Question

A fire hose sends 2429 gallons of water per minute against a burning building. The water strikes the building at 66 m/s and does not bounce back. There are 3.785 L/gal Liters in a gallon, and the density of water is 1 kg/L.
a) What is the magnitude of the rate of change of momentum of the water? Answer in units of N.
b) The rate of change of momentum of the water 1. is negative. 2. cannot be determined. or 3. is positive?
c ) What force does the water exert on the building in 1.2 minutes? Answer in units of N.

Answer 1

Answer:

a)   Δp = - 10113.2 Kg m / s, b) he rate of change is negative, c)    F = 140.46N

Explanation:

a) For this part let's analyze a water particle, it has a velocity of 66 m / s and when it collides with the building its velocity changes to zero, so the change in moment is

           Δp = mv_f - m v₀

           Δp = -m v₀                              (1)

the change of the moment in a second is

           

if 2429 gallons arrive in in minute (60s) in a second how many gallons arrive      

            c_agua = 2429/60

            c_water = 40,483 gallon/ s

let's use the concept of density to find the mass

            ρ = m / V

            m = ρ V

let's reduce gallons to liters

             c_water = 40,483 gal (3,785 l / 1 gal) = 153.23 l

           

            m = 1 153.23

            m 153.23 kg

           

we substitute in 1

            Δp = - 153.23 66

            Δp = - 10113.2 Kg m / s

b) From the previous result the rate of change is negative

c) Let's use the impulse ratio

             I = f t = Δp

             F t = Δp

               

              F = Δp / t

              F = $\frac{10113.2}{1.2 \ 60}$

              F = 140.46 N