represented by Fn
Force of Friction
• Friction is a force that
opposes applied force
• Static friction is the force
that is exerted on a
motionless object, and is
always equal but opposite
to an applied force. It is
represented by Fs.
• There is a limit where the
static friction can no
longer keep the object
motionless. This limit is
called the Fs,max
Force of Friction
• Kinetic friction is the
force that opposes
motion of a moving
object. It is a fixed
amount that depends
on the surfaces
involved. It is
represented by the
symbol Fk
Force of Friction
• The coefficient of friction describes the relative
amount of friction between two surfaces. It is
represented by μs or μk
• It can be calculated by:
μs= Fs,max / Fn
• μk = Fk / Fn
6.3 Equilibrium and Hooke's
Law
• When the net force acting on an object is
zero, the forces on the object are
balanced.
• We call this condition equilibrium.
6.3 Equilibrium and Hooke's
Law
• A moving object continues to move with the same speed
and direction.
• Newton’s second law states that for an object to be in
equilibrium, the net force, or the sum of the forces, has
to be zero.
6.3 Equilibrium and Hooke's
Law
• Acceleration results from a net force that is
not equal to zero.
Calculating the net force from
four forces
Four people are pulling on the same 200 kg box with the
forces shown. Calculate the acceleration of the box.
1.
2.
3.
4.
–
You are asked for acceleration.
You are given mass and force.
Use a = F ÷ m.
First add the forces to find the net force.
F = - 75N - 25N + 45N + 55N = 0 N, so a = 0
6.3 Free-body diagrams
• To keep track of the
number and
direction of all the
forces in a system, it
is useful to draw a
free-body diagram.
• A free-body diagram
makes it possible to
focus on all forces
and where they act
6.3 Free-body diagrams
• Forces due to weight or
acceleration may be assumed
to act directly on an object,
often at its center.
• A reaction force is usually
present at any point an object
is in contact with another
object or the floor.
• If a force comes out negative, it
means it opposes another
force.
6.3 Applications of equilibrium
What is the upward force in
each cable?
• If an object is not
moving, then you know it
is in equilibrium and the
net force must be zero.
• You know the total
upward force from the
cables must equal the
downward force of the
sign’s weight because
the sign is in equilibrium.
Using equilibrium to find an
unknown force
Two chains are used to lift a small boat. One of
the chains has a force of 600 newtons. Find the
force on the other chain if the mass of the boat is
150 kilograms.
1.
2.
3.
4.
5.
You are asked for the force on one chain.
You are given 2 forces and the mass.
Use: net force = zero, Fw = mg and g = 9.8 N/kg.
Substitute values: Fw = mg = (150 kg)(9.8 N/kg) = 1,470 N.
Let F be the force in the other chain, equilibrium requires:
–
F + (600 N) = 1,470 N F = 1,470 N – 600 N
–
F = 870 N.
6.3 Applications of equilibrium
• Real objects can move in
three directions: up-down,
right-left, and front-back.
• The three directions are
called three dimensions and
usually given the names x,
y, and z.
• When an object is in
equilibrium, forces must
balance separately in each
of the x, y, and z
dimensions.
6.3 The force from a spring
• A spring is a device designed
to expand or contract, and
thereby make forces in a
controlled way.
• Springs are used in many
devices to create force.
• There are springs holding up
the wheels in a car, springs to
close doors, and a spring in a
toaster that pops up the toast.
6.3 The force from a spring
• The most common type of spring is a coil
of metal or plastic that creates a force
when it is extended (stretched) or
compressed (squeezed).
6.3 The force from a spring
• The force from a spring has
two important
characteristics:
– The force always acts in
a direction that tries to
return the spring to its
unstretched shape.
– The strength of the force
is proportional to the
amount of extension or
compression in the
spring.
6.3 Restoring force and Hooke’s
Law
• The force created by an extended or
compressed spring is called a “restoring
force” because it always acts in a
direction to restore the spring to its
natural length.
• The change a natural, unstretched
length from extension or compression is
called deformation.
• The relationship between the restoring
force and deformation of a spring is
given by the spring constant (k).
6.3 Restoring force and Hooke’s
Law
• The relationship between force, spring
constant, and deformation is called Hooke’s
law.
• The spring constant has units of newtons
per meter, abbreviated N/m.
6.3 Hooke's Law
Force (N)
F=-kx
Deformation (m)
Spring constant N/m
• The negative sign indicates that positive
deformation, or extension, creates a
restoring force in the opposite direction.
Calculate the force from a spring
A spring with k = 250 N/m is extended
by one centimeter. How much force
does the spring exert?
1.
2.
3.
4.
You are asked for force.
You are given k and x.
Use F = - kx
Substitute values: F = - (250 N/m)(0.01 m)
N
F = - 2.5
6.3 More about action-reaction and normal
forces
• The restoring force
from a wall is
always exactly
equal and opposite
to the force you
apply, because it is
caused by the
deformation
resulting from the
force you apply.
Calculate the restoring force
The spring constant for a piece of solid wood is 1
× 108 N/m. Use Hooke’s law to calculate the
deformation when a force of 500 N (112 lbs) is
applied.
1.
2.
3.
4.
5.
You are asked for the deformation, x.
You are given force, F and spring constant, k.
Use F = - kx, so x = - F ÷ k
Substitute values: x = - (500 N/m) ÷ (1 × 108 N/m)
x = - 5 × 10-6 meters (a very small deformation)