Area of orifice is a. Due to ejection of water of density p at a constant speed, the equilibrium compression in spring is x. The speed of ejection of water is... (Please answer …

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asked Jan 3, 2019 181k views

1 Answer

Igor Kvasha · Answer 1 · 2019-01-07T15:41:31+0000

Thrust force due to ejection of water on the cart is counter balanced by spring force on the cart

so we can write

F_t = v (dm)/(dt)

here we have

(dm)/(dt) = rate of mass ejection

$(dm)/(dt) = \rho a(dx)/(dt) = \rho a v$

now from above formula

$F_t = \rho a v(v) = \rho av^2$

Now by force balance equation

F_t = F_s

$\rho a v^2 = kx$

by rearranging the terms now

$v= \sqrt{(kx)/(\rho a)}$