a man has a mass of 70kg on Earth he is walking on a new planet that has a mass four times that of the Earth and the radius is the same as that of the Earth[Me=6x10 to the power of 24 kg re=6x10 to the power of 6 m calculate the man's weight
To calculate the man's weight on the new planet, we need to understand the concept of gravitational force and how it depends on mass and distance.
The gravitational force experienced by an object is given by the formula:
F = (G * m1 * m2) / r^2
Where:
- F is the gravitational force between two objects.
- G is the gravitational constant (approximately 6.67430 × 10^-11 N(m/kg)^2).
- m1 and m2 are the masses of the two objects.
- r is the distance between the centers of the two objects.
In this case, we can assume that the man's mass (m1) remains the same, the gravitational constant (G) remains constant, and the radius (r) is the same as Earth's radius.
Let's calculate the weight of the man on the new planet.
Step 1: Calculate the mass of the new planet.
Given:
Mass of the Earth (m2) = 6 × 10^24 kg
Mass of the new planet (M) = 4 * (Mass of the Earth)
M = 4 * (6 × 10^24 kg)
M = 24 × 10^24 kg
Step 2: Calculate the weight of the man on the new planet.
Weight (W) = gravitational force on the man
Using the formula, F = (G * m1 * m2) / r^2, we can calculate the weight:
W = (G * m1 * M) / r^2
Plug in the given values:
W = (6.67430 × 10^-11 N(m/kg)^2 * 70 kg * 24 × 10^24 kg) / (6 × 10^6 m)^2
After simplification, we can calculate the value using a calculator:
W ≈ 127.090 N
Therefore, the man's weight on the new planet is approximately 127.090 Newtons.