A square$-$thread power screw has a major diameter of $16$ mm and a pitch of $2$ mm with double threads and transmits an axial load of $2$ kN $.$ A $24$ mm collar provides the bearing surface for the reaction force. The friction coefficient of the threads and collar are $\backslash (\backslash$mathrm$\{$f$\}=\backslash$mathrm$\{$fc$\}=0\mathrm{.}08\backslash ).$

Q$1$ Find the thread depth

Q$2$ Find the thread width

Q$3$ Find the pitch diameter

Q$4$ Find the minor diameter

Q$5$ Find the lead.

Q$6$ Calculate the torque required to raise the load.

Q$7$ Calculate the torque required to lower the load.

Q$8$ Calculate the efficiency during lifting the load.

Q$9$ Find the body shear stress $($torsional$)$

Q$10$ Find the body shear stress $($compressive$)$

Q$11$ Find the bearing stress on the first thread.

Q$12$ Find the thread bending stress at the root of the first thread.

Q$13$ Calculate the tangential shear stress on the first thread

Q$14$ Determine the von Mises stress at the critical stress element

where the root of the first thread interfaces with the screw body.

SECTION B $-$ Mechanical Springs

A helical compression spring is made of $2$ mm diameter music wire. The outside coil diameter of the spring is $35$ mm $.$ The ends are squared and there are $14$ total coils.

Q$1$ Estimate the tensile strength of the wire

Q$2$ Estimate the torsional yield strength of the wire

Q$3$ Calculate the static load corresponding to the yield strength.

Q$4$ Calculate the stiffness of the spring

Q$5$ Estimate the deflection that would be caused by the static load in Q$3$

Q$6$ Estimate the solid length of the spring

Q$7$ What length should the spring be to ensure that when it is compressed solid and then released, there will be no permanent change in the free length?

Q$8$ At what length will the spring buckle?

Q$9$ What is the pitch of the body coil?