Answer:
(a) W = 635.9 N
(b) W = 475.2 N
(c) W = 677.3 N
(d) W = 655.3 N
Explanation:
A person weight is given by the following equation:
[tex] W = mg [/tex] (1)
Where W: is the person weight, m: is the person mass, and g is the acceleration due to gravity.
The acceleration due to gravity, g, is:
[tex] g = \frac{GM}{r^{2}} [/tex] (2)
Where G: is the gravitational constant = 6.67x10⁻¹¹ m³kg⁻¹s⁻², M: is the planet mass, and r: is the total radius
By introducing equation (2) into (1), we have:
[tex] W = m \frac{GM}{r^{2}} [/tex] (3)
With equation (3) we will find the weight of the person in all locations:
(a) On the surface of the Earth, r is the Earth's radius = 6.38x10⁶m and M is the Earth's mass = 5.97x10²⁴kg:
[tex] W = m \frac{GM}{r^{2}} = 65.0 kg \frac{6.67 \cdot 10^{-11} \frac{m^{3}}{kg.s^{2}} \cdot 5.97 \cdot 10^{24} kg}{(6.38 \cdot 10^{6}m)^{2}} = 635.9 N [/tex]
(b) 1000 km above the surface of Earth, r = 6.38x10⁶m + 10⁶m = 7.38x10⁶m:
[tex] W = m \frac{GM}{r^{2}} = 65.0 kg \frac{6.67 \cdot 10^{-11} \frac{m^{3}}{kg.s^{2}} \cdot 5.97 \cdot 10^{24} kg}{(7.38 \cdot 10^{6}m)^{2}} = 475.2 N[/tex]
(c) On the surface of Saturn, r = 6.03x10⁷m, and M= 5.68x10²⁶kg:
[tex] W = m \frac{GM}{r^{2}} = 65.0 kg \frac{6.67 \cdot 10^{-11} \frac{m^{3}}{kg.s^{2}} \cdot 5.68 \cdot 10^{26} kg}{(6.03 \cdot 10^{7}m)^{2}} = 677.3 N[/tex]
(d) 1000 km above the surface of Saturn, r = 6.03x10⁷m + 10⁶m = 6.13x10⁷m:
[tex] W = m \frac{GM}{r^{2}} = 65.0 kg \frac{6.67 \cdot 10^{-11} \frac{m^{3}}{kg.s^{2}} \cdot 5.68 \cdot 10^{26} kg}{(6.13 \cdot 10^{7}m)^{2}} = 655.3 N[/tex]
I hope it helps you!
