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 lbF1 = 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 ADVANTAGEThe 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 ADVANTAGEIn 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