A solid cylindrical specimen, made of a material that behaves according to the following equation

$400.,$ is being upset between flat dies with coefficient of friction $0\mathrm{.}3.$ The

process is being carried out by a falling weight, as in a drop hammer with a mass $500$ and

fall height $5.$ The initial diameter of the workpiece is $150$ and the initial height

is $60.$ After several hits the height of the specimen has decreased to $40.$ Using

the average pressure formula:

$($a$)$ Determine the change in height $$ in the next hit.

$($b$)$ If$,$ instead of being cylindrical, the workpiece has initial rectangular cross sectional area equal

to that of cylindrical one, with $2$ and also its height has decreased from initial height of

$60$ to a new height of $40,$ determine the change in height $$ in the next hit.

$($It takes several hits to reduce initial height of $60$ to $40.$ Next hit means the next stroke

right after height reaches $40.$

Hint $1$: assume the weight is always released from $5$ above the current surface of the workpiece

Hint $2$: assume there is no side flow of material in direction of in case $($b$).$

$($a$)($b$)$