Grade 9 Unit P 5 Moments and Levers

Grade 9 Unit P. 5 – Moments and Levers Teacher’s Notes ﻣﻼﺣﻈﺎﺕ ﻟﻠﻤﺪﺭﺱ A slide contains teacher’s notes wherever this icon is displayed – ﺍﻟﺸﺮﻳﺤﺔ ﺍﻟﺘﻲ ﺗﺤﺘﻮﻱ ﺫﻟﻚ ﺍﻟﺮﻣﺰ ﺑﻬﺎ ﻣﻼﺣﻈﺎﺕ ﻟﻠﻤﺪﺭﺱ To access these notes go to ‘Notes Page View’ (Power. Point 97) or ‘Normal View’ (Power. Point 2000). Notes Page View Normal View Flash Files A flash file has been embedded into the Power. Point slide wherever this icon is displayed – These files are not editable.

Grade 9 Unit P. 5 – Moments and Levers Moments ﺍﻟﻌﺰﻭﻡ

Grade 9 Unit P. 5 – Moments and Levers Force and rotation pivot The left goes down - an anticlockwise turn. ﺗﺪﻭﺭ ﺍﻟﺮﺍﻓﻌﺔ ﻓﻲ ﻋﻜﺲ ﺍﺗﺠﺎﻩ ﻋﻘﺎﺭﺏ ﺍﻟﺴﺎﻋﺔ A turning force is called a moment. ﺗﺄﺜﻴﺮ ﺍﻟﺪﻭﺭﺍﻥ ﻳﺴﻤﻰ ﻋﺰﻡ ﺍﻟﺪﻭﺭﺍﻥ

Grade 9 Unit P. 5 – Moments and Levers Increasing the moment 1. Increase the distance from the force to the pivot - apply the force at the end or use a longer spanner. ﺇﻣﺎ ﻋﻦ ﻃﺮﻳﻖ ﺯﻳﺎﺩﺓ ﺫﺭﺍﻉ ﺍﻟﻘﻮﺓ Pivot ﻧﻘﻄﺔ ﺍﻻﺭﺗﻜﺎﺯ Distance from force to pivot ﺫﺭﺍﻉ ﺍﻟﻘﻮﺓ Force ﺍﻟﻘﻮﺓ

Grade 9 Unit P. 5 – Moments and Levers Increasing the moment 2. Increase the force applied - push/pull harder or get someone stronger to do it! ﻭﺇﻣﺎ ﻋﻦ ﻃﺮﻳﻖ ﺯﻳﺎﺩﺓ ﺍﻟﻘﻮﺓ ﺍﻟﻤﺆﺜﺮﺓ pivot Distance from force to pivot Force

Moment Grade 9 Unit P. 5 – Moments and Levers The moment of a force is given by the relationship: ﻳﺤﺴﺐ ﻋﺰﻡ ﺍﻟﺪﻭﺭﺍﻥ ﻣﻦ ﺍﻟﻌﻼﻗﺔ ﺍﻟﺘﺎﻟﻴﺔ Moment = ﺍﻟﻌﺰﻡ Force ( ﺍﻟﻘﻮﺓ N) x Distance (ﻃﻮﻝ ﺍﻟﺬﺭﺍﻉ cm or m). Moments are measured in Newton centimetre (Ncm) or Newton metre (Nm). ﻣﺘﺮ. ﺳﻢ ﺃﻮ ﻧﻴﻮﺗﻦ. ﻳﻘﺎﺱ ﺍﻟﻌﺰﻡ ﺑﻮﺣﺪﺓ ﺍﻟﻨﻴﻮﺗﻦ moment F x d

Grade 9 Unit P. 5 – Moments and Levers Moments calculation Gina weighs 500 N and stands on one end of a seesaw. She is 0. 5 m from the pivot. Click for solution What moment does she exert? ﺍﺣﺴﺐ ﻋﺰﻡ. ﻧﻴﻮﺗﻦ ﺗﻘﻒ ﻋﻠﻰ ﻟﻮﺡ ﺧﺸﺒﻲ ﻋﻠﻰ ﻣﺴﺎﻓﺔ ﻧﺼﻒ ﻣﺘﺮ ﻣﻦ ﻧﻘﻄﺔ ﺍﻻﺭﺗﻜﺎﺯ 500 ﻭﺯﻥ ﺟﻴﻨﺎ ﺍﻟﺪﻭﺭﺍﻥ moment = 500 x 0. 5 = 250 Nm 0. 5 m 500 N pivot

