Concept Questions: During a lightening flash a potentialdifference V cloud - V g

Question

Concept Questions: During a lightening flash a potentialdifference Vcloud - Vground existsbetween a cloud and the ground. As a result, negativeelectric charge moves from the ground to the cloud. (a) Asthe charge moves from the ground to the cloud, work is done on thecharge by the electric force. How is this work related to thepotental difference and the charge q? (b). If this work could beused to accelerate an automobile's final speed? Express youranswer in terms of the potential difference, the charge, adn themass of the automobile. (c) If this work could all beconverted into heat, what mass m of water could beheated so that its temperature increases by deltaT? Writeyour answer in terms of the potential difference, the charge, themass, the specific heat capacity c of water. anddeltaT.
Problem: Suppose a potential difference ofVcloud - Vground = 1.2 X109 V exists between the cloud and the ground, andq = -25 C of charge is transferred from the ground to the cloud. (a) HOw much work Wground-cloud is done onthe charge by the electric force? (b) If the work done by theelectric force were used to accelerate a 1100-kg automobile fromrest, what would be its final speed? (c) If the work done bythe electric force were converted into heat, how many kilograms ofwater at 0 degrees C could be heated to 100 degrees C?
Problem: Suppose a potential difference ofVcloud - Vground = 1.2 X109 V exists between the cloud and the ground, andq = -25 C of charge is transferred from the ground to the cloud. (a) HOw much work Wground-cloud is done onthe charge by the electric force? (b) If the work done by theelectric force were used to accelerate a 1100-kg automobile fromrest, what would be its final speed? (c) If the work done bythe electric force were converted into heat, how many kilograms ofwater at 0 degrees C could be heated to 100 degrees C?

Explanation / Answer

(a)    the work WAB done by the electricforce in moving a charge q from A to B isrelated to the potential difference    VA - VBbetween the two points by    WAB = q(VA - VB)    letting A = ground and    B = cloud, the work done can be written as    Wground-cloud = q(Vground - Vcloud)                          = -q (Vcloud - Vground) (b)    according to the work-energy theorem thework W done on an object of mass m is equal to its final    kinetic energy (1 / 2) mvf2 minus its initial kineticenergy (1 / 2) m vo2    setting W = Wground-cloud andnoting that    vo = 0 m/s,    since the automobile starts from rest, thework-energy theorem takes the form    (1 / 2) m vf2 =Wground-cloud    the final speed of the car is    vf = [2Wground-cloud / m]        = [- 2 q(Vcloud - Vground) / m] (c)    if the work Wground-cloud wereconverted completely into heat Q, this heat could be usedto raise the temperature of    water    the relation between Q and the changeT in the temperature of the water is    Q = c m T    where c is the specific heat capacity ofwater and m is its mass    solving this expression for m yields    m = Q / c T        =Wground-cloud / c T        = - q(Vcloud - Vground) /c T

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