Answer to Question #87685 in Mechanics | Relativity for Opopipo

Question

A 50 mm diameter stream of water strikes a 0.5 m by 0.5 m square plate which is at an angle of 30 degrees with the stream’s direction. The velocity of the water in the stream is 20 m/s and the jet strikes the door at its centre of gravity. If the plate is hinged at A, by neglecting the friction and self-weight of the plate, determine the normal force P applied at the upper edge of the plate to keep the plate in equilibrium. You may assume that the velocities of the jet remain unchanged after split.

Please help me

Answer 1

Newton’s second law:

$F_w \Delta t = m(v-0)\\$

$F_w\Delta t = \rho V v$

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

$F_w = \rho\frac{\pi d^2}{4} v^2 = 1000 \frac{kg}{m^3} \frac{\pi \cdot 25 \cdot 10^{-4}m^2}{4} \cdot 400 \frac{m^2}{s^2} = 250\pi N$

$P = \sin (\phi) F_w = sin(30^\circ) F_w = 250\pi \cdot 0.5N = 125\pi N = 392.7N$

Answer: 392.7N