I think your question is ___"Why is the work output less when the force is exerted at an angle than when the force is exerted parallel to the direction of motion?"
Is that your question? If it is, then the answer is quite simple.
We know that work is a vector quantity (i.e. it posseses both magnitude and direction). So even if the direction of of the force is change, keeping the magnitude constant, the resulting work done is affected. This can be shown by the following calculation ____
When th force is applied in the direction of motion, and the object is in a steady state of motion, then he wok is given by
W = FD [where, F=Force applied; D=Displacement of the body]
Note that, here, the force is acting parallel to the direction of motion. And since F and D are both vectors, their Dot product gives us the above result.
That is___
W = F.D
= FDcos@
[where, @ = The angle between the direction of the force applied and the horizontal]
But here, since the force is parallel to the horizontal, therefore,
@ = zero degrees.
Which gives us the result W = FD [Since cos(0) = 1]
But, if the force is exerted at an angle, say 60 degrees, then the value of work reduces, as shown below___
(Lei the new work done be W")
W" = FDcos(60)
= FD(0.5)
Which means that in the above example, the work is reduced to half.
Thus, the work output is less when a force is applied at an angle than when it is exerted parallel to the direction of the motion of the body.
Cheers & Best of Luck.
