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Work Done by a Constant Force

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So, we have discussed the introduction to work and energy in the previous section.

Now let's discuss about work done by a constant force.

Work is defined as the product of the magnitude of the displacement and the component of the force in the direction of the displacement. W=F.d = Fd.cos

Work is a scalar quantity because it is defined as the dot product or scalar product two vectors force and displacement and the scalar product of two vectors gives the scalar quantity

 


Special Cases

  1. When  and  are directed in same direction then θ=0. So,
                W= FDcos0 =F.D
  2. When  and  are directed in opposite direction, then θ=180. So, 
                 W= FD.cos180 = -F.D
  3. When  and are perpendicular to each other, then θ=90. So,
                 W= FD.cos90 = 0
    So, work done by a force is zero if a body is displaced in a direction perpendicular to the direction of the applied force. For example, if a body is moving in a circle with constant speed, then the centripetal force and the displacement are mutually perpendicular at every point. Therefore, the work done by the centripetal force is zero.

Units and Dimension of Work

 We have, W=FD

 In SI units, unit of work is Nm or Joules(J). Work done is said to be 1 Joule if a force of 1 Newton displaces a body through 1 meter in the direction of the force.

   Also, 1 Joule=1Nm=1N x 1m=105dynes x 100 cm=107 dynes. cm

             1 Joule= 107 erg

  The dimensional formula of work is [ M  L2  T-2 ]