Moment of force

 STATIC- deals with the bodies in
equilibrium, meaning the net force is equal
to zero, provided these forces are
concurrent (their lines of action intersect).
 The effectiveness of a force in changing
the rotational motion of a body depends on
its perpendicular from the axis of rotation
to the line of action of the forces.

 Torque or Moment due to force about an axis (O)
is a measure of the effectiveness of the force in
producing rotation about an axis. It is defined as
the product of the force (F) and the
perpendicular distance (d) from the axis of
rotation to the line of action of the force
 For a fixed moment arm, the greater the force,
the greater the effect upon the rotational
motion. This perpendicular distance is called
Lever arm or momentum arm. Units of
momentum/torque are Nm in Si/mks.

F
O
F
O
d
d
Moment= Force x Moment arm
Mo= Fd

Moment= Force x Moment arm
M= F d but sin Ɵ= c/d or d= c/sin Ɵ
Mo = F [ c/ sin Ɵ ]
Mo = F(d sin Ɵ)
F
O
d
c

A light horizontal bar is 4 m long. A 3 N force acts vertically upward
on it 1 m from the right end find the moment about each end.
F= 3N
3 m 1 m
4 m
Solution:
a.) For axis of rotation taken at
the right end:
M= F d
M= 3N(1m)
M= 3N/m
b.) For axis of rotation
taken at the left end:
M= F d
M= 3N(3m)
M= 3N/m

 For the object to be in equilibrium under the
action of a set of forces, the vector sum of
all moments about any axis must be zero.
This is equivalent to saying that the sum of
the Mc about any axis equals the sum of the
Mcc about that axis

 Sign Convention
Negative Moment- moment causing clockwise
rotation.
Positive Moment- moment tending to cause
counter-clockwise rotation.
 Parallel Forces
- are non-concurrent forces whose lines of
action are parallel. They act in the same, or
opposite direction

 Canter of gravity of an object is the point at
which the entire weight of the object may be
considered concentrated(the line of action of
the weight passes through the center of
gravity). When suspended at this point(c.g.),
there is no tendency for the body to rotate.
It is the point where sum of moments is
equal to zero(ΣM=0). For uniform objects,
c.g. is at its geometric center. For other
objects, plumb line method is used to obtain
the center of gravity (c.g.).

 If the sum of the moment is zero about one
axis for a body that also obeys the force
condition, It is zero about other axes parallel
to the first. Choose the axis in such a way
that the line of an unknown force goes
through the intersection point of the axis and
the plane. The lever arm (and moment or
torque) of the unknown force is zero and so
this unknown force does not appear in the
moment equation.

Quantity System of Units
MKS / SI CGS FPS / ENGLISH
Torque or Moment
M
Newton meter Dyne centimeter Pound foot
Force
F
Newton Dyne Pound
Moment arm
d
Meter Centimeter Foot

Sample Problems:
A uniform bar , 9 ft long and weighing 5 lb is supported by a fulcrum 3 ft
from the left end. If a 12-lb load is hung from the left end,(a) what
downward pull at the right end is necessary to hold the bar in equilibrium?
(b) With what force does the fulcrum push up against the bar?
3 ft 4.5 ft
9 ft
W= 5 lb
F1 = 12 lb F3 F2
Mc
Mc
Mcc

Solution:
ΣF=0
F3 –F1 -W-F2=0
F3 -12lb-5lb-F2=0
F3 =17lb+F2
F3 =17 lb + F2
= 17 lb+ 4.75lb
= 21.75 lb

Simple Machines
GROUP 1
ALONSABE BELGIRA
ARGUELLES BENDICO
ASPERA CALDERON
BAYLON
BULATAO

Simple machines are tools
used to make work easier.

You have probably used some simple
machines, but did not realize that
they were actually called simple
machines!

Simple machines do not make less
work; they just make it easier to do
work.
It would be hard to cut
this wood without the
saw!

There are 6 different types of
simple machines:
•(1)lever
•(2)scre
w
•(3)pulley
•(4)wheel & axle
•(5)inclined
plane
•(6)wedge

(1) LEVER
A lever is a stiff bar that moves about a
fixed point (fulcrum).
A lever is used to push, pull, or lift things.

