Turning Forces

IGCSE textbook Chapter 5, p. 42

1.25 know and use the relationship between the moment of a force and its distance from the pivot:

moment = force × perpendicular distance from the pivot1.26 recall that the weight of a body acts through its centre of gravity1.27 know and use the principle of moments for a simple system of parallel forces acting in one plane1.28 understand that the upward forces on a light beam, supported at its ends, vary with the position of a heavy object placed on the beam

Turning Forces

• Who wins, the woman trying to open the door or the man trying to keep it closed?

• Why?

Turning Effect

• When a force is applied to an object with a fixed pivot point (or fulcrum) it can have a turning effect.

• This turning effect is called a moment.• A lever is a simple machine which uses

moments.• So how does it work?

Levers

• The length of the lever seems to increase or reduce the ability of the applied force to turn things.

• The same turning effect can be achieved by a bigger force nearer the pivot or a smaller force further from the pivot

• Distance and force seem to compensate for each other

Archimedes: "Give me a place to stand, and I shall move the Earth with it"

Moment

moment= force perpendicular distancefrom pivot to line of action

newton metres(Nm)

force (N)

metres (m)

SpannersTough nut

pivot10 Newtons

10 Newtons

0.1m

0.2m

Force on spanner causes turning effect

Moment = 10 x 0.1 = 1 Nm

Bigger spanner has a bigger distance from pivot .Moment = 10 N x 0.2m = 2 N m

Much easier to turn nut for person.

To get the maximum moment you need to push at right angles to the spanner.

Force times which distance?

• Size of force• times• perpendicular distance

from pivot to line of action of the force

Force on the hammer, F = 50 NDistance from pivot, d = 0.30 mMoment = 50 N 0.30 m

= 15 Nm

Changing the force

Force on the hammer = 70 NDistance from pivot = 0.30 mMoment = 70 N 0.30 m

= 21 Nm

Changing the distance

Force on the hammer = 50 NDistance from pivot = 0.20 mMoment = 50 N 0.20 m

= 10 Nm

Principle of Moments• If a body is acted on by more than one turning

force and remains in equilibrium (doesn’t turn), then:

Sum of clockwise moments

Sum of anticlockwise moments

=

500 N 750 N

3 m ?

a) Who is lighter, Dawn or Jasmine?

Dawn Jasmine

2.5 m 2.0 m

b) Jasmine weighs 425 N

Dawn Jasmine

2.5 m 2.0 m

425 NWD = ? N

WD 2.5 m = 425 N 2.0 m

WD = 425 N 2.0 m/2.5 m

= 340 N

Now divideboth sidesby 2.5 m

c) John weighs 450 N

John Jasmine

d1 2.0 m

425 N450 N

450 N d1 = 425 N 2.0 m

d1 = 425 N 2.0 m/450 N

= 1.9 m (to two s.f.)

Now divideboth sidesby 450 N

Centre of Gravity

• The centre of gravity of an object is the point at which all its weight seems to act.– To balance an object, it must be supported in line

with its centre of gravity– why?

• For a symmetrical object it will be where the lines of symmetry cross.

• ...G

Finding Centre of Gravity

Step 1Suspend the object:

Centre of gravity lies somewhere along this line

Finding Centre of Gravity

Centre of gravity lies where the lines cross

Step 2Suspend the object from

a different point:

To Find the Centre of Gravity• Hang the shape from a pin

and let it swing freely.• Use a ‘plumb line’ to draw a

vertical line on the shape from the pin downwards.

• Now repeat this procedure with the shape suspended from a different point to give another line.

• The centre of gravity of the shape is where the two lines meet.

Pivot not at Centre of Gravity

• If the pivot point is at the centre of gravity, the weight of the object has no moment.

• If the pivot is offset from the C of G, the weight produces a turning effect

Click to find the centre of gravity.

Click to find the centre of gravity.

Click to find the centre of gravity.

Click to find the centre of gravity.

Click to find the centre of gravity.

Stability & Toppling

• The position of the centre of gravity affects an object’s stability.

• If an object is tilted and the line of force from the centre of gravity remains within the base, it will not topple over.

• If it is tilted so far that the line of force from the centre of gravity moves outside the base, it will topple over.

• Can you explain the design of this C18th ship’s decanter?

• When will it topple over, when will fall back upright?• “Stable” means it will fall back to its upright

position: the moment acting restores it as it was.• “Unstable” means the moment acting will move it

further away from its original position.

• Buses• Tractors• F1 cars• High chairs for baby• Skittles

• What is done to make these more stable?– As wide a base as possible– As low a centre of gravity as

possible.

Forces on a beam

• If the boy and beam are not moving, the forces must be in equilibrium– The total downward force (his weight) is equal to

the total upward force (from supports at each end)• How much support force is provided by each

end?• What happens if he moves towards one end?

Forces on a beam• The support force provided by each

end depends on the object’s position

L R

Object position

Supp

ort F

orce

L R

The two support forces always add up to the object’s weight

Left supportRight support

1.25 know and use the relationship between the moment of a force and its distance from the pivot:

moment = force × perpendicular distance from the pivot1.26 recall that the weight of a body acts through its centre of gravity1.27 know and use the principle of moments for a simple system of parallel forces acting in one plane1.28 understand that the upward forces on a light beam, supported at its ends, vary with the position of a heavy object placed on the beam