w=Cr^-2 Suppose that an object is 100 pounds when it is at sea level. Find the value of C that makes the equation true. (Sea level is 3,963 miles from the center of the earth.)
r is the distance from the center of the Earth. w is the weight of that bject
100 = C/(3963)^2
C = (3963)^2 x 100
Do the numbers.
C = 1.352*10^9 lb*mile^2
The equation applies to THAT WEIGHT only
w=Cr^-2 Suppose that an object is 100 pounds when it is at sea level. Find the value of C that makes the equation true. (Sea level is 3,963 miles from the center of the earth.)
The Law of Universal Gravitation states that each particle of matter attracts every other particle of matter with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. Expressed mathematically, F = GM(m)/r^2, where F is the force with which either of the particles attracts the other, M and m are the masses of two particles separated by a distance r, and G is the Universal Gravitational Constant. The product of G and, lets say, the mass of the earth, is sometimes referred to as GM or mu (the greek letter pronounced meuw as opposed to meow), the earth's gravitational constant. Thus the force of attraction exerted by the earth on any particle within, on the surface of, or above, is F = 1.40766x10^16 ft^3/sec^2(m)/r^2 where m is the mass of the object being attracted and r is the distance from the center of the earth to the mass. The force of attraction which the earth exerts on our body, that is, the pull of gravity on it, is called the weight of the body, and shows how heavy the body is. Thus, our body, being pulled down by by the earth, exerts a force on the ground equal to our weight. The ground being solid and fixed, exerts an equal and opposite force upward on our body and thus we remain at rest. A simple example of determining this force, or our weight, is to calculate the attractive force on the body of a 200 pound man standing on the surface of the earth. Now the man's mass is his weight divided by the acceleration due to gravity = 200/32.2 = 6.21118 lb.sec^2/ft. The radius of the surface from the center of the earth is 3963 miles x 5280 ft/mile = 20924640 feet. Thus the attractive force on his body is 1.40766x10^16(6.21118)/20924640^2 = 200 pounds. What do you know? The mans weight.
Therefore, your C = 4.371615x10^16(m).
Thus, any object's weight is
F = W = 4.371615x10^16(m)/r^2 where m is the mass of the object, W/g.
x+5=5
To find the value of C that makes the equation true, we need to substitute the given information into the equation and solve for C.
The equation is w = Cr^(-2), where:
- w is the weight of the object,
- C is the constant we want to find,
- r is the distance from the center of the Earth.
Given information:
- Weight of the object (w) = 100 pounds,
- Distance from the center of the Earth (r) = 3,963 miles.
Substituting these values into the equation, we get:
100 = C(3,963)^(-2)
To solve for C, we need to isolate it on one side of the equation. Let's start by rearranging the equation:
C(3,963)^(-2) = 100
Now, we can solve for C by dividing both sides of the equation by (3,963)^(-2):
C = 100 / (3,963)^(-2)
To simplify this, we can rewrite (3,963)^(-2) as 1 / (3,963^2):
C = 100 / (1 / 3,963^2)
Next, we can simplify further by dividing 100 by 1:
C = 100 * 3,963^2
Calculating this expression, we get:
C ≈ 157,271,569
Therefore, the value of C that makes the equation true is approximately 157,271,569.