Question

Derive the formula W=F cos theta​

Answer 1

Question:-

Derive the formula W=F cos theta

Formula used:-

$\large\rm { \cos \theta = \frac{ adjacent}{hypotenuse} }$

Proof:-

We know that,

$\large\rm { \cos \theta = \frac{ adjacent}{hypotenuse} }$

so

$\large\rm { \cos \theta = \frac{F_{perp}}{F_{g}} }$

$\large\rm { ( F_{g} ) \cos \theta = ( F_{g} ) \frac {F_{perp}}{F_{g}} }$

$\large\rm {( F_{g}) \cos \theta = \cancel{F_{g}} \frac{F_{perp}}{\cancel{F_{g}}} }$

$\large\boxed{\rm { \therefore F_{perp} = F_{g} \cos \theta}}$

where $\large\rm { F_{perp} = W}$

hence proven.