Machinery's Handbook, 31st Edition
Simple Mechanisms 175 is equal to a force of Wg newtons, where g is approximately 9.81 m/s 2 . Thus, supposing that in the first example l = 0.4 m, L = 1.2 m, and W = 30 kg, then the weight of W is 30 g newtons, so that the force F required to balance the lever is . . . F g g 12 30 04 10 981N. # = = = This force could be produced by suspending a mass of 10 kg at location F . Table of Forces on Inclined Planes
The table below is used to find the force required to move a load on an inclined plane. Friction on the plane is not taken into account. The column headed “Tension P per Ton” gives the pull in pounds required for moving one ton (2000 lbs) along the inclined surface. The fourth column gives the perpendicular or normal pressure of the load. If the coefficient of friction m is known, the added pull to overcome friction is: Additional pull per ton = Q × μ Example: A 200 lb. body pulled up a 14% grade when friction ( m ) is 0.3 requires a force P = (0.1)(277.3) + (0.1)(1980.68)(0.3) = 87.15 lbs.
P
Rise
90°
Q
100 ”
Percent of Grade, Rise in ft per 100 ft
Perpendicular Pressure Q on Plane per Ton
Percent of Grade, Rise in ft per 100 ft
Perpendicular Pressure Q on Plane per Ton
Tension P in Cable per Ton
Tension P per Ton
Angle α
Angle α
20.00 39.99 59.97 79.94 99.88 119.78 139.66 159.49 179.28 199.01 218.68 238.29 257.83 277.30 296.68 315.98 335.19 354.31 373.32 392.23 411.03 429.72 448.30 466.75 485.07 503.27 521.33 539.26 557.05 574.70 592.20 609.55 626.76 643.81 660.70 677.44 694.02 710.44 726.69 742.78 758.71 774.47 790.06 805.48 820.73 835.81 850.72 865.46 880.03 894.43
1999.90 1999.60 1999.10 1998.40 1997.50 1996.41 1995.12 1993.63 1991.95 1990.07 1988.01 1985.75 1983.31 1980.68 1977.87 1974.88 1971.71 1968.37 1964.85 1961.16 1957.31 1953.29 1949.11 1944.77 1940.29 1935.65 1930.86 1925.93 1920.86 1915.65 1910.31 1904.85 1899.26 1893.55 1887.72 1881.77 1875.72 1869.57 1863.31 1856.95 1850.50 1843.96 1837.34 1830.63 1823.84 1816.98 1810.05 1803.05 1795.98 1788.85
51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98
27.02 27.47 27.92 28.37 28.81 29.25 29.68 30.11 30.54 30.96 31.38 31.80 32.21 32.62 33.02 33.42 33.82 34.22 34.61 34.99 35.37 35.75 36.13 36.50 36.87 37.23 37.60 37.95 38.31 38.66 39.01 39.35 39.69 40.03 40.36 40.70 41.02 41.35 41.67 41.99 42.30 42.61 42.92 43.23 43.53 43.83 44.13 44.42 44.71 45.00
908.65 922.71 936.59 950.30 963.84 977.21 990.41 1003.44 1016.30 1028.99 1041.52 1053.88 1066.08 1078.11 1089.98 1101.68 1113.23 1124.62 1135.85 1146.92 1157.84 1168.61 1179.22 1189.69 1200.00 1210.17 1220.19 1230.06 1239.80 1249.39 1258.84 1268.16 1277.34 1286.38 1295.30 1304.08 1312.73 1321.26 1329.65 1337.93 1346.08 1354.11 1362.03 1369.82 1377.50 1385.06 1392.52 1399.86 1407.09 1414.21
1781.67 1774.43 1767.15 1759.81 1752.43 1745.01 1737.55 1730.06 1722.54 1714.99 1707.41 1699.81 1692.18 1684.54 1676.89 1669.22 1661.54 1653.85 1646.16 1638.46 1630.77 1623.07 1615.37 1607.68 1600.00 1592.32 1584.66 1577.00 1569.36 1561.74 1554.13 1546.54 1538.96 1531.41 1523.88 1516.37 1508.89 1501.43 1493.99 1486.59 1479.21 1471.86 1464.54 1457.26 1450.00 1442.77 1435.58 1428.43 1421.30 1414.21
1 2 3 4 5 6 7 8 9
0.57 1.15 1.72 2.29 2.86 3.43 4.00 4.57 5.14 5.71 6.28 6.84 7.41 7.97 8.53 9.09
10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
9.65 10.20 10.76 11.31 11.86 12.41 12.95 13.50 14.04 14.57 15.11 15.64 16.17 16.70 17.22 17.74 18.26 18.78 19.29 19.80 20.30 20.81 21.31 21.80 22.29 22.78 23.27 23.75 24.23 24.70 25.17 25.64 26.10 26.57
99 100
Tensions and pressures in pounds per 1 ton (2000 lbs) load weight.
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