Question

The weight of an astronaut plus his space suit on the Moon is only 250 N. (a) How much does the suited astronaut weigh on Earth? (b) What is the mass on the Moon? On Earth?

Answer 1

Answer:

(a) 1500N

(b) 150kg, 150kg

Explanation:

Consider the following equation from Newton's law of gravitational force between two bodies A and B;

$F_{g}$ = m x g

Where;

$F_{g}$ = 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 ($g_{e}$) on the earth is 6 times the acceleration due to gravity ($g_{m}$) on the moon. i.e

$g_{e}$ = 6 x $g_{m}$

=> $g_{m}$ = $g_{e}$ / 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;

$F_{ge}$ = m x $g_{e}$          ------------------(ii)

Where;

$F_{ge}$ = gravitational force between suited astronaut and Earth on Earth = Weight of the suited astronaut on Earth.

m = mass of suited astronaut

$g_{e}$ = acceleration due to gravity on the Earth (e.g moon or earth)

And;

$F_{gm}$ = m x $g_{m}$           ------------------(iii)

Where;

$F_{gm}$ = 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 $g_{e}$ = 6 x $g_{m}$], substitute this into equation (ii) as follows;

$F_{ge}$ = m x 6 x $g_{m}$         [re-arranging]

$F_{ge}$ = 6 x m x $g_{m}$         [Put $F_{gm}$ for m x $g_{m}$  ]

$F_{ge}$ = 6 x $F_{gm}$             ------------------(iv)

(a) To get the weight of the suited astronaut on Earth, we use equation (iv) as follows;

$F_{ge}$ = 6 x $F_{gm}$  ------------------------(v)

Where;

$F_{gm}$ = the weight of the suited astronaut on the moon = 250N

Substitute this into equation (v)

$F_{ge}$ = 6 x 250

$F_{ge}$ = 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;

$F_{gm}$ = m x $g_{m}$

Where;

$F_{gm}$ = 250N and

$g_{m}$ = $g_{e}$ / 6             [$g_{e}$  = g = 10m/s²]

$g_{m}$ = 10 / 6

$g_{m}$ = 1.6666667m/s²

Substitute these values into the equation above;

250 = m x 1.6666667

Solve for m;

m = $\frac{250}{1.6666667}$

m = 150kg

(ii) to get the mass on the Earth, use equation (ii) as follows;

$F_{ge}$ = m x $g_{e}$

Where;

$F_{ge}$ = 1500N and $g_{e}$  = g = 10m/s²

Substitute these values into the equation above;

1500 = m x 10

Solve for m;

m = $\frac{1500}{10}$

m = 150kg

Therefore the masses of the suited astronaut on Moon and on Earth are the same and equal to 150kg

Answer 2

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