Question

Find the magnitude of the torque about \(P\) if a \(36 - lb\)force is applied as shown.

Short answer

The magnitude of the torque about \(P\) is \(173{\rm{Ib}} \cdot {\rm{ft}}\).

Step-by-step solution

Formula and concept used to find the magnitude of torque

The expression to find magnitude of the torque.

\(|\tau | = |{\rm{r}}||{\rm{F}}|\sin \theta \)

Here,

\(r\)is the vector position,

\(F\)is the force, and

\(\theta \)is the total angle between\(r\)and\(F\).

Calculation used to find the magnitude of torque

It is given that \(|{\bf{r}}| = 4{\rm{ft}},|{\bf{F}}| = 50\;{\rm{N}}\) and the value of \(\theta \) is \({90^^\circ } - {30^^\circ } = {60^^\circ }\).

Substitute \(|{\bf{r}}| = 4{\rm{ft}},|{\bf{F}}| = 50\;{\rm{N}}\) and \(\theta = {60^^\circ }\) in \(|\tau | = |{\bf{r}}||{\bf{F}}|\sin \theta \).

\(\begin{array}{l}|\tau | = (4)(50)\sin (60)\\ = 200\left( {\frac{{\sqrt 3 }}{2}} \right)\\ \approx 173{\rm{Ib}} \cdot {\rm{ft}}\end{array}\)

Therefore, the magnitude of the torque about \(P\) is \(173{\rm{Ib}} \cdot {\rm{ft}}\).