Answer:
if an astronaut weighs 981 N on Earth and only 160 N on the Moon, then what is his mass on the Moon?
ANSWER 256n
The mass of the astronaut on the moon as compared to the earth will be [tex]M_m=97.85\ lg[/tex]
The mass of any substance or body is defined as how much quantity of matter is present.
Now it is given in the question:
Weight of the astronaut on earth [tex]W_E=981\ N[/tex]
Weight of the astronaut on earth [tex]W_M=160\ N[/tex]
The mass of the astronaut on the moon will be calculated as:
Weight on the moon will be given as:
[tex]W_M=M_M\times g_m[/tex]
Weight on the earth will be given as:
[tex]W_E=M_E\times g_e[/tex]
The ratio of the gravity of the earth to the moon is given as
[tex]\dfrac{g_e}{g_m} =\dfrac{9.81}{1.62} =6[/tex]
The mass of the earth will be calculated as
[tex]W_E=M_E\times ge[/tex]
[tex]M_E=\dfrac{981}{9.81} =100\ kg[/tex]
Now taking the ratio of the weight of the earth to the moon :
[tex]\dfrac{W_E}{W_M} =\dfrac{M_E\times g_e}{M_M\times g_m}[/tex]
[tex]M_M= \dfrac{W_M\times M_E}{W_E} \times \dfrac{g_e}{g_m}[/tex]
Now by putting the value in the formula we get;
[tex]M_M=\dfrac{160\times 100}{981} \times 6=97.85\ kg[/tex]
Thus the mass of the astronaut on the moon as compared to the earth will be [tex]M_m=97.85\ lg[/tex]
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