A fire hose 4.79 cm in diameter is capable of spraying water at a velocity of 17.1 m/s. For a continuous horizontal flow of water, what horizontal force should a fireman exert on the hose to keep it stationary?
To determine the horizontal force required to keep the fire hose stationary, we need to apply Newton's second law of motion. According to this law, the force (F) is equal to the mass (m) multiplied by the acceleration (a). In this case, the mass of the water is not given, but we can calculate it using the density (ρ) and the volume of water flowing per unit time (V).
First, let's find the volume of water flowing per unit time using the diameter of the hose.
The radius of the hose can be calculated by dividing the diameter by 2:
radius (r) = diameter / 2
So, the radius of the hose is:
r = 4.79 cm / 2 = 2.395 cm = 0.02395 m
The cross-sectional area of the hose (A) can be calculated using the formula for the area of a circle:
A = π * r^2
Substituting the values:
A = π * (0.02395 m)^2 = 0.001804 m^2
Now, let's calculate the volume of water flowing per unit time (V) using the velocity of the water:
V = A * v
Substituting the values:
V = 0.001804 m^2 * 17.1 m/s = 0.030944 m^3/s
Next, we can find the mass of the water (m) using the density of water (ρ):
m = ρ * V
The density of water is approximately 1000 kg/m^3, so:
m = 1000 kg/m^3 * 0.030944 m^3/s
Now we have the mass of the water flowing per second.
Finally, we can calculate the force required to keep the fire hose stationary by multiplying the mass by the acceleration:
F = m * a
Since the hose is stationary, its acceleration is 0 m/s^2:
F = m * 0 = 0 N
Therefore, the horizontal force that the fireman needs to exert on the hose to keep it stationary is 0 Newtons.