Moments, Levers & Couples

K WARNE

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Moments and levers

Definition

Principle of moments

Couples

Calculations

Classes

Mechanical advantage

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Moment of Force

The moment of a force about a point is the PRODUCT of the magnitude of the force and the perpendicular distance from the point to the line of the force.

MOMENT = FORCE X DISTANCE

= 5 x 0.25

= 1.25 N.m

5 N25 cm

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Calculate the moment of the force, or ……….., due to each force

when several forces act on the same object using the equation:

= F … r

F

Calculating Torque

F1

F2

= F x r = (F1x …1) + (F2x …2)

When calculating torque the ………….of all the PERPENDICULAR FORCES

must be used.

TORQUE

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Equilibrium For an object to be in equilibrium BOTH the sum of the ……………..

acting on the object and the sum of the …………….of the forces must

be ZERO.

Solve problems involving objects in equilibrium.

F2

F3F1

FORCES (Linear) in equilibrium .: F1 + F2 + F 3 = ……

MOMENTS in equilibrium .: ……………. a fulcrum. (F1)

(F1….) + (F2…..) + (F3……) = 0

x1

x2

If a 60 Kg person

stands 2 meters from

one end of a 3 meter

scaffolding plank what

force is needed to

support each end of the

plank?

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Equilibrium Question

F2

(F1. x1) + (F2. x2) + (F3.0) = 0

(F1.1)+((60x10)x2) + (F3x0) = 0

F1 + (1200) + 0 = 0

F1 = -1200 N .: F1 = 1200 N anticlockwise!

A 1200 N force is needed at F1 to balance the plank!

x1 x2

If a 60 Kg person stands on one end of a 3 meter scaffolding plank what force is

needed to support him on the other end of the plank if the plank is balancing on

a fulcrum 2m away from the 60kg person?

??

60kg

2mF3

1 m

F1 ??

Sum of all moments = zero

Choose clockwise as

POSITIVE!

F3 = fulcrum

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Levers• Describe the terms “load” and “effort” for a lever

• Define “mechanical advantage” as the ratio of

“load/effort” and calculate the mechanical advantage for

simple levers

…………..................

……........

If in equilibrium: …… x ….. = …… x …..

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Levers• Describe the terms “load” and “effort” for a lever

• Define “mechanical advantage” as the ratio of

“load/effort” and calculate the mechanical advantage for

simple levers

LoadEffort

el

If in equilibrium: E x e = L x l

Mechanical

Advantage

Load Force

Effort Force

F

EOR =

e

l= =

Effort distance

Load distance=

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Mechanical Advantage

Mechanical Advantage is the RATIO of the LOAD to the EFFORT.

Apply the concept of mechanical advantage to everyday

situations.

Mechanical

Advantage

Load Force

Effort Force

NLoad

LEffort

E

l

e

F

EOR =

e

l= =

Effort distance

Load distance=

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Types of Levers

Class 1Effort

Load

Class 2

Effort

Load

Class 3

Effort

Load Load

Load

Effort

Effort

o.75

o.25

o.75

o.75

o.25

o.25

Type 1 F in middle

MA = e/l= 0.75/0.25 = 3

Type 2 F at end L in middle

M.A. = e/l = 1/0.25 = 4

Type 3 F in mid L at end

M.A. = e/l = 0.25/0.75 = 0.3

The weight of the lever helps

in type 1 but not T2!

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Examples of Levers

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Force CoupleA special case of moments is a

couple.

A couple consists of two

parallel forces that are equal in

magnitude, opposite in

direction and do not act in a

straight line but are separated

by a distance (d).

It does not produce any

translation, only rotation.

The resultant force of a couple is zero. BUT, the resultant of a couple is

not zero; it is a pure moment.

Example: A steering wheel of diameter 0.75 m is turned by a force of

20 N applied to each end. Calculate the magnitude of the force couple:

Couple = F x d = (20 x 0.75) = 15 N.m

F F

d

d

2

d

2

Couple = Total Turning

Moment

= (F x d/2) + (F x d/2)

= ½ (F x d) + ½ (F x

d)

= F x d

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Hi -

This is a SAMPLE presentation only.

My FULL presentations, which contain loads more slides (with all the gaps filled in) as well as

other resources, are freely available on my resource sharing website:

www.warnescience.net

(paste into your browser if link above does not work)

Have a look and enjoy!

Keith Warne