Assume that you have a mass of [tex]50.0 \, \text{kg}[/tex] and Earth has a mass of [tex]5.97 \times 10^{24} \, \text{kg}[/tex]. The radius of Earth is [tex]6.38 \times 10^{6} \, \text{m}[/tex]. What is the force of gravitational attraction between you and the Earth?
Answer (3)
490 N is the force of gravitational attraction between the person and the Earth.
To determine the force of gravitational attraction between you and the Earth, we use Newton's law of universal gravitation:
F = G r 2 m 1 m 2
Plugging in the values, we get:
F = G r 2 m 1 m 2 = 6.674 × 1 0 − 11 ( 6.38 × 1 0 6 m ) 2 ( 50.0 kg ) ( 5.97 × 1 0 24 kg )
First, calculate the denominator:
r 2 = ( 6.38 × 1 0 6 m ) 2 = 4.07 × 1 0 13 m 2
Next, calculate the numerator:
m 1 m 2 = ( 50.0 kg ) ( 5.97 × 1 0 24 kg ) = 2.985 × 1 0 26 kg 2
Now, put it all together:
F = 6.674 × 1 0 − 11 4.07 × 1 0 13 m 2 2.985 × 1 0 26 kg 2
F = 6.674 × 1 0 − 11 × 7.336 × 1 0 12 N
F ≈ 4.90 × 1 0 2 N
Therefore, the force of gravitational attraction between you and the Earth is approximately 490 N.
The force of gravitational attraction between you (of mass 50kg) and the Earth (of mass 5.97x10^24 kg) can be calculated using Newton's Universal Law of Gravitation. Substituting the respective values in the formula, the calculated force is approximately 490.5 N. ;
The force of gravitational attraction between you and the Earth can be calculated using Newton's Universal Law of Gravitation, resulting in approximately 490.5 N. This value represents your weight at the Earth's surface. The calculation involves the mass of you and the Earth along with the distance between their centers.
;
