Question

A man weighs 750N on the surface of the earth. What would be his weight when standing on the moon? The masses of the earth and the moon are respectively (5.98 x 10 raise to power 24) kg and (7.36 x 10 raise to power 22) kg. Their radii are (6.37 x 10 raise to power 3) km and (1.74 x 10 raise to power 3) km respectively.

Answer 1

Answer on Question 55221, Physics, Mechanics | Kinematics | Dynamics

Question:

A man weighs $750N$ on the surface of the Earth. What would be his weight when standing on the Moon? The masses of the Earth and the Moon are respectively $5.98 \cdot 10^{24}kg$ and $7.36 \cdot 10^{22}kg$. Their radii are $6.37 \cdot 10^{3}km$ and $1.74 \cdot 10^{3}km$ respectively.

Solution:

Let's write the acceleration due to gravity on the surface of the Earth:

$$g_{E} = \frac{GM_{E}}{R_{E}^{2}},$$

where, $G$ is the gravitational constant, $M_{E}$ is the mass of the Earth and $R_{E}$ is the radius of the Earth.

Similarly we can write the acceleration due to gravity on the surface of the Moon:

$$g_{M} = \frac{GM_{M}}{R_{M}^{2}},$$

where, $G$ is the gravitational constant, $M_{M}$ is the mass of the Moon and $R_{M}$ is the radius of the Moon.

Let's take the ratio between $g_{E}$ and $g_{M}$:

$$\frac{g_{E}}{g_{M}} = \frac{M_{E} R_{M}^{2}}{R_{E}^{2} M_{M}}.$$

From this expression we can find $g_{M}$:

$$g_{M} = g_{E} \frac{R_{E}^{2} M_{M}}{M_{E} R_{M}^{2}} = 9.8 \frac{m}{s^{2}} \cdot \frac{(6.37 \cdot 10^{6} m)^{2} \cdot 7.36 \cdot 10^{22} kg}{5.98 \cdot 10^{24} kg \cdot (1.74 \cdot 10^{6} m)^{2}} = 1.62 \frac{m}{s^{2}}.$$

By the definition of the weight we have:

$$W_{E} = m g_{E},$$

where, $W_{E}$ is the weight of the man on the surface of the Earth, $m$ is the mass of the man, and $g_{E}$ is the acceleration due to gravity on the surface of the Earth.

Then, from this formula we can find the mass of the man:

$$m = \frac {W _ {E}}{g _ {E}} = \frac {750\,N}{9.8\,\frac {m}{s^{2}}} = 76.5\,kg.$$

Finally, from the similar formula we can find the weight of the man on the surface of the Moon:

$$W _ {M} = m g _ {M} = 76.5\,kg \cdot 1.62\,\frac {m}{s^{2}} = 124\,N.$$

Answer:

$$W _ {M} = 124\,N.$$

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