The weight of body on surface of earth is 980 N and 490 N at a certain height. What is the value of gravitational acceleration and what is the height?
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answers:
electron1 say: The following equation is used to determine an object’s weight.
Fg = G * M * m ÷ d^2
d is the distance from the center of earth to the object. According to this equation, the weight is inversely proportional to the square of this distance. The radius of the earth is 6.38 * 10^6 meters.
980 = G * M * m ÷ (6.38 * 10^6)^2
490 = G * M * m ÷ d^2
Let’s divide these two equations.
2 = d^2 ÷ (6.38 * 10^6)^2
d^2 = 2 * (6.38 * 10^6)^2 = 8.14088 * 10^13
d = √8.14088 * 10^13
This is approximately 9.02 * 10^6 meters. To determine the height, subtract the radius of the earth.
h = √8.14088 * 10^13 – 6.38 * 10^6
This is approximately 2.64 * 10^6 meters
Weight = m * g
m * g = G * M * m ÷ d^2
g = G * M ÷ d^2
G * M = 6.67 * 10^-11 * 5.98 * 10^24 = 3.98866 * 10^14
g = 3.98866 * 10^14 ÷ d^2
Let’s use the value of d in this equation to determine g.
g = 3.98866 * 10^14 ÷ 8.14088 * 10^13
This is approximately 4.9 m/s^2.
The weight of body on surface of earth is 980 N and 490 N at a certain height.
Since the mass is constant, the value of g is directly proportional to its weight. Since the weight at this height is one half of its actual weight, the value of g should be one half the g at the surface of the earth. This is an easy way to answer the first question. I hope some of this is helpful for you.
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Ricki say: F = m * g
and
F = G * m1 * m2 / distance^2
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oldschool say: Weight = G*Me*m/Re² where G is the gravitational constant, Me is the mass of the earth, Re is the radius of the earth and m is the mass in question. G*Me/Re² = 9.8m/s² = g
mg = 980N -----> m = 980/g = 980/9.8 = 100kg
The height where the weight = 490N is where G*Me/Rx² = G*Me/(Re*√2)² = G*Me/(2*Re²)
Re*√2 = Re + 0.414Re
So the altitude above the surface of the earth = 0.414Re = 2639km or about 2640km
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donpat say: You have constant mass :
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WE = ( mB ) ( gE )
mB = WE / gE = 980 N / 9.8 m/s^2 = 100 kg
WHT = ( mB ) ( gHT )
gHT = ( WHT ) / ( mB ) = ( 490 N ) / ( 100 kg ) = 4.9 m/s^2 <---------------------
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