Question

3.1 a foot valve for a pneumatic system is hinged at b. knowing that α = 28°, determine the moment of the 16 - n force about point b by resolving the force into horizontal and vertical components.

Explanation:

Step1: Calculate the perpendicular - distance from point B to the line of action of the force.

First, find the angle between the rod and the vertical. The angle between the rod and the vertical is \(20^{\circ}\). The angle of the force with respect to the vertical is \(\theta=20^{\circ}+\alpha = 20^{\circ}+28^{\circ}=48^{\circ}\). The perpendicular distance \(d\) from point B to the line of action of the 16 - N force can be calculated using trigonometry. The horizontal distance from B to the line of action of the force is \(d = 170\sin\theta\) (in mm).

Step2: Calculate the moment about point B.

The moment \(M\) of a force \(F\) about a point is given by \(M = F\times d\), where \(F = 16\ N\) and \(d\) is the perpendicular distance from the point to the line of action of the force. Substituting \(F = 16\ N\) and \(d=170\sin48^{\circ}\times10^{- 3}\ m\) into the moment formula \(M = F\times d\), we have \(M=16\times170\times\sin48^{\circ}\times10^{-3}\ N\cdot m\).
\[M = 16\times0.17\times\sin48^{\circ}\ N\cdot m\]
\[M = 16\times0.17\times0.7431\ N\cdot m\]
\[M = 1.999\approx2.00\ N\cdot m\]

Answer:

\(2.00\ N\cdot m\)