Answer:
(a) v = 10.6m/s
(b) E = 387.6J
(c) U = 387.6J
(d) ΔT = 0.022°C
Step-by-step explanation:
(a) In order to calculate the speed of the hose we will use the work-energy theorem. In simple terms it is a theorem that states that the work done is equal to the change in energy
Workdone = Force × distance
W = Fd
The above equation states that the total workdone is equal to the applied force times the distance over which the force was applied. In this problem a force of 13.6N is applied on the hose, moving one end of it over a distance of 28.5m from where the hose is located to the edge of the garden. Since the point of of application of the force moves the end over that distance, we only take this into consideration and not the length of the whole hose. So
workdone = 13.6 × 28.5 = 387.6J
This workdone is converted into the kinetic energy given to hose in moving it over this distance.
So
W = 1/2×mv²
v² = 2×W/m
v = √(2×W/m) = √(2×387.6/6.9) = 10.6m/s
(b) ΔE = 387.6 (work-energy theorem)
(c) From the first law of thermodynamics
Q = ΔU + W
Q = Heat supplied or taken from the hose
ΔU = change in internal energy of the hose
W = workdone by or on the hose = –387.6 (work is done on the hose. That's the reason for the negative sign)
So substituting their value,
0 = ΔU + (–387.6)
ΔU = 387.6J
(d) ΔU = mCv×ΔT
Given Cv = 2.5kJ/kg°C = 2500J/kg°C
387.6 = 6.9×2500×ΔT
387.6 = 17250ΔT
ΔT = 387.6/17250
ΔT = 0.022°CΔ