Quantcast Composition of Forces

put on an object directly through physical contact. An example of contact force is the force your hand exerts when you push your coffee cup across a table. Contact force may act in several different directions at once as well. For example, the force exerted by water in a can is equally exerted on the sides and the bottom of the can. In addition, an upward force is transmitted to an object on  the  surface  of  the  water.  Forces  that  act  through empty space without contact are known as action at a distance force. An example of this force is gravity. Vectors Problems often arise that make it necessary to deal with  one  or  more  forces  acting  on  a  body.  To  solve problems  involving  forces,  a  means  of  representing forces must be found. True wind speed at sea involves two different forces and is obtained through the use of the  true  wind  computer.  Ground  speed  and  course  of aircraft are computed by adding the vector representing aircraft   heading   and   true   air   speed   to   the   vector representing the wind direction and speed. In computation  of  the  effective  fallout  wind  and  other radiological fallout problems, the addition of forces is used.   From   these   examples,   it   is   evident   that   the addition and subtraction of forces has many applications in meteorology. A force is completely described when its magnitude,   direction,   and   point   of   application   are given. A vector is a line that represents both magnitude and  direction;  therefore,  it  may  be  used  to  describe  a force. The length of the line represents the magnitude of  the  force.  The  direction  of  the  line  represents  the direction  in  which  the  force  is  being  applied.  The starting   point   of   the   line   represents   the   point   of application  of  the  force.  (See  fig.  2-1.)  To  represent  a force of 10 pounds or 10 knots of wind acting toward due east on point A, draw a line 10 units long, starting at point A and extending in a direction of 090°. Composition of Forces If two or more forces are acting simultaneously at a point, the same effect can be produced by a single force of  the  proper  size  and  direction.  This  single  force, which is equivalent to the action of two or more forces, is   called   the   resultant.   Putting   component   forces together to find the resultant force is called composition of  forces.  (See  fig.  2-2.)  The  vectors  representing  the forces  must  be  added  to  find  the  resultant.  Because  a vector  represents  both  magnitude  and  direction,  the method  for  adding  vectors  differs  from  the  procedure used   for   scalar   quantities   (quantities   having   only magnitude and no direction). To find the resultant force when a force of 5 pounds and a force of 10 pounds are applied at a right angle to point A, refer to figure 2-2. The   resultant   force   may   be   found   as   follows: Represent  the  given  forces  by  vectors  AB  and  AC drawn  to  a  suitable  scale.  At  points  B  and  C  draw dashed lines perpendicular to AB and AC, respectively. From point A, draw a line to the point of intersection X, of the dashed lines. Vector AX represents the resultant of the two forces. Thus, when two mutually perpendicular    forces    act    on    a    point,    the    vector representing  the  resultant  force  is  the  diagonal  of  a rectangle. The length of AX, if measured on the same scale as that for the two original forces, is the resultant force;  in  this  case  approximately  11.2  pounds.  The angle  gives  the  direction  of  the  resultant  force  with respect to the horizontal. Mathematically, the resultant force of perpendicular   forces   can   be   found   by   using   the Pythagorean theorem which deals with the solution of right triangles. The formula is C2 = a2 + b2. This states that  the  hypotenuse,  side  “C”  (our  unknown  resultant force) squared is equal to the sum of side “a” (one of our known  forces)  squared  and  side  “b”  (another  of  our known forces) squared. 2-3 N A 10 LB AG5f0201 Figure 2-1.—Example of a vector. AG5f0202 C X 5 LB 10 LB B A Figure 2-2.—Composition of two right angle forces.


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