Question

Energy is energy. It comes in a variety of guises, but they are all responsible for affecting change to the world. Here, we will use an unconventional, but surprisingly useful form of energy to power something important... and hopefully aid you in grappling with how much energy humans consume on a daily basis. An MRI machine typically requires 20.1 kW of power to operate, and on average a single session lasts 30 minutes. In a disaster area where the electric grid is down, this machine needs to operate. Let's say you rig up a system to convert gravitational potential energy into electricity at 90% efficiency. That's REALLY good and likely unrealistic, but let's just go with it for now. You hook up a strong cable system to an electric generator so that when the rope moves, it spins a turbine and generates electricity similar to a hydroelectric power plant. You attach the cable to a 100 m tall building; this is the distance you have to work with. How heavy of a mass (in kg) would need to be hoisted to the top and allowed to fall to generate enough energy to power the MRI machine for a single session? 36,918 kg O 41 kg 52,420 41,020 kg 683 kg

Answer 1

Given that Power required by MRI machine = P = 20.1 kW = 20100 W

average time for single session = 30 min = 1800 sec

Energy required for single session = Power*time

E = P*t/n = 20100*1800 = 36180000 J = 3.618*10^7 J

Now given that efficiency of your system which converts GPE into electricity is 90%,

So efficiency of electricity generation = 90%

total potential energy required to generate = E0 = E/n

E0 = 3.618*10^7/0.90 = 4.02*10^7 J

Now potential energy generated by falling 'm' mass from 'h' height will be:

PE = E0 = m*g*h

m = mass required = E0/(g*h)

h = height of building = 100 m

g = 9.8 m/s^2

So,

m = 4.02*10^7/(9.8*100)

m = 41020 kg = mass required

Correct option is D.