Principle of moments Grade 9 Unit P. 5 – Moments and Levers The green girl exerts an pivot anti-clockwise moment equal to. . . ﺍﻟﻔﺘﺎﺓ ﺍﻟﺨﻀﺮﺍﺀ ﺗﺆﺜﺮ ﻓﻲ ﻋﻜﺲ ﺍﺗﺠﺎﻩ ﺍﻟﻌﻘﺎﺭﺏ The yellow girl exerts a clockwise moment equal to. . . ﺍﻟﻔﺘﺎﺓ ﺍﻟﺼﻔﺮﺍﺀ ﺗﺆﺜﺮ ﻓﻲ ﺍﺗﺠﺎﻩ ﻋﻘﺎﺭﺏ ﺍﻟﺴﺎﻋﺔ her weight x distance from pivot.

Principle of moments Grade 9 Unit P. 5 – Moments and Levers The principle of moments can be investigated using 10 g masses with this balance. ﺟﻢ ﻣﻊ ﺍﻟﺮﺍﻓﻌﺔ 10 ﻗﺎﻧﻮﻥ ﺍﻟﺮﻭﺍﻓﻊ ﻳﻤﻜﻦ ﺍﺳﺘﻨﺘﺎﺟﻪ ﺑﺎﺳﺘﺨﺪﺍﻡ ﺛﻘﻞ ﺍﻟﺘﺎﻟﻴﺔ 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. ﻛﻼ ﺍﻟﻌﺰﻣﻴﻦ ﻣﺘﺴﺎﻭﻳﺎﻥ ﻭﻟﺬﻟﻚ ﺗﺘﺰﻥ ﺍﻟﺮﺍﻓﻌﺔ

Why don’t cranes fall over? Tower cranes are essential at any major construction site. ﺭﻭﺍﻓﻊ ﺍﻷﺒﺮﺍﺝ ﻣﻬﻤﺔ ﻓﻲ ﻋﻤﻠﻴﺎﺕ ﺍﻟﺘﺸﻴﻴﺪ ﻓﻲ ﺍﻟﻤﻮﺍﻗﻊ load arm trolley counterweight loading platform tower Concrete counterweights are fitted to the crane’s short arm. Why are these needed for lifting heavy loads? ﺗﻮﺿﻊ ﺃﺜﻘﺎﻝ ﺍﻷﺴﻤﻨﺖ ﻋﻠﻰ ﺍﻟﺬﺭﺍﻉ ﺍﻟﻘﺼﻴﺮ ﻟﻠﺮﺍﻓﻌﺔ ﻋﻨﺪ ﺭﻓﻊ ﺃﺜﻘﺎﻝ ﻛﺒﻴﺮﺓ ﻋﻦ ﻃﺮﻳﻖ ﺍﻵﻠﺔ

Why don’t cranes fall over? Using the principle of moments, when is the crane balanced? ﻣﺘﻰ ﺗﺘﺰﻥ ﺍﻟﺮﺍﻓﻌﺔ ؟ ، ﻓﻲ ﺿﻮﺀ ﻗﺎﻧﻮﻥ ﺍﻟﺮﻭﺍﻓﻊ 3 m 6 m ? moment of load 10 000 N = moment of counterweight If a 10 000 N counterweight is 3 metres from the tower, what weight can be lifted when the loading platform is 6 metres from the tower?