A shovel is an example of a lever.
A seesaw is another example of a lever.

(2)
SCREW
A screw is an inclined plane wrapped
around a cylinder or cone.
A common use of the screw is to hold
objects together.

A jar lid and a wood screw are examples
of a screw.

(3) PULLEY
A pulley is a wheel that has a rope
wrapped around it.
Pulleys can be used to lift heavy
objects by changing the direction or
amount of the force.

A flagpole uses a pulley to raise the
flag.

A bicycle wheel, roller skates, and a
doorknob are all examples of a wheel &
axle.

(4) WHEEL & AXLE
A wheel & axle consists of a rod
attached to a wheel.
A wheel & axle makes it easier to move
or turn things.

(5) INCLINED PLANE
An inclined plane is a flat surface that
is raised so that one end is higher than
the other.
An inclined plane helps move heavy
objects up or down.

A ramp is an example of an inclined
plane.
Let’s add inclined plane to our list of simple
machines (along with levers, screws, pulleys, and
wheels & axles).

(6) WEDGE
A wedge is wide at one end and pointed
at the other to help cut or split other
objects.

Examples of wedges: a knife or an ax

A machine is a device for applying energy to do work in a way
suitable for a given purpose. No machine can create energy. To
do work, a machine must receive energy from some source,
and the maximum work it does cannot exceed the energy it
receives.
Machines may receive energy in different forms, such as
mechanical energy, heat, electric energy, or chemical energy.
We are here considering only machines that employ
mechanical energy and do work against mechanical forces. In
the so-called “simple machines”, the energy is supplied by a
single applied force and the machine does useful work against
a single resisting force. The frictional force which every
machine encounters in action and which causes some waste of
energy will be neglected for simplicity in treating some of the
simple machines.

There are two major classes of simple machines, the lever and the inclined
plane. However, these usually have been modified into more specialized
simple machines so that it may be considered that there are the following six
simple machines: the lever, the pulley, the wheel and axle, the inclined plane,
the screw, and the wedge.
ACTUAL MECHANICAL ADVANTAGE
The utility of the machine is chiefly that it enables a person to perform some
desirable work by changing the amount, the direction, or the point of
application of force. The ratio of the output of force F exerted by the machine
on a load to the input force Fi exerted by the operator on the machine is
defined as the actual mechanical advantage (AMA) of the machine.
Where: AMA = actual mechanical advantage of the machine
Fo= force exerted by the machine on a load
Fi = force used to operate the machine

IDEAL MECHANICAL ADVANTAGE
In any machine, because of the effects of friction, the useful work done by the
machine is always less than the work done on the machine. The input work done by
the applied force Fi is measured by the product of Fi and the distance si through
which it acts. The output work is measured by the product of the output force Fo and
the distance so through which it acts.
F0 s0 < Fi s0
If we divide each member of the inequality by Fi soi
That is, the ratio of forces Fo/Fi is less than the ratio of the distances si/so for any
machine. If the effect of the friction are very small, the value of the output work
approaches that of the input work, or the value of FO/Fi becomes nearly that of si/so. The
ideal mechanical advantage (IMA) is defined as the ratio of the distance si through which
the input force acts to the distance so though which the output force acts.
Where:
IMA = ideal mechanical advantage of a machine
si = distance moved by input force
so = distance moved by load

EFFICIENCY
Because of frictional losses the other losses in all moving machinery, the
useful work done by a machine is less than the energy supplied to it. From
the principle of conservation of energy,
Energy input = energy ouput + energy wasted
Assuming no energy is stored in the machine.
The efficiency of a machine is defined as the ratio of its output work to its
input work.
This ratio is always less than 1, and is usually multiplied by 100 percent (%)
and expressed in percent. A machine has a high efficiency if a large part of
the energy supplied to it is expended by the machine on its load and only a
small part is wasted. The efficiency (eff) may be as high as 98 percent for a
large electric generator and will be less than 50 percent for a screw jack.

Also
since;
• Note that the work input times the efficiency is equal to the work
output

Moment of force

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