Universal Gravitation (Note: time must be expressed in seconds when using G) 7.
ID: 119654 • Letter: U
Question
Universal Gravitation (Note: time must be expressed in seconds when using G) 7. A ball of lead has a mass of 12.0000Kg and is separated from another ball by a distance of 1.00230 m. If the mass of the second ba is 21.0000Kg. compute the gravitational attraction between them. 8. Using the above table, compute the gravitational attraction between the sun and Saturn. 9. Two identical balls are placed 2.566 m apart. If the gravitational attraction hetween 10. One ball has a mass, which is three times the other. If a distance of 1.450 m separates them is 1.855 x 101 N, compute the masses of the balls. them and they experience a gravitational attraction of 2.650 x 101 N. compute their 11. Calculate the mass of the earth give the fact that the gravitational attraction between the earth and a 2.00 Kg mass is 19.60N and the tadius of the earth is 6.40 X 10 m. 12. What is the circumference, C of the Earth? 13. It takes the Earth 24 hours to rotate once. What is the rotational velocity if you were standing on the equator? (velocity C/(24 hoars). 14. What is the orbital velocity of the Earth as it moves aroend the Sun? I5. Using the speed of light, determine how long it will take light to travel from the Sun to the Earth?Explanation / Answer
7) The mass of the two balls are 12,000 kg and 21,000 kg respectively. They are separated by a distance of 100230m.
m1 = 12,000 kg and m2 = 21,000 kg, r = 100230m
The gravitational attraction between them is (F) = (G.m1m2) / r2
G = Universal Gravitational Constant = 6.674 * 10 -11 m3kg-1s-2 .
F = (6.674 * 10 -11 * 12000 * 21000) / (100230)2
= 1.674 * 10-10 N
8) Gravitational attraction between Sun and Saturn.
As there is no table I am takimg the value from a standerd book.
Mass of the Sun (m1) = 1.989 * 1030
Mass of the Saturn (m2) = 5.684 * 1026
Distance between them is (r) = 1.43 billion km = 1.43 * 109 * 103 = 1.43 * 1012 m
So, F = (G.m1m2) / r2 = (6.674 * 10-11 * 1.989 * 1030 * 5.684 * 1026) / (1.43 * 1012)2
= 36.898 * 1021 N
9) Two identical balls are placed ata distance 2.566 m apart.
Gravitational attraction between them is 1.855 * 10-12 N.
(G.m1m2) / r2 = 1.855 * 10-12
(6.674 * 10-11 * m * m) / (2.566)2 = 1.855 * 10-12
m2 = 1.83 * 10-1
m2 = 0.183
m = 0.43 kg
10) One ball having a mass which is 3 times greater than the other, i.e., mass is m and 3m respectively.
Distance (r) = 1.45 m
F= 2.650 * 10-12N
(G * m * 3m) / r2 = 2.650 * 10-12
(6.674 * 10-11 * m * 3m) / (1.45)2 = 2.650 * 10-12
3m2 = 0.835 * 10-1
3m2 = 0.0835
m = 0.527 kg
11) Mass of the Earth = m
Mass of the object = 2kg
F = 19.60 N
r = 6.40 * 106 m
(G * m * 2) / (6.40 * 106) 2 = 19.60
(6.674 * 10-11 * m * 2) / (6.40 * 106) 2 = 19.60
m = 60.15 * 1023
m = 6.015 * 1024
12) Circumference of the Earth = 2r
Here r = 6.40 * 106 m
Circumference of the Earth = 4.02 * 107 m
13) Rorational speed of the earth at equator = 460 m/s
Equatorial Circumference is 4.02 * 107 m
Therefore rotational velocity = 4.02 * 107 / 460 = 0.00874 * 107 m/s = 8.74 * 104 m/s
14) The orbital velocity of the Earth is = 30 km/s.
15) Speed of light = 299792 km/s = 3 * 105 km/s
Distance from Earth to Sun is 150 million km = 150 * 106 km
Time = Distance from Earth to Sun / Speed of light = 500 second = 8.33 second.
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