A young engineer has been given the task of developing a new method for determin
ID: 1710716 • Letter: A
Question
A young engineer has been given the task of developing a new method for determining the weight of commercial trucks at permanent roadside checkpoints. The engineer decides to use her knowledge of fluid mechanics to devise the system. She has a shallow metal box constructed. The construction of the box allows the top to move up and down but not tilt. There is negligible resistance between the metal top and the sides of the box containing mercury. The metal top of the box weighs 18, 700 lbf. The engineer fills the box with mercury and attaches a graduated, vertical glass tube (3/4-inch diameter) to an outlet from the box. a) For the dimensions shown in the figure below, where is the mercury surface in the vertical tube before the truck drives onto the metal plate? b) What is the largest weight that can be measured using this system? c) What is the largest mass the system can measure? d) Is the device affected by changes in atmospheric pressure? Why or why not? The weighing box is 10 ft wide into the page. It is restrained so one end does not sink into the mercury when truck starts driving onto the metal top and is only partially on the metal top.Explanation / Answer
SOLUTION:-THE METAL TOP OF THE BOX WEIGHTS=18700 lbf g= 32 ft/sec.2
(a) WEIGHT OF TUBE= DENSITY *g*HEIGHT
=13.55*32*H
WEIGHT OF BOX = WEIGHT OF TUBE+WEIGHT OF BOTTOM PORTION
18700= 13.55*32 *HEIGHT +13.55*32*5/12.54
HEIGHT= 42.73 ft
(b) LARGEST WEIGHT =WEIGHT OF TUBE+WEIGHT OF BOTTOM PORTION
= 13.55*32*3 +13.55*32*5/12.54
=1473.69 lbf
(c) LARGEST MASS= WIEGHT/g
=1473.69/32
=46.053 lbm
(d) THE DEVIVE MAY BE AFFECTED BY ATMOSPHERIC PRESSURE, IF DEVICE IS OPEN
BUT HERE WE CAN SEE THE DEVIVE IS CLOSED.
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