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An open rectangular tank 1 m wide and 2 m long contains gasoline to a depth of 3 m. If the height of the tank sides is 4 m. What is the maximum horizontal acceleration (along the long axis of the tank) that can develop before the gasoline would begin to spill?

Answer :

Answer:

ay max = 4.91 m/s²  

so here acceleration would be either right or left

Explanation:

given data

wide b = 1 m

long l  = 2 m

depth d = 3 m

height of  tank sides h = 4 m

solution

here for prevent spilling condition is

[tex]\frac{dz}{dy}[/tex] ≤ [tex]- \frac{1.5 - 1 }{1}[/tex]  ..........1

[tex]\frac{dz}{dy}[/tex]  ≤ - 0.50

and when here

[tex]\frac{dz}{dy}[/tex] =  -   [tex]\frac{ay}{g + az}[/tex]    ......2  

when az is 0 ay will be

ay = -  [tex]\frac{dz}{dy} g[/tex]    

and ay max will be

ay max = -( -0.50) (9.81 )

ay max = 4.91 m/s²  

so here acceleration would be either right or left

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