## Physics of Superman

Alison Ball

Superman is a classic icon in American culture, and he is capable of super-human feats. Take for instance the classic scenario--Lois Lane is in trouble and manages to fall from the top of an extremely large building. Superman simply flies up to catch her, thus saving the day. However, this situation has several factors that would be problematic.

Lois Lane dangles from the top of a building and then falls. From the video, it is difficult to tell just how tall the building is, or how far she fell. I assumed that she fell about 20 stories, or 200 feet (61 meters). If the absence of air resistance is assumed, you can find her final velocity using the equation:

Vf ^2=Vi ^2 -2g(yf - yi)

We know her initial velocity was 0 m/s, acceleration due to gravity is 9.8 m/s^2, and she fell 61 meters. After plugging in these values, the final velocity was determined to be 34.6 m/s. To put this in terms that can be visualized, Lois Lane was falling at a speed of about 77mph when superman caught her.

I then assumed that Lois Lane had a mass of about 60 kg, and used this to calculate how much work she was doing.

Since, F=ma,
F=(9.8m/s^2)(60 kg)=588N

Work=Fdcos(theta)
Work =(588N)(61m)=35868J or about 40,000 J.

If you were to figure out the power behind the fall,

Power= Work/time

Time can be found using Vf=Vi-gt, and time is equal to 3.5 seconds.

Power=(40000J/3.5s)=11428 watts or about 10,000 watts.

When Superman actually catches Lois, he is accelerating upward, therefore decreasing the amount of time it takes to bring her to a stop. It is difficult to determine exactly how long it took for her motion to stop, but I am going to assume it was around 0.3 seconds. Since this time is short, I can expect the force it takes to bring her to a stop to be very large.

Using the equation:

The sum of the Forces= (m*(vf - vi))/t

With the numbers plugged in, this gives:

F= (60kg*(-34.6m/s))/.3s
F=-6920N
F=-7000N

Therefore it takes 7000N (7 kN) of force for Superman to catch Lois, but this is a lot of force. To put this in perspective, the human forehead can withstand about 6.0 kN of force, and the cheek bone can withstand much less (1.3 kN). This means that the catch would not happen as effortlessly as the video would imply. Although Superman may appear to be fine (he is a superhero, after all), Lois may not be doing so well. It is very possible that she could have broken bones, and at the very least, a lot of bruising.