What would be the weight of a 59.1-kg astronaut on a planet with the same density as Earth and having twice Earth's radius? . . I am getting 290, but I dont know if that is correct... . A) 580N. B) 290N. C) 1160N. D) 2320N. E) 1200N

Question

23-06-2016
Physics

contestada

What would be the weight of a 59.1-kg astronaut on a planet with the same density as Earth and having twice Earth's radius? . . I am getting 290, but I dont know if that is correct... . A) 580N. B) 290N. C) 1160N. D) 2320N. E) 1200N

Respuesta :

Otras preguntas

When liquid water is heated to 100° c, it boils and becomes water vapor. when the vapor is cooled below 100° c, it turns back into a liquid. what is the correct

Find the largest cold front located on the map. the likely air mass to the west of the cold front is a _______ air mass which is likely to be __________ than th

The area of a rectangular wall of a barn is 208 square feet. It’s length is 10 feet longer than twice it’s width. Find the length and width of the wall of the b

Between january 2010 and january 2016, u.s. employment increased by 12.1 million workers, but the number of unemployed workers declined by only 7.3 million. tru

¿ cuáles son ejemplos de platos españoles ?

In the Roman republic _____.

What evidence does the author provide in the opening sentence of the story and the paragraph that follows to suggest the risk that the main character will take

Point R on the coordinate grid below shows the location of a car in a parking lot. A second car needs to park 7 units above R to leave room for a utility truck.

Which statement is a likely interpretation of Williams's use of the word "unsignificantly" in his poem? A. Icarus was punished for his immense pride. B. The s

The science class is taking a trip to the science center. there are 20 students and an unknown number of adult chaperones going. the bus holds at most 35 people

meerkat18 meerkat18 · Answer 1 · 2016-07-03T10:25:42+02:00

The astronaut's weight on the Earth's surface can be determined from
F = m g = 579.2 N subsituting mass equal to 59.1 kg and acceleration due to gravity equal to 9.8 m/s². When the variables are mass of the earth and the radius of the earth, F = k m / r². Thus, doubling the mass of the earth would double his weight and doubling the radius would decrease the original weight by 1/4. Hence, 579.2 N* 2* 1/4 equal to 290 N. Answer is B.

johanrusli johanrusli · Answer 2 · 2019-12-21T04:28:05+01:00

The weight of a 59.1-kg astronaut on a planet would be about

C) 1160 N

[tex]\texttt{ }[/tex]

Further explanation

Newton's gravitational law states that the force of attraction between two objects can be formulated as follows:

[tex]\large {\boxed {F = G \frac{m_1 ~ m_2}{R^2}} }[/tex]

F = Gravitational Force ( Newton )

G = Gravitational Constant ( 6.67 × 10⁻¹¹ Nm² / kg² )

m = Object's Mass ( kg )

R = Distance Between Objects ( m )

Let us now tackle the problem !

[tex]\texttt{ }[/tex]

Given:

mass of the astronaut = m = 59.1 kg

density of Earth = density of Planet = ρ

radius of Earth = R₁ = R

radius of Planet = R₂ = 2R

Asked:

weight of the astronaut on planet = w₂ = ?

Solution:

We will compare the weight of the astronaut on planet and earth as follows:

[tex]w_2 : w_1 = mg_2 : mg_1[/tex]

[tex]w_2 : w_1 = g_2 : g_1[/tex]

[tex]w_2 : w_1 = G\frac{m_2}{(R_2)^2} : G\frac{m_1}{(R_1)^2}[/tex]

[tex]w_2 : w_1 = G\frac{\rho V_2}{(R_2)^2} : G\frac{\rho V_1}{(R_1)^2}[/tex]

[tex]w_2 : w_1 = \frac{V_2}{(R_2)^2} : \frac{V_1}{(R_1)^2}[/tex]

[tex]w_2 : w_1 = \frac{\frac{4}{3} \pi (R_2)^3}{(R_2)^2} : \frac{\frac{4}{3} \pi (R_1)^3}{(R_1)^2}[/tex]

[tex]w_2 : w_1 = R_2 : R_1[/tex]

[tex]w_2 : w_1 = 2R : R[/tex]

[tex]w_2 : w_1 = 2 : 1[/tex]

[tex]w_2 = 2w_1[/tex]

[tex]w_2 = 2m g_1[/tex]

[tex]w_2 = 2(59.1)(9.8)[/tex]

[tex]w_2 \approx 1160 \texttt{ Newton}[/tex]

[tex]\texttt{ }[/tex]

Learn more

Impacts of Gravity : https://brainly.com/question/5330244
Effect of Earth’s Gravity on Objects : https://brainly.com/question/8844454
The Acceleration Due To Gravity : https://brainly.com/question/4189441

[tex]\texttt{ }[/tex]

Answer details

Grade: High School

Subject: Physics

Chapter: Gravitational Fields