Question
Asked Sep 1, 2019

The Moon’s mass is 1/80 that of Earth, and the lunar radius is 1/4 of Earth’s radius. Based on these figures, calculate the total weight on the Moon of a 100-kg astronaut with a 50-kg spacesuits and backpack, relative to his or her weight on Earth.

 

check_circleExpert Solution
Step 1

Given:

-(Where ME is the mass of the earth)
80
Mass of the moon, =
Lunar radius of moon, RM
(Where RE is the radius of the earth)
4
Total mass of the astronaut along with bagpack and spacesuit 150 kg
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-(Where ME is the mass of the earth) 80 Mass of the moon, = Lunar radius of moon, RM (Where RE is the radius of the earth) 4 Total mass of the astronaut along with bagpack and spacesuit 150 kg

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Step 2

Calculating the relation between acceleration due to gravity of moon and earth:

Let the acceleration due to gravity on moon is gM and on earth it is gE.

Acceleration due to gravity is defined as
GMg
gE=
-(1)
Similarly on moon, gM= GMM
Substitute My and R/
80
in equation (2),
4
E
G
80
GMg
gM
4
1GM
5R
E
gM
Using equation (1). gM =(g))
help_outline

Image Transcriptionclose

Acceleration due to gravity is defined as GMg gE= -(1) Similarly on moon, gM= GMM Substitute My and R/ 80 in equation (2), 4 E G 80 GMg gM 4 1GM 5R E gM Using equation (1). gM =(g))

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Step 3

Calculating the weight of the astronaut on the moon:

...
Total mass of the astronaut = (100+50) kg 150 kg
As we know, Weight (Mass) x (Acceleration due to gravity)
Acceleration due to gravity on earth, gE
9.81 m/s2
Weight of the astronaut on the earth = (Total mass) x (gE)
Weight of the astronaut on the earth
WE (150 kg)) X (9.81 m/s2) 1471.5 N ..(4)
9.8196 m/s
Acceleration due to gravity
(gz )=
on moon, gM
(gM)
Hence, weight of the astronaut on the moon =
(Total mass)
X
Total weight on moon, WM (150 kg) x (1.96 m/s2) 294.3 N ...(5)
294.3
W
From equation4 and 5,
1
W 1471.5 5
E
help_outline

Image Transcriptionclose

Total mass of the astronaut = (100+50) kg 150 kg As we know, Weight (Mass) x (Acceleration due to gravity) Acceleration due to gravity on earth, gE 9.81 m/s2 Weight of the astronaut on the earth = (Total mass) x (gE) Weight of the astronaut on the earth WE (150 kg)) X (9.81 m/s2) 1471.5 N ..(4) 9.8196 m/s Acceleration due to gravity (gz )= on moon, gM (gM) Hence, weight of the astronaut on the moon = (Total mass) X Total weight on moon, WM (150 kg) x (1.96 m/s2) 294.3 N ...(5) 294.3 W From equation4 and 5, 1 W 1471.5 5 E

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