Earth has a mass of 5.97 x 1024 kg and a radius of 6.38 x 106 m, while saturn has a mass of 5.68 x 1026 kg and a radius of 6.03 x 107 m. find the weight of a 65.0 kg person at the following locations? a) on the surface of the earth. b) 1000 km above the surface of earth. c) on the surface of saturn. d) 1000 km above the surface of saturn.

Asked by maham237 @ 13/01/2021 in Physics viewed by 571 People

Answered by maham237 @ 13/01/2021

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:

$W = mg$ (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:

$g = \frac{GM}{r^{2}}$ (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:

$W = m \frac{GM}{r^{2}}$ (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:

$W = m \frac{GM}{r^{2}} = 65.0 kg \frac{6.67 \cdot 10^{-11} \frac{m^{3}}{kg.s^{2}} \cdot 5.97 \cdot 10^{24} kg}{(6.38 \cdot 10^{6}m)^{2}} = 635.9 N$

(b) 1000 km above the surface of Earth, r = 6.38x10⁶m + 10⁶m = 7.38x10⁶m:

$W = m \frac{GM}{r^{2}} = 65.0 kg \frac{6.67 \cdot 10^{-11} \frac{m^{3}}{kg.s^{2}} \cdot 5.97 \cdot 10^{24} kg}{(7.38 \cdot 10^{6}m)^{2}} = 475.2 N$

(c) On the surface of Saturn, r = 6.03x10⁷m, and M= 5.68x10²⁶kg:

$W = m \frac{GM}{r^{2}} = 65.0 kg \frac{6.67 \cdot 10^{-11} \frac{m^{3}}{kg.s^{2}} \cdot 5.68 \cdot 10^{26} kg}{(6.03 \cdot 10^{7}m)^{2}} = 677.3 N$

(d) 1000 km above the surface of Saturn, r = 6.03x10⁷m + 10⁶m = 6.13x10⁷m:

$W = m \frac{GM}{r^{2}} = 65.0 kg \frac{6.67 \cdot 10^{-11} \frac{m^{3}}{kg.s^{2}} \cdot 5.68 \cdot 10^{26} kg}{(6.13 \cdot 10^{7}m)^{2}} = 655.3 N$

I hope it helps you!

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