Answer:
64.945 miles per hour
Explanation:
Since the frequency of sound heard is higher than actual frequency, the ambulance is moving towards you!
The frequency of sound waves as heard from a distance for a sound wave coming towards one at v₀ m/s and whose real frequency is f₀ is given by
+f = f₀/[1 - (v₀/v)]
+f = frequency of sound as heard from the distance away = 8.61 KHz
f₀ = real frequency of sound = 7.87 KHz
v₀ = velocity at which the sound source is moving towards the reference point = ?
v = velocity of sound waves = 343 m/s
8.61 = 7.87/(1 - (v₀/v))
1 - (v₀/343) = 0.9141
v₀/343 = 1 - 0.9141 = 0.0859
v₀ = 343 × 0.0859 = 29.48 m/s = 64.945 miles per hour
Answer:
Part a)
P = 13.93 kW
Part b)
R = 8357.6 Cents
Explanation:
Part A)
heat required to melt the aluminium is given by
![Q = ms\Delta T + mL](https://tex.z-dn.net/?f=Q%20%3D%20ms%5CDelta%20T%20%2B%20mL)
here we have
![Q = 40(950)(680 - 32) + 40(450 \times 10^3)](https://tex.z-dn.net/?f=Q%20%3D%2040%28950%29%28680%20-%2032%29%20%2B%2040%28450%20%5Ctimes%2010%5E3%29)
![Q = 24624 kJ + 18000 kJ](https://tex.z-dn.net/?f=Q%20%3D%2024624%20kJ%20%2B%2018000%20kJ)
![Q = 42624 kJ](https://tex.z-dn.net/?f=Q%20%3D%2042624%20kJ)
Since this is the amount of aluminium per hour
so power required to melt is given by
![P = \frac{Q}{t}](https://tex.z-dn.net/?f=P%20%3D%20%5Cfrac%7BQ%7D%7Bt%7D)
![P = \frac{42624}{3600} kW](https://tex.z-dn.net/?f=P%20%3D%20%5Cfrac%7B42624%7D%7B3600%7D%20kW)
![P = 11.84 kW](https://tex.z-dn.net/?f=P%20%3D%2011.84%20kW)
Since the efficiency is 85% so actual power required will be
![P = \frac{11.84}{0.85} = 13.93 kW](https://tex.z-dn.net/?f=P%20%3D%20%5Cfrac%7B11.84%7D%7B0.85%7D%20%3D%2013.93%20kW)
Part B)
Total energy consumed by the furnace for 30 hours
![Energy = power \times time](https://tex.z-dn.net/?f=Energy%20%3D%20power%20%5Ctimes%20time)
![Energy = 13.93 kW\times 30 h](https://tex.z-dn.net/?f=Energy%20%3D%2013.93%20kW%5Ctimes%2030%20h)
![Energy = 417.9 kWh](https://tex.z-dn.net/?f=Energy%20%3D%20417.9%20kWh)
now the total cost of energy consumption is given as
![R = P \times 20 \frac{Cents}{kWh}](https://tex.z-dn.net/?f=R%20%3D%20P%20%5Ctimes%2020%20%5Cfrac%7BCents%7D%7BkWh%7D)
![R = 417.9 kWh\times 20 \frac{cents}{kWh}](https://tex.z-dn.net/?f=R%20%3D%20417.9%20kWh%5Ctimes%20%2020%20%5Cfrac%7Bcents%7D%7BkWh%7D)
![R = 8357.6 Cents](https://tex.z-dn.net/?f=R%20%3D%208357.6%20Cents)
Answer:
66.2 sec
Explanation:
C₁ = 1.0 F
C₂ = 1.0 F
ΔV = Potential difference across the capacitor = 6.0 V
C = parallel combination of capacitors
Parallel combination of capacitors is given as
C = C₁ + C₂
C = 1.0 + 1.0
C = 2.0 F
R = resistance = 33 Ω
Time constant is given as
T = RC
T = 33 x 2
T = 66 sec
V₀ = initial potential difference across the combination = 6.0 Volts
V = final potential difference = 2.2 volts
Using the equation
![V = V_{o} e^{\frac{-t}{T}}](https://tex.z-dn.net/?f=V%20%3D%20V_%7Bo%7D%20e%5E%7B%5Cfrac%7B-t%7D%7BT%7D%7D)
![2.2 = 6 e^{\frac{-t}{66}}](https://tex.z-dn.net/?f=2.2%20%3D%206%20e%5E%7B%5Cfrac%7B-t%7D%7B66%7D%7D)
t = 66.2 sec
Working...
length of wire L = 1.5 m
current I = 7 A
potential difference V = 68 Volt
According to Ohm's Law
V = IR
R = V/I
R = 68/7
R = 9.7 Ω