
A force acts on a body and displaces it by a distance S in a direction at an angle with the direction of force. What should be the value of to get the maximum positive work ?
Answer
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Hint:In order to solve above problem first write the formula of work done in terms of i.e.,
Now use the concept that for maximum work done i.e., for maximum LHS, RHS also should be maximum.Hence, we will get a desired solution.
Complete step by step answer:
We know that if a body displaces by distance S on acting the force F, then work done by the force is
…..(1)
Where is the angle between force F and displacement S.
Here, we have to calculate for maximum work done W. So, for maximum work done RHS of equation 1 will also be maximum.
We know that the maximum value of is 1.
Thus, displacement of the body must be in the same direction as that of force to get the maximum positive work.
Note: In many problems, student may get confused between maximum and minimum values of and which are given as,
And when is very small then,
Now use the concept that for maximum work done i.e., for maximum LHS, RHS also should be maximum.Hence, we will get a desired solution.
Complete step by step answer:
We know that if a body displaces by distance S on acting the force F, then work done by the force is
Where
Here, we have to calculate
We know that the maximum value of
Thus, displacement of the body must be in the same direction as that of force to get the maximum positive work.
Note: In many problems, student may get confused between maximum and minimum values of
And when
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