Why don’t cranes fall over? moment of load ﻟﻤﺎﺫﺍ ﻻ ﺗﻘﻊ ﺍﻟﺮﻭﺍﻓﻊ = load x distance of load from tower = ? x 6 moment of = counterweight x distance of counterweight from tower = 10 000 x 3 = 30 000 Nm moment of load = moment of counterweight ? x 6 = 30 000 ? = 30 000 6 ? = 5000 N

Crane operator activity Where should the loading platform be on the loading arm to carry each load safely? ﻣﺎ ﻫﻮ ﺃﻔﻀﻞ ﻣﻜﺎﻥ ﺗﻘﻒ ﻓﻴﻪ ﺍﻟﻜﺘﻠﺔ ﺣﺘﻰ ﺗﺤﻤﻞ ﺍﻟﺮﺍﻓﻌﺔ ﺍﻟﺜﻘﻞ ﺑﺄﻤﺎﻥ ؟

Moments activity ﻧﺸﺎﻁ ﻋﻦ ﺍﻟﻌﺰﻭﻡ Grade 9 Unit P. 5 – Moments and Levers

Using moments in calculations Grade 9 Unit P. 5 – Moments and Levers 1. Two girls are on a seesaw. One weighs 200 N and is 1. 5 m from the pivot. Where must her 150 N friend sit if the seesaw is to balance ? . ﻧﻴﻮﺗﻦ ﻋﻠﻰ 200 ﻓﺘﺎﺗﺎﻥ ﻋﻠﻰ ﺍﻟﺮﺍﻓﻌﺔ ﺇﺣﺪﺍﻫﻦ ﺗﺰﻥ ﻧﻴﻮﺗﻦ 150 ﺃﻴﻦ ﻳﺠﺐ ﺃﻦ ﺗﻘﻒ ﺍﻷﺨﺮﻯ ﺍﻟﺘﻲ ﺗﺰﻥ. ﻣﺘﺮ ﻣﻦ ﻧﻘﻄﺔ ﺍﻻﺭﺗﻜﺎﺯ 1. 5 ﺑﻌﺪ Click for solution ﺣﺘﻰ ﺗﺘﺰﻥ ﺍﻟﺮﺍﻓﻌﺔ At balance total “c. m. ” = total “a-c. m. ” 200 x 1. 5 = 150 x distance “c. m. ” = clockwise moment 200 x 1. 5 = distance 150 “a-c. m. ” = distance = 2 m anti-clockwise moment

Grade 9 Unit P. 5 – Moments and Levers Pressure and Hydraulics ﺍﻟﻀﻐﻂ ﻭﺍﻟﻀﻐﻂ ﺍﻟﻤﺎﺋﻲ

Grade 9 Unit P. 5 – Moments and Levers Pressure is exerted whenever a force is applied over an area. ﻳﻘﻊ ﺍﻟﻀﻐﻂ ﻋﻠﻰ ﺍﻟﻤﻜﺎﻥ ﺍﻟﺘﻲ ﺗﺆﺜﺮ ﻓﻴﻪ ﺍﻟﻘﻮﺓ 1. 2. Which one exerts the biggest pressure, 1 or 2? ﺃﻰ ﺍﻟﻘﻮﻯ ﺗﻮﻟﺪ ﺿﻐﻄ ﺃﻜﺜﺮ؟

Grade 9 Unit P. 5 – Moments and Levers Pressure is the force per unit area so is calculated using the expression shown below: ﺍﻟﻀﻐﻂ ﻳﺴﺎﻭﻱ ﺍﻟﻘﻮﺓ ﺍﻟﻤﺆﺜﺮﺓ ﻋﻠﻰ ﻭﺣﺪﺓ ﺍﻟﻤﺴﺎﺣﺎﺕ Pressure = F Force Area P x A Pressure is measured in: ﻳﻘﺎﺱ ﺍﻟﻀﻐﻂ ﺑﻮﺣﺪﺍﺕ Newtons per metre squared (N/m 2) which is called a PASCAL (Pa) Pressure can also be measured in: Newtons per millimetre squared (N/mm 2); Newtons per centimetre squared (N/cm 2).

