Answer:
207.4 N
Explanation:
The torque [tex]\tau[/tex] on a body is
[tex]\tau = r* F[/tex] where r is the radius vector from the point of rotation to the point at which force F is applied.
The product of r and F is equal to the product of magnitude of r and F multiplied by the sine of angle between both vectors.
Therefore, torque is also given by
[tex]\tau = rF\sin \theta[/tex]
Where [tex]\theta[/tex] is the angle between r and F.
Use the expression of torque.
Substitute L for r in the equation [tex]\tau = rF\sin \theta[/tex]
[tex]\tau = LF\sin \theta[/tex]
Where L is the length of the wrench.
Making F the subject
[tex]F = \frac{\tau }{{L\sin \theta }}[/tex]
Force required to pull the wrench is given as,
[tex]F = \frac{\tau }{{L\sin \theta }}[/tex]
Substitute [tex]47{\rm{ N}} \cdot {\rm{m}}[/tex] for [tex]\tau[/tex], 25 cm for L, and 115o for [tex]\theta[/tex]
[tex]\begin{array}{c}\\F = \frac{{47{\rm{ N}} \cdot {\rm{m}}}}{{\left( {25{\rm{ cm}}} \right)\sin {{115}^{\rm{o}}}}}\left( {\frac{{1{\rm{ cm}}}}{{{{10}^{ - 2}}{\rm{ m}}}}} \right)\\\\ = 207.435{\rm{ N}}\\\\ \approx 207.4{\rm{ N}}\\\end{array}[/tex]
