Question

Q1.A square plate of uniform thickness and length of side 30 cm hangs vertically from hinges at its top edge. When a horizontal jet strikes the plate at its centre, the plate is deflected and comes to rest at an angle of 30 to the vertical. The jet is 25 mm in diameter and has velocity of 6 m/s. Calculate the mass of the plate and give the distance along the plate from the hinge, of the point at which the jet strikes the plate in its deflected position.
Help me please

Answer 1

Let find the force which water presses on plate:

$F_w \Delta t = m(v-0)$ (second Newnon's law)

$F_w \Delta t = \rho V v= \rho S v \Delta t v$ then

$F_w = \rho S v^2 = \rho \pi (\frac{d}{2})^2 v^2 = 1000 \frac{kg}{m^3} \cdot \pi (\frac{2,5m \cdot 10^{-2}}{2})^2 \cdot 36 \frac{m^2}{s^2} = 17.67N$

AC - plate start position.

AC' - plate deflected position.

$\alpha = 30^\circ$

$AB' = \frac{AB}{\cos \alpha} = \frac{l}{2\cos \alpha} = 17.32cm$ - second Question

$h_2 = AB' \cdot \cos \alpha = \frac{l}{2}$

$h_1 = \frac{l}{2} \cdot \sin \alpha = \frac{l}{2} \cdot \sin 30^\circ = \frac{l}{4}$

moment of mg = moment of water force:

$mgh_1 = F_wh_2$

$m = \frac{F_w h_2}{g h_1} = \frac{2F_w}{g}$

$m = \frac{2\cdot 17.67N}{10 \frac{N}{kg}} = 3.534kg$

So the answer:

1) 3.534kg

2) 17.32cm