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5.5 Some applications of turning effects of forces including levers

Many of the examples described below involve a lever, which is a means of increasing the rotational effect of a force.

You push down on one end of a lever, and the rotation about the pivot point can cause the other end to rise with a greater force.

The diagram below illustrates the principle of lever to gain a mechanical advantage - its all about the d1/d2 ratio.

F is the force involved (N) and d (m) is the (shortest) perpendicular distance from the pivot point to the point where the force is applied OR generated.

F1 = the applied input force, d1 = the distance from the pivot to where the force F1 is perpendicularly applied

F2 = the output force, d2 = the distance from the pivot to where the force F2 is perpendicularly generated

When balanced, i.e. just before something is 'levered' and caused to move

input moment = F1 x d1 = output moment = F2 x d2

From F1 x d1 = F2 x d2, rearranging gives F2 = F1 x d1/d2

Therefore by making d1 much bigger than d2 you can produce a much bigger output force compared to the original input force.

Generally speaking you make the distance d1 much bigger than distance d2 - you can see this using scissors, levering a lid off a can  and its a very similar situation when using a fork to lift deep tough roots out of the soil or moving a heavy stone with a pole.

So, levers are very useful because they make lifting and moving things much easier by reducing the input force necessary to perform the task.

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Q1 Example of a lever question

Suppose a heavy manhole cover requires a force of 160N to open it. Imagine you have a steel bar 1 metre long pivoted at a point 0.1 m (10 cm) from the end to lever open the heavy manhole cover.

If you press down with a force of 20 N, will the upward force you generate be enough to lift the manhole cover?

Worked out ANSWERS

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Q2 A hole punch of some description

A punch press machine

The diagram shows a simple machine to punch holes in a sheet of material.

The lever is pulled down to produce the hole.

The pivot point (turning point) is on the left.

(a) If d1 is 10 cm, d2 120 cm and the pull down force F2 required is 2 N, what punch force F1 is produced?

Worked out ANSWERS

(b) If d2 is 80 cm and the pull force F2 used is 4 N, what is the maximum length d1 can be to produce a minimum required punch force F1 of 40 N?

Worked out ANSWERS

(c) If d1 is 9 cm, d2 108 cm and the punch force F1 required is 60 N, what is the minimum pull down force F2 required?

Worked out ANSWERS

(d) When d1 is 12 cm, the punch force required F1 is 36 N if a pull-down force F2 of 3N is applied.

 What is the minimum length of the lever d2 required to punch the hole?

Worked out ANSWERS

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Other examples of the application of the principle of levers and turning effect

Scissors

When you press the scissor hands together you create a powerful turning force effect close to the pivot point.

F1 x d1 = F2 x d2, rearranging gives F2 = F1 x d1/d2

So, by making d1 >> d2, you create a much bigger out force F2, sufficient to crisply cut through paper or card.

That's why you apply the blades to whatever you are cutting as near as possible to the pivot point.

You don't cut using the ends of the scissor blades where you gain little mechanical advantage i.e no significant multiplication of the force you apply. Its the same principle as described in the whole punch machine described in (a) above.

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Levering the lid of a can

You can use a broad bladed screwdriver to get the lid off a can of paint. The pivot point is the rim of the can.

The length of the screwdriver to the pivot point (d2) is much greater than tip of the screwdriver beyond the rim (d1).

F1 x d1 = F2 x d2, F1 = F2 x d2/d1, so if d2 is much bigger than d1, you get a great magnification of the force you apply (F2) to give a much greater up force (F1) to force the lid off.

Another example of needing less force to get the same moment to do the job of opening the can.

 

The relatively long handle of a spanner

 

Spanners have long handles to give a strong turning force effect.

Generally speaking, the larger the nut to be tightened, the longer the spanner.

Spanners were discussed in detail at the start of the page.

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A cork screw

The radius of the handle is much greater than the boring rod.

The great difference in radius gives you a much greater torque (turning force effect) to bore into the cork stopper of a wine bottle.

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The screwdriver

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A wheelbarrow

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

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Key points about turning forces - various applications of the lever principle

Moments are everywhere once you start looking — they’re the reason doors open, bikes move, and bridges stay standing. Here are some real-world applications of moments that show how forces cause rotation around a pivot:

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Everyday Examples of Moments

Opening a Door

• The hinges act as the pivot.
• Pushing near the handle (far from the pivot) requires less force to rotate the door.
• This is why handles are placed far from the hinges — to maximize the moment.

Using a Spanner (Wrench)

• Turning a bolt involves applying force at a distance from the bolt’s axis.
• A longer spanner increases the perpendicular distance, so you need less force to achieve the same turning effect.

Steering a Car

• The steering wheel is designed with a large radius.
• Applying force at the rim creates a larger moment, making it easier to turn the wheels.

Sitting on a Seesaw

• The pivot is the central fulcrum.
• Balance is achieved when the clockwise and anticlockwise moments are equal.
• Heavier person sits closer to the pivot, lighter person sits farther away — classic moment balancing!

Pedalling a Bicycle

• Force applied to the pedals creates a moment about the crank’s axis.
• The length of the crank arm affects how efficiently force is converted into rotational motion.

Lifting with a Lever

• A lever uses a pivot (fulcrum) and a long arm to lift heavy loads.
• The greater the distance from the pivot, the greater the moment for the same force.

Wind Turbines and Steam Turbines

• Blades experience force from wind or steam.
• This force, applied at a distance from the turbine’s axis, creates a moment that spins the generator to produce electricity.

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Keywords, phrases and learning objectives for turning forces

Be able to describe, explain and apply the principle of moments to applications of the turning effects of forces including the principle of lever opening cans, operation of a  punch press machine, moment calculations of scissors, spanners and screwdriver and a wheelbarrow.

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