AP Physics B 2.1 Newtonian Mechanics
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AP Physics B: Newtonian Mechanics Section Drill 2, problem 1. What is the acceleration due to gravity for objects dropped near the surface of Europa?
|AP Physics B||Newtonian Mechanics|
|AP Physics B/C||Newtonian Mechanics|
|AP Physics C||Newtonian Mechanics|
Well, it's not asking about the gravitational pull in Europe, for starters.
Even if some of their hair-dos over there do seem to defy gravity... they're pretty
much abiding by the same laws of physics that we do in the States.
Instead, the focus is on Europa, one of Jupiter's moons.
To solve this problem, we use Newton's law of gravitation:
For our equation, we use
m1g... the force of gravity on earth... is equal to big G, the gravitational constant,
times m1 times m2 divided by r squared.
In this equation, m represents the mass of an object,
and r is the distance between the two objects.
We can divide the m1... your mass...
out of both sides...
...and here's what we get: the acceleration of gravity on earth is equal
to the Gravitational constant...
...multiplied by the mass of the Earth all over the radius squared.
We can write this same equation for Europa.
Now, by substituting the values for Europa we can get the acceleration of gravity on that moon.
The mass for Europa is one tenth that of Earth, so we multiply mEarth by .1.
The distance between the center of Europa and whatever this slippery object is that
we've dropped... is one fourth of Earth, so we multiply r by .25.
We have to make sure we multiply R by .25 before we square it.
Simplifying what we have, we get that the gravity on Europa is equal to .1 over .25
squared or 1.6 times the gravity of Earth or 1.6 times stronger.
Maybe it's time for someone to invest in a utility belt...