Universal Gravitation problems

November 8, 2015


Applications of Newton s Laws


The purpose of this problem is to determine the possible nature of the planet Krypton. Begin by reading the introduction from the 1950s TV series Superman.

Faster than a speeding bullet. More powerful than a locomotive. Able to leap tall buildings in a single bound.

Look, up in the sky! It's a bird! It's a plane! It's Superman!

Yes, it's Superman, strange visitor from another planet who came to Earth with powers and abilities far beyond those of mortal men. Superman, who can change the course of mighty rivers, bend steel with his bare hands, and who, disguised as Clark Kent, mild-mannered reporter for a great metropolitan newspaper, fights a never-ending battle for truth, justice and the American way.

Superman's strength is partly attributed to the gravity of his home planet, Krypton. The people of Krypton evolved to stand, walk, and lift ordinary objects in Krypton's strong gravitational field. When Superman came to Earth, he found that his Kryptonian physique was sort of over-designed. When Superman came to Earth he found he could "leap tall buildings in a single bound". This is much like when humans go to the moon. They find themselves strong enough to do all sorts of things they couldn't do on Earth (like run effortlessly with long strides while wearing an 80 kg (180 lb) space suit, for example).

Think of how high a typical human can jump on Earth. Assume Superman can only jump as high as that on Krypton. Then consider how high Superman can jump on Earth. Use this knowledge to determine the physical characteristics of Krypton. (State all values on Krypton in comparison to their values on Earth. Do not state them with a number and a unit.)

Derive an expression that relates height jumped to the acceleration due to gravity when take off speed is constant. Use the expression derived in part a to compare on the surface of Krypton to on the surface of the Earth. Derive an expression that relates on the surface of a spherical planet to the density and radius of the planet (instead of the mass and radius, which is the usual way it is stated). Use the expression derived in part b to determine the radius of Krypton assuming it has the same average density as the Earth. How likely is one to find a terrestrial planet with a radius like this? Use the expression derived in part b to determine the average density of Krypton assuming it has the same radius as the Earth. How likely is one to find a terrestrial planet with a density like this?
Source: physics.info
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Sample problems on law of universal gravitation?

determine the gravitational force between a 60kg and a 70 kg person who are both standing 2.0 m apart.
Fg=GM1M2
r^2
g=6.67x10^-11
M1=^0 kg
M2=70 kg
R= 2 m
.
just substitute..

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