Question

2/6 the control rod ap exerts a force f on the sector as shown. determine both the x - y and the n - t components of the force.

Explanation:

Step1: Find x - component of force

The x - component of the force \(F\) can be found using the angle \(\alpha\) and \(\beta\). The x - component \(F_x\) is given by \(F_x=-F\cos\beta\sin\alpha\).

Step2: Find y - component of force

The y - component of the force \(F\) is given by \(F_y = F\cos\beta\cos\alpha\).

Step3: Find n - component of force

The n - component of the force \(F\) is \(F_n=F\sin\beta\).

Step4: Find t - component of force

The t - component of the force \(F\) is \(F_t = 0\) (since there is no force acting along the tangential direction in the given problem setup related to the \(n - t\) coordinate system shown).

Answer:

\(F_x=-F\cos\beta\sin\alpha\), \(F_y = F\cos\beta\cos\alpha\), \(F_n=F\sin\beta\), \(F_t = 0\)