Chris needs to move a 480 pounds barrel of fire retardant to

Chris needs to move a 480 pounds barrel of fire retardant to a loading platform that is 6\' up Chris has irritated calculated over the last two days that he can apply a force of 72.5pounds by hand to the barrel rolling it up a ramp he has discovered that the actual rolling distance of the ramp is indirectly proportional to the force applied (disregarding friction ) can you help Chris calculate the minimum length of the ramp and the slope of ramp

Solution

if the angle that ramo makes with the ground is x deg. then the force required to push the barrel up will be mgsin(x)

maximum force which can be applied is 72.5 pounds

72.5 = 480 sin(x)

x = 8.63 deg

tan(x) =0.15 = slope

minimun length = 6 feets/sin(x) = 6/0.15 =40 feets