A trough is 12m long, 5m wide, and 2m deep. The vertical cross-section of the tr

Question

A trough is 12m long, 5m wide, and 2m deep. The vertical cross-section of the trough parallel to an end is shaped like an isosceles triangle (with height 2m, and base, on top, of length 5m). The trough is full of water (density 1000kg/m^3 and g = 9.8m/s^2 is the acceleration due to gravity). a) Find the amount of work in joules required to empty the trough by pumping the water over the top. b) Find the amount of work in joules required to empty the trough by pumping the water out of a spout 3m high.

Explanation / Answer

From the given question,

length(l)=12 m

width(w)=5 m

depth(h)=2 m

area of isosceles triangle= (1/2)(5)(2)= 5 m2

Volume of trough= area of isosceles triangle x length

=5*12= 60 m3

Mass= volume*density

=60*1000=60,000 kg

center of gravity of isosceles triangle is 1/3 of height from base=(1/3)*2

a) Amount of work done= force . displacement

=m*g*h

=60000*9.8*(2/3)

=392,000 J

b)Amount of work done=m*g*h

=60000*9.8*[3+(2/3)]

=2,156,000 J

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