Question

an open rectangular tank 1.0 meter wide and 2.0 meter long contains gasoline to a depth of 1.5 meters. if the height of the tank is 2.0 meters, what is the maximum horizontal acceleration in m/s2 (along the axis of the tank) that can develop before the gasolie would begin to spill (over the sides)?

Answer 1

The maximum horizontal acceleration is solved to be 4.91 m/s^2

What is acceleration?

This is a term in physics that refers to change in velocity with time.  Acceleration can be positive or negative or zero,

Given data

open rectangular tank

width = 1.0 m

length = 2.0 m

gasoline depth level = 1.5 m

height of the tank = 2.0 m

How to solve for maximum horizontal acceleration

lets represent the volume with x, y, and z such that z corresponds to height, y corresponds to wide or width, and x corresponds to length.  

dz / dy = - ay / ( g + az )

where

ay = acceleration in the y direction

az = acceleration in the z direction which is equal to zero

g = acceleration due to gravity

plugging in az = 0

dz / dy = - ay / ( g )

ay = - ( dz / dy ) * g

to prevent spilling

dz / dy = -  ( 1.5 - 1 ) / 1

dz / dy = -  0.5

ay = - ( - 0.5 ) * 9.81

ay = 4.91 meters per second square

Hence the maximum horizontal acceleration is solved to be 4.91 m/s^2

Read more on acceleration here: brainly.com/question/605631

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