Mechanics lesson Sa Rmechanics lgfl net Objectives To

Mechanics lesson Sa. Rmechanics. lgfl. net Objectives: To use angle knowledge to solve problems that the Coastguard face To apply trigonometry to work out loads and tensions To solve problems with friction

Job Requirements Maths required: • Angle facts • Trigonometry • Exponential calculations • Using radian measure • Converting units Search and Rescue – sar. lgfl. net Equipment required: • Protractor • Ruler • Pencil • Pen • Rubber • Calculator © 2016 London Grid for

Videos • Introduction to Coastguard rescue teams • What Maths is involved in rescue systems? • Bridle rope arrangement • Rope friction - tensionless hitch 1 Search and Rescue – sar. lgfl. net © 2016 London Grid for

Bridle ropes Watch this video: Bridle rope arrangement 1000 kg This angle affects the

Bridle ropes You can use trigonometry to find the loads. 75 o 30 o 1000 kg 75 o If you measure the angle at the connection, you can work out the angles where the rope is connected to the load as you have an isosceles triangle. Search and Rescue – sar. lgfl. net © 2016 London Grid for

Bridle ropes You can use trigonometry to find the loads. 75 500 kg o The 1000 kg weight is distributed between the two ropes. 1000 kg 75 o Search and Rescue – sar. lgfl. net 500 kg You can use trigonometry or a conversion table to find the tension put on each rope. © 2016 London Grid for

Bridle ropes You can use trigonometry to find the loads. Hyp 75 o 15 o 500 kg Adj 1000 kg To find the tension on the hypotenuse, we use trigonometry: Hyp = Adj/cos(θ) = 500/cos(15) = 518 kg Search and Rescue – sar. lgfl. net © 2016 London Grid for

Bridle ropes You can use trigonometry to find the loads. 75 o 518 k g 30 o 75 o g 518 k Search and Rescue – sar. lgfl. net 1000 kg By finding out the angle, we can work out the tension on each rope. Or, if we know the tension limit, we could work out the minimum angle. © 2016 London Grid for

Table of factors (no trigonometry) You can use the factors in this table to

Tensionless hitch Watch this video: Rope friction - tensionless hitch 1 A tensionless hitch harnesses the power of friction around an object to create a very strong holdfast. You can use the Capstan equation to calculate the hold tension (Thold) required for any load tension (Tload) using the friction coefficient (μ) and the total angle of turns around the object (θ - measured in Search and Rescue – sar. lgfl. net © 2016 London Grid for radians).

Capstan equation table No of turns Coefficient of friction μ 0. 1 0. 2 0. 3 0. 4 0. 5 0. 6 0. 7 1 1. 9 3. 5 6. 6 12 23 43 81 2 3. 5 12 43 152 535 1881 6661 3 6. 6 43 286 1881 12392 81612 437503 4 12 152 1881 23228 286751 3540026 43702631 5 23 535 12392 286751 6635624 153552935 3553321281 Tload = Tholdeμθ T: tension e: e μ: coefficient of friction θ: Search total = 1 London full Grid turn andangle Rescue – made sar. lgfl. netby rope (radians) 2π radians © 2016 for

Rope strength Rope Diameter Minimum Breaking Strength 1 kg = 9. 81 N = 0. 00981 k. N ≈ 102 kg Safe Load (Safety Factor 12) (in) (mm) (lbf) (k. N) (lbf) 3/16 5 880 3. 91 73. 3 0. 326 0. 009 0. 013 1/4 6 1486 6. 61 124 0. 551 0. 016 0. 023 5/16 8 2295 10. 2 191 0. 851 0. 025 0. 036 3/8 10 3240 14. 4 270 1. 2 0. 036 0. 053 7/16 11 4320 19. 2 360 1. 6 0. 048 0. 071 1/2 12 5670 25. 2 473 2. 1 0. 063 0. 094 9/16 14 7200 32 600 2. 67 0. 08 5/8 16 8910 39. 6 743 3. 3 0. 099 0. 147 3/4 18 12780 56. 8 1070 4. 76 Search and Rescue – sar. lgfl. net (k. N) Weight (lbm/ft) (kg/m) 0. 119 0. 143 0. 213 © 2016 London Grid for