Question

1. A flywheel is the shape of a sphere of radius R. Calculate the stored energy again for rotation time T and total mass M. Do not attempt to use moment of inertia or rotational mechanics, do it the way we did in class.

2. Find an exercise calorie website, and for a 70 kg person walking on a treadmill at 5 kilometers per hour, by varying the grade of the treadmill, plot the work output power (of lifting the person) vs. the fuel (food) consumption input power of the person. That is, for different grades, (% incline), find the fuel consumption in watts, and calculate the work output of the person lifting themselves against gravity, and plot work output vs. fuel consumption. Note that a 10 % grade means climbing 15 feet for every 100 feet of horizontal travel, so you will have to a little trigonometry here. What is the differential efficiency of the person, that is, for dx increase in fuel consumption, which results in dy increase in work output, the differential efficiency is dy/dx. Where does the input power that does not result in useful lifting work go?

Answer 1

solution:-

Flywheel is a Mechanical device Which converts Mechanical energy in to rotational Energy or it absorbs Energy till the time it is connected to powers supply and it releses energy when power supply is disconnected. In other words we can say Flywheel is a heavy mass device which continues the power supply by absorbing Energy in itself.

Now we can take by the equation of motion

v²= u² +2as

so that s =(v² - u²/2a)

We know that

Work Done (w) = Stored Energy (E)

E = w = F. s

E = M. a. s

E = M. a. (v² - u²/2a)

now, E = M(v² - u²) /2

for initial condition:-

initial velocity, u=o

final velocity, v =v

now putting these value in above equarion of energy, we get

E = Mv²/2

because Moment of inertia, I = M. R²

and v = R.

we can write

E = M x (R ) ²/2

E = I ²/2