Hello, I have some rather fun questions below which I was wondering if anyone could help me with in terms of improving or correctly my answers. I would be very thankful of any help or responses👌
Question i Currents of approximately 10000 A are common for lightning bolts. Lightning only lasts for approximately 1 millisecond.
1. Calculate the charge passing during this time.
I=Q/t
Therefore, Q=I*t
Q=10,000 A * (1.0*10^-3) s
Q= 10 C
2. In the film Back to the Future, a conducting rod was used to power the DeLorean time machine. Assuming the potential difference between the charged cloud and the conducting rod is 100 million volts (a standard result, but values can vary considerably), calculate:
a. The energy transferred along the conducting rod.
100 million volts = 100 MV
Voltage = energy transferred/charge passing
Energy transferred = voltage * charge
E=100,000,000 * 10 C
E= 10,000,000 J or 1.0 * 10^7J
b. The theoretical power generated.
Power = E/ t
Power = 10,000,000 J /0.001 s
Power =10,000,000,000 W or 1.0 * 10^10 W
3. Doc Brown from the film said 1.21 Giga Watts were required. Does your answer suggest there was sufficient power? What else might need to be considered?
Yes, there is sufficient power since 10,000,000,000 W = 10 GW ~ 10 times the required power. However, I am not sure what else might need to be considered?
Question ii In an experiment with an electric motor, an object of mass 550 g was lifted a height of 1.5 m in 12.1 s. A voltmeter read the potential difference across the motor as 5.1 V and an ammeter read the current to the motor as 1.41 A.
1. How much work was done lifting the load?
Work done= mgh
Work done = 0.5*9.81*1.5
Work done =7.3575 ~ 7.40 J
2. What was the power output?
Power=work done/time taken
P=7.3575/12.1
P=0.60805785 ~ 0.608 W
3. What was the power input to the motor?
Energy input = electrical energy used = VIt
VIt=5.1*1.41*12.1=87.0111 ~ 87 W
4. What was the efficiency?
Efficiency =useful energy output/total energy input
Efficiency =0.608 /87.0111
Efficiency = 0.00698 * 100% = 0.698%
I think this is wrong would it rather be:
Efficiency =mgh/total energy input
Efficiency =7.3575/87.0111
Efficiency =0.08455*100% =8.455%
5. Suggest where energy might have been wasted.
Energy may have been wasted as thermal energy resulting from the friction of the rope raising the mass and slightly as sound.
Question iii.
In Question i, a calculation was done on lightning being conducted via a lightning rod to power a DeLorean time machine. If the length of wire was 8.5 m long, with a diameter of 2.4 mm and had a resistance of 9 Ω:
a. What was the resistivity of the material?
R=pL/A
A = π r^2 or πd^2/4
Rearranging:
p=RA/L
p=R*( πd^2/4)/L
p=9*(π*2.4^2/4)/8.5
p=4.79 Ωm
b. How much power was dissipated due to the resistance of the wire for a current of 10000 A? Does this affect your answer to Question ii 3?
Power dissipation equation:
P=I^2R
P=10000^2*9
P=900,000,000 W or 9.0 * 10^8 W
I am not sure how this effects the power input to the motor?