Grade 9 Unit P. 5 – Moments and Levers The same force spread over a big area means low pressure. ﻧﻔﺲ ﺍﻟﻘﻮﺓ ﺗﺆﺜﺮ ﻋﻠﻰ ﻣﺴﺎﺣﺔ ﺃﻜﺒﺮ ﻣﻤﺎ ﻳﻌﻨﻲ ﺿﻐﻄ ﺃﻘﻞ Which shoes would you choose for walking over a muddy field? ﺃﻰ ﺍﻷﺤﺬﻳﺔ ﺗﺨﺘﺎﺭ ﻟﻠﺴﻴﺮ ﻓﻮﻕ ﺃﺮﺽ ﻃﻴﻨﻴﺔ

Grade 9 Unit P. 5 – Moments and Levers The boots on the right spread the weight over a larger area. Therefore, the pressure exerted on the ground is low. ﺍﻟﺤﺬﺍﺀ ﺍﻷﻴﻤﻦ ﻣﺴﺎﺣﺘﻪ ﻛﺒﻴﺮﺓ ﻳﻮﻟﺪ ﺿﻐﻄ ﺃﻘﻞ In contrast, fashion shoes have a smaller area and exert a higher pressure. These shoes are likely to sink into soft ground.

Application of pressure ﺗﻄﺒﻴﻘﺎﺕ Grade 9 Unit P. 5 – Moments and Levers A force spread over a large area means low pressure, e. g. skis and snowboards. ﺍﻟﻘﻮﺓ ﻣﻮﺯﻋﺔ ﻋﻠﻰ ﻣﺴﺎﺣﺔ ﺃﻜﺒﺮ 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. ﻛﻠﻤﺎ ﺯﺍﺩﺕ ﺍﻟﻤﺴﺎﺣﺔ ﻗﻞ ﺍﻟﻀﻐﻂ ﻋﻠﻰ ﻟﻮﺣﺔ ﺍﻟﺘﺰﺣﻠﻖ ﻣﻤﺎ ﻳﻘﻠﻞ ﺍﻟﻀﻐﻂ

Application of pressure ﺗﻄﺒﻴﻘﺎﺕ Grade 9 Unit P. 5 – Moments and Levers 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. ﺣﺪﺓ ﺣﺬﺍﺀ ﺍﻟﺘﺰﺣﻠﻖ ﻳﺠﻌﻞ ﺍﻟﻀﻐﻂ ﻋﻠﻰ ﺍﻟﺜﻠﺞ ﻛﺒﻴﺮ ﻣﻤﺎ ﻳﺬﻳﺒﻪ ﻟﻴﺴﻬﻞ ﻋﻤﻠﻴﺔ ﺍﻟﺘﺰﺣﻠﻖ On the cutting edge of a knife a very high pressure is exerted - this makes it easier to cut. ﺣﺪﺓ ﺷﻔﺮﺓ ﺍﻟﺴﻜﻴﻦ ﻳﺠﻌﻞ ﺍﻟﻘﻮﺓ ﺍﻟﻤﺆﺜﺮﺓ ﺗﻮﻟﺪ ﺿﻐﻄ ﻛﺒﻴﺮ ﻳﺴﻬﻞ ﻋﻤﻠﻴﺔ ﺍﻟﻘﻄﻊ

Pressure in liquids ﺍﻟﻀﻐﻂ ﻓﻲ ﺍﻟﺴﻮﺍﺋﻞ Grade 9 Unit P. 5 – Moments and Levers In a liquid: ﻓﻲ ﺍﻟﺴﻮﺍﺋﻞ Pressure acts in all directions and pressure increases with depth. ﻳﺆﺜﺮ ﺍﻟﻀﻐﻂ ﻓﻲ ﻛﻞ ﺍﻻﺗﺠﺎﻫﺎﺕ ﻭﻳﺰﻳﺪ ﺍﻟﻀﻐﻂ ﺑﺰﻳﺎﺩﺓ ﺍﻟﻌﻤﻖ

Grade 9 Unit P. 5 – Moments and Levers The relationship between pressure and depth is shown by a water bottle with holes along its length. low pressure High pressure Pressure (N/m 2) = 10 N/Kg x depth (m) x density (Kg/m 3) The pull of gravity The deeper you go, the higher the pressure The denser the liquid, the heavier it is!

