Answer:
a)1500N
b)153.06kg
Explanation:
F = ma
g(moon) = is the acceleration due to gravity on the moon
g(earth) is the acceleration due to gravity on the earth
g(moon) = 1/6g(earth)
g(earth) =6g(moon)
F(gearth) = mg(earth)
= m 6g(moon)
= 6 × 250
= 1500N
b) F(gearth) = mg(earth)
m = F /g
= 1500/9.8
= 153.06kg
(a) 1500N
(b) 150kg, 150kg
Consider the following equation from Newton's law of gravitational force between two bodies A and B;
[tex]F_{g}[/tex] = m x g
Where;
[tex]F_{g}[/tex] = gravitational force between A and B on a space (e.g moon or earth)
m = mass of A or B
g = acceleration due to gravity on the given space. (e.g moon or earth)
Also;
The acceleration due to gravity ([tex]g_{e}[/tex]) on the earth is 6 times the acceleration due to gravity ([tex]g_{m}[/tex]) on the moon. i.e
[tex]g_{e}[/tex] = 6 x [tex]g_{m}[/tex]
=> [tex]g_{m}[/tex] = [tex]g_{e}[/tex] / 6
Assume in this case and;
Let body A be the suited astronaut
Let body B be the moon or the earth
This implies that;
[tex]F_{ge}[/tex] = m x [tex]g_{e}[/tex] ------------------(ii)
Where;
[tex]F_{ge}[/tex] = gravitational force between suited astronaut and Earth on Earth = Weight of the suited astronaut on Earth.
m = mass of suited astronaut
[tex]g_{e}[/tex] = acceleration due to gravity on the Earth (e.g moon or earth)
And;
[tex]F_{gm}[/tex] = m x [tex]g_{m}[/tex] ------------------(iii)
Where;
[tex]F_{gm}[/tex] = gravitational force between suited astronaut and the moon = Weight of the suited astronaut on the moon
m = mass of suited astronaut
g = acceleration due to gravity on the moon.
From equations (ii) and (iii)
[Remember that [tex]g_{e}[/tex] = 6 x [tex]g_{m}[/tex]], substitute this into equation (ii) as follows;
[tex]F_{ge}[/tex] = m x 6 x [tex]g_{m}[/tex] [re-arranging]
[tex]F_{ge}[/tex] = 6 x m x [tex]g_{m}[/tex] [Put [tex]F_{gm}[/tex] for m x [tex]g_{m}[/tex] ]
[tex]F_{ge}[/tex] = 6 x [tex]F_{gm}[/tex] ------------------(iv)
(a) To get the weight of the suited astronaut on Earth, we use equation (iv) as follows;
[tex]F_{ge}[/tex] = 6 x [tex]F_{gm}[/tex] ------------------------(v)
Where;
[tex]F_{gm}[/tex] = the weight of the suited astronaut on the moon = 250N
Substitute this into equation (v)
[tex]F_{ge}[/tex] = 6 x 250
[tex]F_{ge}[/tex] = 1500N
Therefore, the weight of the suited astronaut on the Earth is 1500N
(b)
(i) to get the mass on the moon, use equation (iii) as follows;
[tex]F_{gm}[/tex] = m x [tex]g_{m}[/tex]
Where;
[tex]F_{gm}[/tex] = 250N and
[tex]g_{m}[/tex] = [tex]g_{e}[/tex] / 6 [[tex]g_{e}[/tex] = g = 10m/s²]
[tex]g_{m}[/tex] = 10 / 6
[tex]g_{m}[/tex] = 1.6666667m/s²
Substitute these values into the equation above;
250 = m x 1.6666667
Solve for m;
m = [tex]\frac{250}{1.6666667}[/tex]
m = 150kg
(ii) to get the mass on the Earth, use equation (ii) as follows;
[tex]F_{ge}[/tex] = m x [tex]g_{e}[/tex]
Where;
[tex]F_{ge}[/tex] = 1500N and [tex]g_{e}[/tex] = g = 10m/s²
Substitute these values into the equation above;
1500 = m x 10
Solve for m;
m = [tex]\frac{1500}{10}[/tex]
m = 150kg
Therefore the masses of the suited astronaut on Moon and on Earth are the same and equal to 150kg
