Question $3(40$ marks$)$

Scrapers are to be used to move $\backslash (20000\backslash$mathrm$\{$~m$\}^\{3\}\backslash )$ from a cutting at the top of a hill to an embankment in a valley. The bank density of the material is $\backslash (1700\backslash$mathrm$\{$~kg$\}/\backslash$mathrm$\{$m$\}^\{3\}\backslash ),$ the swell factor is $\backslash (15\backslash \%\backslash )$ and the shrinkage factor is $\backslash (25\backslash \%\backslash ).$

The haulage road is straight, has a gradient of $\backslash (9\backslash \%\backslash ),$ traction of $\backslash (75\backslash \%\backslash )$ and a rolling resistance of $\backslash (3\backslash \%\backslash ).$ The length of this road is $600$ m $.$

The scrapers to be used are Catepillar model $621$E and have a bucket capacity of $\backslash (15\mathrm{.}3\backslash$mathrm$\{$~m$\}^\{3\}\backslash )$ and a rated load of $21775$ kg $.$ A job factor of $0\mathrm{.}8$ applies and a management factor of $0\mathrm{.}9.$ The scrapers take $90$ seconds to load and $60$ seconds to dump. The return time is $2\mathrm{.}5$ minutes. Assume a $\backslash (50-\backslash )$ minute hour. More information about the scraper is provided on the next page.

$($a$)$ Determine the loose volume of material to be moved. $(5$ marks$)$

$($b$)$ Determine the haul time. Note: The scraper is travelling downhill when it is full. $(10$ marks$)$

$($c$)$ Determine the production rate of one scraper. Note: The return time is given above, you do not need to calculate it$.(5$ marks$)$

$($d$)$ A single $3$ m wide sheep's$-$foot roller is available for compaction. The material must be compacted in $200$ mm layers with $8$ passes for each layer at an average speed of $\backslash (4\backslash$mathrm$\{$~km$\}/\backslash$mathrm$\{$hr$\}\backslash ).$ A combined job$/$management factor of $0\mathrm{.}8$ applies. Assume a $50-$minute hour. Determine the production rate of the roller. $(5$ marks$)$

$($e$)$ What is the most economical number of scrapers to use if a scraper costs $\backslash (\backslash$$ $120/\backslash$mathrm$\{$h$\}\backslash )$ and the compactor costs $\backslash$$$150/$h$?(10$ marks$)$

$($f$)$ In $5$ lines or less, list the effects that wet weather will have on the job. $(5$ marks$)$