Dr$.$ Afaq Altaf $9$:$00$ AM

Question $3[10$ marks$]$

a$)$ A lead screw is being used on a lathe machine to advance the carriage of the lathe in time with the rotation of the spindle. The screw has an effective diameter of $50$ mm and a lead $5$ mm $.$ the screw must exert an axial thrust of $1\mathrm{.}5$ KN for driving the carriage. An effort of $100$ N is required to create the movement. Calculate the operating efficiency of the lead screw.

b$)$ A jackscrew is used to raise and lower a $\backslash (100-\backslash$mathrm$\{$kg$\}\backslash )$ block as shown in below figure. The screw has a pitch $\backslash ($ P$=15\backslash$mathrm$\{$~mm$\}\backslash ),$ mean radius $\backslash ($ r$=10\backslash$mathrm$\{$~mm$\}\backslash ),$ and is single$-$threaded. The coefficient of static friction between the screw and the supporting thread of the base is $\backslash (\backslash$mu$=0\mathrm{.}25\backslash ).$ Determine the operating efficiency of the screw.

Dr$.$ Afaq Altaf $9$:$00$ AM

Questiou $4[15$ marks$]$

A $\backslash (20-\backslash$mathrm$\{$kg$\}\backslash )$ block moves between vertical guides as shown. The block is pulled $40$ mm down from its equilibrium position and released. For each spring arrangement $($parallel and series$),$ determine

a$)$ the period of the vibration,

b$)$ the maximum velocity of the block, and

c$)$ the maximum acceleration of the block.