The moon is the Earth's nearest neighbour in space. The radius of the moon is approximately one quarter of the Earth's radius, and its mass is one eightieth of the Earth's mass.

a) Culculate the weight of a man with a mass of 80kg on the surface of the moon.

b) Culculate the weight of a man with a mass of 80kg when it is at a distance equal to three times the moon's radius away from the moon.

What is asked o fAndy has a mass of 68.5 kg.What is his weight on earth and in the moon.

a)156N

b)17,4N

a) F= 1/80/(1/4d)^2

F=1/80/1/16d^2
F=1/80X16/1
F=answer
step2
F=9,8XanswerX80
F=156N or 156,8N

b)F=156/(3d)^2
156/9d^2
F=17,4N

To calculate the weight of a man on the surface of the moon and at a distance away from the moon, we need to use the formula for weight:

Weight = mass x gravitational acceleration

The gravitational acceleration on the surface of the moon is approximately one-sixth of the gravitational acceleration on Earth. Let's denote Earth's gravitational acceleration as g and the moon's gravitational acceleration as g_moon.

a) To calculate the weight of a man with a mass of 80kg on the surface of the moon:

Weight = mass x g_moon
Weight = 80kg x (1/6)g (since the moon's gravitational acceleration is one-sixth that of Earth)

To find the value of g, which is the gravitational acceleration on Earth, we can use the formula:

g = G x (M/r^2)

where G is the gravitational constant, M is the mass of Earth, and r is the radius of Earth.

Given that the radius of the moon is approximately one-fourth the radius of the Earth, we can write:

r_moon = (1/4) x r

Also, given that the mass of the moon is one-eightieth the mass of Earth, we can write:

M_moon = (1/80) x M

Substituting these values into the formula for gravitational acceleration on Earth, we have:

g = G x (M/r^2)
= G x (M_moon / r_moon^2)
= G x ( (1/80)M ) / ( (1/4)^2 x r^2 )
= G x (1/80)M / (1/16) x r^2
= G x (1/80)M / (1/256) x r^2
= G x 256/80 x M / r^2
= (G x 256/80) x M / r^2
= (256/80)g

So, we find that g = (256/80)g.

Substituting this value of g into the equation for the weight of a man on the moon's surface, we get:

Weight = 80kg x (1/6)g
= 80kg x (1/6) x (256/80)g
= 80kg x (256/480)g
= 42.67kg x g

Therefore, the weight of a man with a mass of 80kg on the surface of the moon is approximately 42.67 kg x g.

b) To calculate the weight of a man with a mass of 80kg when they are at a distance equal to three times the moon's radius away from the moon:

The gravitational acceleration experienced by the man at this distance can be calculated using the formula:

g_distance = G x (M_moon / distance^2)

Substituting the given values, we have:

g_distance = G x ( (1/80)M ) / ( (3 x r_moon)^2 )
= G x ( (1/80)M ) / (9 x r_moon^2)

Now, we can substitute the value of g_distance into the equation for weight:

Weight = 80kg x g_distance
= 80kg x [G x ( (1/80)M ) / (9 x r_moon^2)]

Using the previous calculations, we found that the gravitational acceleration on the moon's surface is (256/80)g. Substituting this value, we get:

Weight ≈ 80kg x [(G x ( (1/80)M ) / (9 x r_moon^2)) / (256/80)g]

Simplifying, we have:

Weight ≈ 80kg x [(G x (1/80) x M) / (9 x r_moon^2 x (256/80))]

Finally, substituting the values of r_moon, M_moon, and G, we get:

Weight ≈ 80kg x [(6.67430 x 10^-11 N m^2/kg^2 x (1/80) x 5.972 x 10^24 kg) / (9 x (1/4)^2 x (2.44 x 10^6 m)^2 x (256/80))]

After simplifying and calculating the value, we can find the weight of a person with an 80kg mass at a distance of three times the moon's radius from the moon.