Question

Imagine a luxury train with its own staff of professional chefs who bake cakes on board. The chefs fill a rectangular cake pan with cake batter, as shown above, until it is % in below the top of the pan. The pan is 11 in long in the direction parallel to the track. What is the maximum horizontal acceleration to prevent the cake batter from spilling? [ft/s?] 10.75 o . , 572 llin

Answer 1

Pcose P Psine

Consider a fluid particle on the surface of the water

P is the pressure force applied by liquid on this particle

W is the weight of this particle

: W = mg

where m is the mass of the fluid particle

Net force on the particle in vertical direction = F, = Pcose - mg

The particle doesn’t move in vertical direction

So, net force on vertical direction is zero

:: Fy = 0

:: Pcoso - mg = 0

...(1)

:: P = mg rose

Net force on the particle in horizontal direction = F = Psin6

(from 1)

mg := Cosesine

...(2)

.: Fg = mgtant

Using newton’s 2^nd law,

force = mass x acceleration

...(3)

:: F = ma

where a_x is the acceleration of particle in horizontal direction

From (2) and (3)

.: max = mgtant

.. ax = gtant

572" llin

From the figure above , we can see that

  

ALD7

g = 32.174 ft/s2

zs/84 79= () (+2+Ze) = ****

This is the maximum allowed acceleration of the train