Hydraulics Grade 9 Unit P. 5 – Moments and Levers 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. ﺍﻟﻨﻈﺎﻡ ﺍﻟﻬﻴﺪﺭﻭﻟﻴﻜﻲ ﻳﻌﺘﻤﺪ ﻋﻠﻰ ﻣﺒﺪﺃ ﺗﺄﺜﻴﺮ ﺍﻟﻀﻐﻂ ﻓﻲ ﺟﻤﻴﻊ ﺍﻻﺗﺠﺎﻫﺎﺕ ﻟﻨﻘﻞ ﺍﻟﺤﺮﻛﺔ ﻣﻦ ﻣﻜﺎﻥ ﻵﺨﺮ All hydraulic systems use two pistons linked via a pipe carrying a special oil called hydraulic fluid. ﻳﺴﺘﺨﺪﻡ ﺍﻟﻨﻈﺎﻡ ﺍﻟﻬﻴﺪﺭﻭﻟﻴﻜﻲ ﻣﻜﺒﺴﻴﻦ ﻣﺘﺼﻠﻴﻦ ﺑﺄﻨﺒﻮﺏ ﻳﺤﺘﻮﻱ ﻋﻠﻰ ﺯﻳﺖ ﻫﻴﺪﺭﻭﻟﻴﻜﻲ Force applied here Force transferred here Pressure inside all parts of the hydraulic system is the same

Hydraulics brakes ﻣﻜﺎﺑﺢ ﻫﻴﺪﺭﻭﻟﻴﻜﻴﺔ Grade 9 Unit P. 5 – Moments and Levers All hydraulic brake systems (e. g. in a car) use a small master piston and a bigger slave piston. ﻣﻦ ﺃﻤﺜﻠﺔ ﺍﻷﻨﻈﻤﺔ ﺍﻟﻬﻴﺪﺭﻭﻟﻴﻜﻴﺔ ﻧﻈﺎﻡ ﻣﻜﺎﺑﺢ ﺍﻟﺴﻴﺎﺭﺓ The master piston is used to apply a force. This puts the liquid under pressure. ﻳﺴﺘﺨﺪﻡ ﺍﻟﻤﻜﺒﺲ ﺍﻟﺮﺋﻴﺴﻲ ﻟﻔﺮﺽ ﻗﻮﺓ ﺗﻮﻟﺪ ﺿﻐﻄ ﻋﻠﻰ ﺍﻟﺰﻳﺖ ﺍﻟﺪﺍﺧﻠﻲ Pressure = Force applied Area master piston The pressure is transmitted to the pistons on all four wheels. ﺍﻟﻀﻐﻂ ﻳﻨﺘﻘﻞ ﻟﻜﻞ ﺍﻹﻃﺎﺭﺍﺕ ﻋﻦ ﻃﺮﻳﻖ ﺍﻟﺴﺎﺋﻞ

Grade 9 Unit P. 5 – Moments and Levers The slave piston always has a much larger area than the master piston. The force exerted can be calculated from the same equation: Pressure = Force exerted Much larger than master piston 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.

The hydraulic brake ﺍﻟﻤﻜﺎﺑﺢ ﺍﻟﻬﻴﺪﺭﻭﻟﻴﻜﻴﺔ Grade 9 Unit P. 5 – Moments and Levers Friction shoes Hydraulic fluid Slave pistons Foot pedal drum Master piston

The hydraulic brake – example ﻣﺜﺎﻝ Grade 9 Unit P. 5 – Moments and Levers The car master piston has an area of 5 cm 2. If a force of 10 N is applied to it, calculate the pressure created in the brake pipes. If the slave piston has an area of 50 cm 2, calculate the force exerted on the brake disc. ﻣﻜﺒﺲ ﻣﺴﺎﺣﺘﻪ ﻧﻴﻮﺗﻦ ﺍﺣﺴﺐ ﺍﻟﻀﻐﻂ ﺍﻟﻨﺎﺷﺊ ﻋﻠﻰ ﺍﻟﻤﻜﺒﺲ ﺍﻟﺜﺎﻧﻲ ﻭﺍﻟﺬﻱ 10 ﻳﺆﺜﺮ ﺑﻘﻮﺓ 2 ﺳﻢ 50 ﻣﺴﺎﺣﺘﻪ Click for solution At the master piston, P=F/A= 10/5 = 2 N/cm 2 At the slave piston, F= Px. A =2 x 50 = 100 N (10 times the original force applied to the master piston).

Hydraulics activity ﻧﺸﺎﻁ ﻋﻠﻰ ﺍﻟﻬﻴﺪﺭﻭﻟﻴﻜﺎ Grade 9 Unit P. 5 – Moments and Levers