1. Many people know that the weight of an object varies on different planets, but did you know that the weight of an object on Earth also varies according to the elevation of the object? In particular, the weight of an object follows this equation: , where C is a constant, and r is the distance that the object is from the center of Earth.
a. Solve the equation for r.
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The weight of an object is essentially calculated using Newton's law of gravitation, given by:
Gm1m2/r², where
G=gravitation constant,
= 6.674 N(m/kg)²
r=distance between the centre of mass of two objects, in this particular case, the centre of the earth, and the object in question (whose weight is to be determined).
On the average, the radius of the earth is 6378.1 km
m1=mass of the earth (in this case)
= 5.974*1024 kg.
m2=mass of the object in question.
Substitute the above values (in the appropriate units) for Gm1/r² should give the value of g, acceleration due to gravity, and should equal approximately 9.81 m/sec² for a mass m2 of 1 kg.
At different heights, the same formula can be used to calculate the acceleration due to gravity, substituting the appropriate values of r.
For more reading, see following article and related references:
http://en.wikipedia.org/wiki/Newton%27s_law_of_universal_gravitation
To solve the equation for r, we need to manipulate the equation to isolate r on one side. The equation is given as:
Weight of object = C / r^2
To solve for r, we can start by multiplying both sides of the equation by r^2:
Weight of object * r^2 = C
Next, we can divide both sides of the equation by the weight of the object:
r^2 = C / Weight of object
Finally, to solve for r, we can take the square root of both sides of the equation:
sqrt(r^2) = sqrt(C / Weight of object)
r = sqrt(C / Weight of object)
Therefore, the equation for r is r = sqrt(C / Weight of object).
To solve the equation for r, we can rewrite it in terms of r:
W = C/r
Next, we can rearrange the equation to solve for r:
r = C/W
In this equation, r represents the distance of the object from the center of Earth, W represents the weight of the object, and C is a constant.
To find the value of r, you will need to know the weight of the object (W) and the constant (C). Once you have these values, you can substitute them into the equation and calculate the distance (r) using the formula provided.