Forces and Motion in Superman

Forces and Motion in Superman

Marlon Brando as Jor-El, with Kal-El played by Lee Quigley. Superman: The Movie Magazine (Photo credit: Wikipedia)

When Jor-El, Superman’s father discovers that his planet of Krypton is about to explode and kill everyone he puts his son in a rocket ship and sends him to Earth so he won’t die. Kal-El (Superman), after landing on Earth, is adopted by the Kents who rename him Clark. As he reaches adulthood he develops many incredible superpowers.  The first incarnation of Superman was very different from the modern one. He had super strength but not to the degree of lifting a continent. It was more along the lines of lifting one car. Most importantly, he could not fly. He was just able to leap long distances. An eighth of a mile was his original distance.

The Physics of Jumping and All Other Motion

Since Superman originally in the Golden Age of Comic books was unable to fly, he jumped extremely high (approximately the height of a 30 to 40 story building).  This was explained as Earth having less of a gravitational pull than Krypton. So what kind of velocity would Superman need to jump 660 feet straight up? Superman’s mass is a constant. His weight changes however and depends on the gravitational attraction of the planet or moon he is on/close to.

In a Single Bound

Superman’s jumping height relies on the square of his starting speed because rising into the air depends on his initial velocity. Using the formula v * v = v^2 = 2gh, we can calculate the relationship between Superman’s initial velocity (v) and his final height (h) of the jump. The acceleration due to gravity (g) is 32 feet per second. So then using the equation we come to the conclusion that Superman’s initial velocity would have to be 205 feet/sec. to leap 660 feet straight up. That’s more than 130 miles an hour which would be ridiculous seeing as in the Golden Age he wasn’t that fast yet.

To accomplish his initial velocity of about 205 feet a second, Superman must crouch down and apply a great deal of force to the ground.  To find the amount of force Superman would need to exert we use Newton’s second law of motion – F = ma. That basically is saying force equals mass times acceleration. Assuming that Superman weighs about 220 Earth pounds, his mass would be 100 kilograms. If Superman takes ¼ of a second to jump, his acceleration equates to a change in speed of 200 feet/sec divided by ¼ of a second or 800 (250 in the metric system)  feet/seconds squared.  Plug in those numbers into F = ma ((100kilograms times 250 meters/seconds squared = 25,000 kilograms meters/seconds squared.) and you get about 5600 pounds.

Superman’s legs would have to be able to deliver a force of 5600 pounds! Kryton’s gravity is supposedly much stronger than Earth. If this force was just 70 percent bigger than the force his legs require to simply stand he would weigh 3,300 pounds on Krypton. If all this is correct then the acceleration due to gravity must be fifteen times larger on Earth than Kryton.