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In the movie, Willy Wonka and the Chocolate Factory, Augustus Gloop leans over the chocolate river to get a drink and falls in. He is sucked through the pipe leading to the fudge room where he is saved by the Oompa Loompa workers. Unfortunately, real-life accidents do not always have such happy endings, even when they involve chocolate. In a tragic 2009 accident, a worker suffered fatal injuries after falling into a cylindrical mixing vat that had an 8-ft diameter and was 8 ft tall. At the time of the accident, the vat was full of molten chocolate. (a) What was the total weight (lbf) of chocolate in the vat? The specific gravity of chocolate is approximately 1.24. (b) Determine the pressure (psig) at the bottom of the tank. (c) Speculate on whether a person would float or sink in the vat and list two possible causes of the worker’s death.

Answer :

danialamin

Answer:

Part a : Weight of chocolate in vat is 31130.17 lbf

Part b : Pressure at the bottom of tank is 4.29 psig

Part c : The body will float as its density is less than that of chocolate.

Explanation:

Part a

Weight of  chocolate in the vat is given as

[tex]W=m \times g\\W= \rho V \times g[/tex]

Here

  • W is the weight of the chocolate which is to be calculated
  • ρ is the density of chocolate which is calculated from following formula[tex]\rho=S \times \rho_{w}[/tex]

        Here

                 S is the specific gravity which is given as 1.24

                 [tex]\rho_w[/tex] is the density of water which is 62.43 [tex]lb_m/ft^3[/tex]

       So density is

                                            [tex]\rho=S \times \rho_{w}\\\rho=1.24 \times 62.43\\\rho=77.41 lb_m/ft^3[/tex]

  • V is the volume of the vat calculated from the diameter and height as below

        [tex]V=\pi d^2 h/4[/tex]

        Here

                d is the diameter of the vat which is 4 ft.

                h is the height of the vat which is 8 ft.

                                             [tex]V=\frac{\pi d^2 h}{4}\\V=\frac{\pi 8^2\times 8}{4}\\V=402.13 ft^3[/tex]

  • Here the value of g is 32.17 [tex]ft/s^2[/tex]. This is used to convert [tex]lb_m[/tex] to [tex]lb_f[/tex]

Substituting values in equation of Weight gives

                                  [tex]W= \rho V \times g\\W= 77.41\, \frac{lb_m}{ft^3} \times 402.13 \, ft^3 \times 32.17 \frac{ft}{s^2} \\W=31130.17 \ \, 32.17 \frac{lb_m ft}{s^2}\\W=31130.17\,lb_f[/tex]

So the weight of chocolate in the vat is 31130.17 lbf

Part b

Pressure is given as

[tex]P=\frac{W}{A}[/tex]

Here

  • W is the weight calculated above
  • A is the area which is calculated as below

                                     [tex]A=\pi r^2\\A=50.26 ft^2[/tex]

Now pressure is given as

[tex]P=\frac{31130.17}{50.26}\\P=619.315 \, lb_f/ft^2\\P=\frac{619.315}{144} lb_f/in^2\\P=4.29 psig[/tex]

So the Pressure is 4.29 psig

Part c

As the average density of human body is given 61.49 [tex]lb_m/ft^3[/tex] which is less than that of chocolate so the body will float in the vat.

The two possible reasons of worker's death can be

  1. Broken ribs/neck resulting in failure of vital organs.
  2. Inhalation of Chocolate and Fillings of Lungs with the Chocolate
  3. Resistance of the mixer blades.

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