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Moments

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**Force and rotation pivot 5N**

A force acting on an object can cause it to turn about a pivot. What would happen to the see-saw above ? Would it turn? If so, clockwise or anti-clockwise?

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**A turning force is called a moment.**

Force and rotation pivot The left goes down - an anticlockwise turn. A turning force is called a moment.

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**Moments Pivot Distance from force to pivot Force**

Suppose you were trying to unscrew a nut using a spanner. The spanner exerts a moment or turning force on the nut. If the moment is big enough it will unscrew the nut. If not there are 2 ways of increasing the moment.

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Increasing the moment 1. Increase the distance from the force to the pivot - apply the force at the end or use a longer spanner. Pivot Distance from force to pivot Force

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Increasing the moment 2. Increase the force applied - push/pull harder or get someone stronger to do it! pivot Distance from force to pivot Force

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**F x d Moment The moment of a force is given by the relationship:**

Moment = Force (N) x Distance (cm or m). Moments are measured in Newton centimetre (Ncm) or Newton metre (Nm). moment F x d

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Moments calculation Gina weighs 500 N and stands on one end of a seesaw. She is 0.5 m from the pivot. What moment does she exert? Click for solution moment = 500 x 0.5 = 250 Nm 0.5 m 500 N pivot

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Principle of moments The green girl exerts an anti-clockwise moment equal to ... her weight x distance from pivot. The yellow girl exerts a clockwise moment equal to... her weight x distance from pivot. pivot

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Principle of moments pivot If the two moments are equal then the seesaw is balanced. This is known as the principle of moments. When balanced Total clockwise moment = total anti-clockwise moment “c.m.” = “a-c.m.”

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**Both moments are equal and so the seesaw is balanced.**

Principle of moments The principle of moments can be investigated using 10g masses with this balance. moment (left) = 10 x 7 = 70 gcm moment (right) = (10 x 3) + (10 x 4) = 70 gcm Both moments are equal and so the seesaw is balanced.

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**Why don’t cranes fall over?**

Tower cranes are essential at any major construction site. load arm trolley Concrete counterweights are fitted to the crane’s short arm. Why are these needed for lifting heavy loads? counterweight loading platform tower

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**Why don’t cranes fall over?**

Using the principle of moments, when is the crane balanced? 3 m 6 m N ? moment of = moment of load counterweight If a N counterweight is 3 metres from the tower, what weight can be lifted when the loading platform is 6 metres from the tower?

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**Why don’t cranes fall over?**

moment of load = = ? x 6 load x distance of load from tower moment of counterweight distance of counterweight from tower = = x 3 = Nm counterweight x moment of load = moment of counterweight ? x 6 = ? = 6 ? = 5000 N

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**Crane operator activity**

Where should the loading platform be on the loading arm to carry each load safely?

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Moments activity

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**Using moments in calculations**

1. Two girls are on a seesaw. One weighs 200N and is 1.5m from the pivot. Where must her 150N friend sit if the seesaw is to balance ?. Click for solution At balance total “c.m.” = total “a-c.m.” 200 x 1.5 = 150 x distance 200 x 1.5 = distance 150 distance = 2 m “c.m.” = clockwise moment “a-c.m.” = anti-clockwise moment

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**Pressure and Hydraulics**

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**Pressure Pressure is exerted whenever a force is applied over an area.**

1. 2. Which one exerts the biggest pressure, 1 or 2?

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1. Case 1. The arm applies a force onto a board via a finger tip. The force applied produces a high pressure because the force acts over a small area.

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2. Case 2. The arm applies the same force onto the board. The force is now acting over a larger area - the area of the palm is greater than the finger tip. Thus, a lower pressure is produced.

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**Force Pressure = Area Pressure F P x A**

Pressure is the force per unit area so is calculated using the expression shown below: Pressure = Area Force Pressure is measured in: Newtons per metre squared (N/m2) which is called a PASCAL (Pa) Pressure can also be measured in: Newtons per millimetre squared (N/mm2); Newtons per centimetre squared (N/cm2).

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**The same force spread over a big area means low pressure. **

Which shoes would you choose for walking over a muddy field?

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**The boots on the right spread the weight over a larger area**

The boots on the right spread the weight over a larger area. Therefore, the pressure exerted on the ground is low. In contrast, fashion shoes have a smaller area and exert a higher pressure. These shoes are likely to sink into soft ground.

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**Application of pressure**

A force spread over a large area means low pressure, e.g. skis and snowboards. The large surface area of the board means the boy exerts very little pressure on the snow. He therefore slides over the top and does not sink in.

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**Application of pressure**

A force concentrated on a small area means high pressure, e.g. razor blades, needles, high heeled shoes, spurs, ice skates, sharp knives. The high pressure on the cutting edge of an ice-skate melts the ice and helps the skater slide across the surface. On the cutting edge of a knife a very high pressure is exerted - this makes it easier to cut.

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**Pressure in liquids In a liquid: Pressure acts in all directions and**

pressure increases with depth.

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**Pressure (N/m2) = 10 N/Kg x depth (m) x density (Kg/m3)**

The relationship between pressure and depth is shown by a water bottle with holes along its length. low pressure High pressure Pressure (N/m2) = 10 N/Kg x depth (m) x density (Kg/m3) The pull of gravity The deeper you go, the higher the pressure The denser the liquid, the heavier it is!

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**Pressure inside all parts of the hydraulic system is the same**

Hydraulic systems use the principle that pressure is transmitted throughout a liquid. They are used to transfer movement from one part of a machine to another without linking them mechanically. All hydraulic systems use two pistons linked via a pipe carrying a special oil called hydraulic fluid. Force applied here Force transferred here Pressure inside all parts of the hydraulic system is the same

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Hydraulics brakes All hydraulic brake systems (e.g. in a car) use a small master piston and a bigger slave piston. The master piston is used to apply a force. This puts the liquid under pressure. Pressure = Force applied Area master piston The pressure is transmitted to the pistons on all four wheels.

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**Force exerted = Pressure x Area slave piston**

The slave piston always has a much larger area than the master piston. The force exerted can be calculated from the same equation: Much larger than master piston Pressure = Force exerted Area slave piston Force exerted = Pressure x Area slave piston So, a greater force is exerted by the brakes than the driver exerted on the pedal.

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**The hydraulic brake Friction shoes Hydraulic fluid Slave pistons**

Foot pedal drum Master piston

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**The hydraulic brake - example**

The car master piston has an area of 5cm2. If a force of 10N is applied to it, calculate the pressure created in the brake pipes. If the slave piston has an area of 50 cm2, calculate the force exerted on the brake disc. Click for solution At the master piston, P=F/A= 10/5 = 2 N/cm2 At the slave piston, F= PxA =2x50 = 100 N (10 times the original force applied to the master piston).

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Hydraulics activity

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