Question

write the expression for work done when force is applied at an angle with the horizontal direction?

Answer 1

Hi friend!

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□ If you apply force at an angle instead of parallel to the direction of motion, you have to supply more force to perform the same amount of work.

□ Work Done = Force x Displacement 
>> W = f x s 
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I hope this helps

Answer 2

work done :- work done is the dot product of FORCE and DISPLACEMENT
e.g W = F.S

we know , according to dot product of two vectors a and b
a.b = | a | | b| cos∅
where ∅ is angle between a and b

here see the figure , if any force applied on a body and inclined with horizontal is ∅ then, component of of Force is
Fcos∅ parellel to displacement of body.

now ,
W = F.S

magnitude of F = Fcos∅
magnitude of S = d
use dot product rule from above ,
W = Fcos∅.d cos0° { because Fcos∅ and S are parallel to each other

so,

:::::: W = F.d cos∅ :::::::