A resident of Southpark, has a smart idea to create a floating cart that will ho
ID: 1843943 • Letter: A
Question
A resident of Southpark, has a smart idea to create a floating cart that will hold a water pump so that future flooding won’t permanently short circuit the town’s water supply. (Since he’s advocating for a cart, let’s call him Cartman) Cartman’s design calls for a pump that weighs 50kg. He has drawn up a sketch where the pump is connected to the town pipeline via a 5m long flexible hose of diameter 0.25m so that the height of the cart can vary up to 4m, based on the variable water levels without rupturing.
a. What maximum weight does the cart need to support? Justify your answer with some calculations.
b. Cartman suggests to make the cart out of steel 2cm thick. If you can estimate the specific gravity of steel to be about 10, how tall should the walls be for the cart to float if the base is 1m x 0.5m?
Explanation / Answer
a)
maximum weight to be supported by cart = mass of pump+mass of water in discharge pipe
therefore mass supported = 50+1000*pi/4*0.25^2*5
=300 kg
b)
weight of steel cart= specific gravity * volume of cart
volume of cart = Area of plates * thickness
Area= base area + lateral area
Area= 1*0.5+2*1*h+2*0.5*h= 0.5+3h where h is the height of the walls in m
volume= (0.5+3h) *2/100
volume= 0.01+0.06h cu.m
mass of cart= volume*s.g*density of water = 100+600h kg
total mass = 300+100+600h = 400+600h kg
for cart to float
weight of cart = weight of water displaced (archimedes principle) or bouyancy principle
(400+600h)*9.81= 1*0.5*h*9.81*1000
400+600h= 500h
h=4 m
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