**Please Help! Impossible Physics Question**

SeanLadd123

Please help me with this impossible question from my physics book.

P.117 Real World Physics
Exc.10.6

12. At what point between the Earth and Moon is the resultant gravitational force zero? Where is it's acceleration zero?

(Distance between Earth and Moon=(3.8 x 10^8m)
Mass of Earth =(6 x 10^24kg)
Mass of Moon = (Mass of Earth/81)
Radius of Earth=(6.4 x 10^6m)
G=(6.7 x 10^-11)

brownlad

3.8x10^6 ...use the formula ...

clartharlear

Let P be the point where resultant force = 0
Suppose P is a distance y from the Earth and a distance x from the moon:

Eqn 1. Use Newton's universal gravitation formula for both the force due to the earth and the force due to the moon and put them equal to each other.

Eqn 2. x + y = 3.8 x10^8

Two equations, two unknowns. It's just sums from here!

stealinhorses

The answer actually works out to be 3.8x10^7.


(badass drawing, I know)





For the resultant force on P to be 0 we need this to happen:




We equate the suckers, and after subbing in the given values and manipulating the formulae we get:



Quadratic formula to solve for x:



Tedious games with the calculator result in two values for x:



so in the end



Naturally, the second value is too great to satisfy this problem (unless P is somewhere deep underneath Sweden :cool: ).

Therefore, the distance at which the net force on P is 0 is 3.8x10^7 metres away from the moon (that's also the correct answer in the Real World Physics book).

lostatsea

Students should strive for elegance when solving problems. After you cancel your constants, take the square root of both sides thereby mitigating the need for an ugly quadratic.