5.3 Moment calculations and a balancing situation (equilibrium)

The left diagram illustrates a balanced situation (equilibrium) where a ruler is pivoted in the middle and two weights w1 and w2 are placed at distances d1 and d2 from the pivot point.

 Remember weight = force in newtons.

The weights hang vertically so the force due to gravity is acting perpendicularly (at 90^o) to the ruler

For the ruler to be balanced in a perfect horizontal position the two turning forces must be equal.

Here we use the terms clockwise moment and anticlockwise moment for the two turning effects of the forces involved.

anticlockwise moment = w1 x d1 (left-hand side of pivot), clockwise moment = w2 x d2 (right-hand side of pivot)

so when w1d1 = w2d2

the ruler is balanced horizontally, at equilibrium when the turning effects of the forces are equal.

 

This situation conforms with the principle of moments which states that when the total sum of the anti clockwise moments is equal to the total sum of the clockwise moments the system is in equilibrium and the object (system) will NOT turn.

When a system is stable (no movement) or balanced it is said to be in equilibrium as all the forces acting on the system cancel each other out.

You see this when you do a simple experiment balancing a rule on a pencil and putting small weights on either side until balanced.

Similarly, when a the nut of a bolt is tightened, there comes a point when the moment you are applying is balanced by the opposing moment of the bolt and nut and you cannot tighten the nut anymore.

The middle of a seesaw is the pivot point. If two people of equal weight sit on either end, the seesaw is balanced horizontally - the clockwise and anticlockwise moments are equal. If the two people differ in weight, the seesaw will drop down on the side of the heaviest person because the clockwise and anticlockwise moments are unequal.

The direction of rotation i.e. clockwise or anticlockwise, will be decided on the relative weights (forces) at each end of the seesaw. One end will fall in the direction of the largest moment

Make sure you have no problem with unit conversions!

1 kg = 1000 g and 100 cm = 1 m,

and here for simplicity, assume g = 10 N/kg (weight = mass x force of gravity)

An example of using the principle of moments - old fashioned kitchen scales

The beam of the scales should be horizontal when the bowl and weights plate are empty (d1 = d2, w1 = w2).

In other words d1w1 = d2w2

When the object to be weighed is placed in the dish, the scales tip anticlockwise down on the left.

You then add weights until the beam is horizontally balanced again, thus giving the weight of the material e.g. flour in the bowl.

Examples of simple calculations using the above situations

Predict what happens in the following situations Q1(a) to (c)

Q1(a) Suppose d1 = 20 cm, w1 = mass of 25 g, d2 = 10 cm, w2 = mass of 50 g

but is it balanced? Any clockwise or anticlockwise movement?

Worked out ANSWERS

 

Q1(b) Suppose d1 is 14 cm, w1 = mass of 52 g, d2 = 12 cm, w2 = mass of 60 g

but is it balanced? Any clockwise or anticlockwise movement?

Worked out ANSWERS

 

Q1(c) Suppose d1 is 2.5 m, w1 = mass of 55 kg, d2 = 3.0 m, w2 = mass of 50 kg

but is it balanced?

but is it balanced? Any clockwise or anticlockwise movement?

Worked out ANSWERS

 

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Index of Forces 5. Turning forces, calculating moments, problem solving