MECHANICS 



271 



SOLUTION. The fractional resistance is 10,000 X .65 6,500 Ib. 



The coefficient of friction of the wheels of suddenly stopping 

 engines and cars on the rails is usually assumed at .20. The 

 rails on bridges or trestles will transfer to the bridge or trestle 

 tower the frictional forces produced by the brakes in order to 

 stop the cars, causing stresses that have to be provided for 

 in the structure. 



EXAMPLE. What is the longitudinal force on a bridge caused 

 by the sudden stopping of a car weighing 60,000 Ib.? 



SOLUTION. 60.000X .20 = 12,000 Ib. 



Angle of Friction. When a body, as B in the accompanying 

 illustration, weighing W Ib. is placed on an inclined plane 

 making an angle a with the horizontal, the normal pressure is 

 jV= Wcos a; and, if the coefficient of friction is denoted by f, 

 the frictional resistance 

 against sliding down of 

 the body is F=fN=fW 

 cos a. This force acts 

 in a direction opposite 

 to that of the force P 

 = W sin a. When the 

 angle a is such that F 

 just balances, or is equal 

 to, P, so that the slight- 

 est force will cause the body to slide, the angle is then called 

 the angle of friction. The tangent of that angle is equal to 

 the coefficient of friction, or/=tan a. 



Angle of Repose. On a sloping bank of loose material, 

 such as sand, earth, etc., when the angle of slope is such that 

 the particles are on the point of moving, the angle is called the 

 angle of repose. It is the same as the angle of friction of the 

 material on itself. The slope is then called the slope of repose, 

 or the natural slope of the material, for it is the slope that the 

 material will assume when subject to gravity only. 



EXAMPLE. The coefficient of friction of dry sand on itself 

 is .65; what is its angle of repose? 



SOLUTION. The angle of repose is the same as the angle of 

 friction, whose tangent equals the coefficient of friction: 

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