A man weighs 750 N 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 0 kg and 7 36 0 kg. Their radii are respectively 6 37 0 km and
1 74 0 km

W = 750N/6 = 125 N. on the moon.

Weight of a person on Earth: 750N

Gravity of Moon:1/6 of Earth's gravity
Weight of a person on Moon:750÷ 6
:125 N

To calculate the weight of a man on the moon, we can use the formula:

Weight = Gravity force = Mass x Acceleration due to gravity

The acceleration due to gravity on the surface of earth (gE) can be calculated using the formula:

gE = (G * ME) / RE^2

where G is the gravitational constant (approximately 6.67 x 10^-11 Nm^2/kg^2), ME is the mass of the Earth, and RE is the radius of the Earth.

Similarly, the acceleration due to gravity on the surface of the moon (gM) can be calculated using the formula:

gM = (G * MM) / RM^2

where MM is the mass of the Moon, and RM is the radius of the Moon.

To find the weight of the man when standing on the moon, we can use the formula:

Weight on Moon = Mass x Acceleration due to gravity on Moon

Now let's perform the calculations step by step.

Step 1: Find the acceleration due to gravity on Earth (gE)
Given:
ME = 5.98 x 10^24 kg (mass of the Earth)
RE = 6.37 x 10^6 m (radius of the Earth)
G = 6.67 x 10^-11 Nm^2/kg^2 (gravitational constant)

Calculation:
gE = (G * ME) / RE^2
= (6.67 x 10^-11 Nm^2/kg^2 * 5.98 x 10^24 kg) / (6.37 x 10^6 m)^2
≈ 9.81 m/s^2

Therefore, the acceleration due to gravity on Earth is approximately 9.81 m/s^2.

Step 2: Find the acceleration due to gravity on the Moon (gM)
Given:
MM = 7.36 x 10^22 kg (mass of the Moon)
RM = 1.74 x 10^6 m (radius of the Moon)

Calculation:
gM = (G * MM) / RM^2
= (6.67 x 10^-11 Nm^2/kg^2 * 7.36 x 10^22 kg) / (1.74 x 10^6 m)^2
≈ 1.62 m/s^2

Therefore, the acceleration due to gravity on the Moon is approximately 1.62 m/s^2.

Step 3: Find the weight of the man on the Moon
Given:
Weight on Earth = 750 N

Calculation:
Weight on Moon = Mass x Acceleration due to gravity on Moon
= Mass x gM

Since the mass of the man does not change, we can directly use the weight on Earth in this step.

Weight on Moon ≈ Weight on Earth x (gM / gE)
= 750 N x (1.62 m/s^2 / 9.81 m/s^2)
≈ 124 N

Therefore, the weight of the man when standing on the Moon is approximately 124 N.

To calculate the weight of a person on the moon, we need to understand the concept of weight and how it is affected by gravity.

Weight is the measure of the gravitational force acting on an object. It depends on the mass of the object and the gravitational acceleration experienced by the object.

On Earth, the weight of an object can be calculated using the equation:

Weight = mass * gravitational acceleration

The mass of the person is not given directly, but instead, we are provided with the weight of the person on Earth, which is 750 N (Newtons). To find the mass, we can rearrange the equation:

mass = Weight / gravitational acceleration

The gravitational acceleration on Earth is approximately 9.8 m/s^2.

Now, let's calculate the mass of the person:

mass = 750 N / 9.8 m/s^2 ≈ 76.53 kg

Now that we know the mass of the person, we can calculate their weight on the moon. The weight of the person on the moon can be calculated using the same equation as before, but this time we need to use the gravitational acceleration on the moon.

The gravitational acceleration on the moon can be calculated using the following formula:

g_moon = (mass_moon * G) / (radius_moon^2)

where:
- mass_moon is the mass of the moon (7.36 x 10^22 kg),
- G is the universal gravitational constant (6.67 x 10^-11 N m^2/kg^2),
- radius_moon is the radius of the moon (1,740 km or 1,740,000 m).

Now, let's calculate the gravitational acceleration on the moon:

g_moon = (7.36 x 10^22 kg * 6.67 x 10^-11 N m^2/kg^2) / (1,740,000 m)^2
≈ 1.62 m/s^2

Finally, we can calculate the weight of the person on the moon using the mass of the person and the gravitational acceleration on the moon:

Weight_moon = mass * gravitational acceleration_moon
= 76.53 kg * 1.62 m/s^2
≈ 124.01 N

Therefore, the person would weigh approximately 124.01 N when standing on the moon.