Question $1$

P$1$ Apply dimensional analysis techniques to solve complex engineering$/$manufacturing problems.

A customer requires cable to lower loaded wagons down a slope, the configuration is shown in Figure $1.$ The cable will be attached to a rope brake to keep the wagons under control. During a site visit, you note that the slope is $35$ m long and has an angle of $5\mathrm{.}71$ with the ground and the wagon speed is $3\mathrm{.}5\frac{m}{s}$ at the end of the incline. You are told that the total mass of the wagons will not exceed $45$ tonnes and that the resistance to motion is $130N$ tonne. Calculate the minimum load that the cable supplied should be able to withstand $($ignoring any regulations about safety factors, for now, assume the wagon is stationary at $t=0).$ You may find the following formula helpful

$V_2=u2+2aS$