3. (30 points) A simple electrical switch in an aircraft panel (shown below in the OFF...

Transcribed Image Text:

3. (30 points) A simple electrical switch in an aircraft panel (shown below in the OFF position) consists of a rigid knob, a flexible shaft, and a rigid (electrically conductive) rocker arm. The flexible shaft has a diameter d, length L, and is made of a material with shear modulus G. The electrical circuit (not shown) is completed by rotating the knob clockwise (as viewed from the front), so that the rocker arm touches the electrical contacts. The shaft of the switch has been press-fit into a panel, and there exists some friction that resists its rotation. (Neglect the small gaps in the x-direction between the knob and rocker arm with the panel.) knob panel electrical contacts rocker. A arm shaft frictional surface b b cross-section back side isometric view (without panel) b A A (a) Assuming that friction causes a uniform distributed torque along the length of the shaft of magnitude to (with units of moment/length in the x-direction), find the torque on the knob necessary to overcome the frictional resistance in order to rotate the rocker arm. (Be sure to draw a free body diagram.) (b) Find the rotation of the knob for which the rocker arm just touches the electrical contacts. An initial gap (A) exists between the contacts and the ends of the rocker arm (assume A < < b). (c) Suppose that a minimum contact force, Fmin, is necessary to ensure a reliable electrical circuit. Find the corresponding minimum rotation of the knob Qmin. (Set up the equations and identify the unknowns, but do NOT solve.) 3. (30 points) A simple electrical switch in an aircraft panel (shown below in the OFF position) consists of a rigid knob, a flexible shaft, and a rigid (electrically conductive) rocker arm. The flexible shaft has a diameter d, length L, and is made of a material with shear modulus G. The electrical circuit (not shown) is completed by rotating the knob clockwise (as viewed from the front), so that the rocker arm touches the electrical contacts. The shaft of the switch has been press-fit into a panel, and there exists some friction that resists its rotation. (Neglect the small gaps in the x-direction between the knob and rocker arm with the panel.) knob panel electrical contacts rocker. A arm shaft frictional surface b b cross-section back side isometric view (without panel) b A A (a) Assuming that friction causes a uniform distributed torque along the length of the shaft of magnitude to (with units of moment/length in the x-direction), find the torque on the knob necessary to overcome the frictional resistance in order to rotate the rocker arm. (Be sure to draw a free body diagram.) (b) Find the rotation of the knob for which the rocker arm just touches the electrical contacts. An initial gap (A) exists between the contacts and the ends of the rocker arm (assume A < < b). (c) Suppose that a minimum contact force, Fmin, is necessary to ensure a reliable electrical circuit. Find the corresponding minimum rotation of the knob Qmin. (Set up the equations and identify the unknowns, but do NOT solve.)