An $18$ mm roller is in contact with a plate cam surface whose radius of curvature

is $80$ mm $.$ If Hertz compressive stress developed is $1800$ MPa for a load of $10$

KN $,$ determine the width of the plate cam surface. The roller and cam are both

made of carbon steel.

A simply supported beam of Length $L,$ Elastic modulus $E,$ Area moment of

inertia I is subjected to a concentrated load $P$ at the mid$-$point. Determine the

expression for the deflection at that point using Castigliano's theorem.

A helical compression spring is designed such that under a $50$ N force, the spring

should compress by $15$ mm $.$ It is manufactured using oil$-$tempered wire with a

diameter of $4$ mm and a spring index of $10.$ The spring has a free length of $80$

mm with plain ends.

$($a$)$ Calculate the spring rate.

$($b$)$ Determine the total number of coils required.

$($c$)$ Find the solid length of the spring.

$($d$)$ Compute the static factor of safety against yielding when the spring is fully

compressed to its solid length.

A journal bearing using SAE$30$ has a diameter of $50$ mm and length of $25$ mm $.$

The load is $2$ kN at a journal speed of $800$ rpm $.$ If the average film temperature

is $46\mathrm{.}5C$ and the clearance is $0\mathrm{.}05$ mm $,$ calculate the frictional power loss,

maximum pressure and minimum film thickness.

Given an outboard$-$mounted pair of bevel gears with the following specifications:

normal pressure angle of $20,$ both gears of equal size $(N=25),$ made from the

same material $,$ Grade $2$ through$-$hardened steel