A magnesium-alloy wire of diameter d = 4 mm and length L rotates inside a flexible tube in order to open or close a switch from a remote location (see figure). A torque T is applied manually (either clockwise or counterclockwise) at end B, thus twisting the wire inside the tube. At the other end A, the rotation of the wire operates a handle that opens or closes the switch.
A torque T0 = 0.2 N ( m is required to operate the switch.
The torsional stiffness of the tube, combined with friction between the tube and the wire, induces a distributed torque of constant intensity t = 0.04 N ( m/m (torque per unit distance) acting along the entire length of the wire.

(b) If the wire has length L = 4.0 m and the shear modulus of elasticity for the wire is G = 15 GPa, what is the angle of twist (in degrees) between the ends of the wire?

Transcribed Image Text:

Tallow Flexible tube To torque of