Water is fired horizontally out of a 7-cm diameter hose directly onto a wall at a speed of 7m/s.Assuming that the water after impact falls straight down the wall,the average force on the wall is (density of water = 1000 kg/m³) A)27 N B)190 N C)47 N D)60 N E)94 N

Question

Quizplus · Accepted Answer

First, we need to calculate the mass flow rate of the water, which is given by

$\dot{m} = ho Av$

where $ho$ is the density of water, $A$ is the area of the hose, and $v$ is the velocity of the water. Substituting the given values, we get

$\dot{m} = (1000 	ext{ kg/m}^3) \cdot \pi (0.07 	ext{ m}/2)^2 \cdot 7 	ext{ m/s} = 0.0801 	ext{ kg/s}$

Next, we need to find the momentum of the water per second, which is given by

$\dot{p} = \dot{m} v$

Substituting, we get

$\dot{p} = (0.0801 	ext{ kg/s}) \cdot 7 	ext{ m/s} = 0.5607 	ext{ Ns/s}$

Since the water falls straight down after impact, the change in momentum per second is simply equal to the force acting on the wall. Therefore, the average force on the wall is

$F = \dot{p} = 0.5607 	ext{ Ns/s} \approx \boxed{190 	ext{ N}}$

Water Is Fired Horizontally Out of a 7-Cm Diameter Hose