A space traveler weighs 620 N on earth. What will the traveler weigh on another planet whose radius is three times that of earth and whose mass is twice that of earth?
To find the weight of the space traveler on another planet, we need to use the formula:
Weight = (mass of the object) × (acceleration due to gravity)
1. First, we need to establish the mass of the space traveler. However, the problem doesn't provide the mass directly, but instead gives us the weight on Earth, which is 620 N.
2. To find the mass, we can use the formula:
Weight = mass × (acceleration due to gravity)
On Earth, the acceleration due to gravity is approximately 9.8 m/s². Rearranging the formula, we have:
mass = Weight / (acceleration due to gravity)
mass = 620 N / 9.8 m/s²
mass ≈ 63.27 kg
3. Now that we have the mass of the space traveler, we can calculate the weight on the other planet.
Given that the other planet has twice the mass of Earth and a radius three times that of Earth, the acceleration due to gravity on the other planet can be computed using the formula:
acceleration due to gravity = (gravitational constant × mass of the planet) / (radius of the planet)²
For this calculation, we will assume Earth's gravitational constant (G) as 6.67 × 10⁻¹¹ N m²/kg².
acceleration due to gravity = (6.67 × 10⁻¹¹ N m²/kg² × 2 × (mass of Earth)) / (3 × (radius of Earth)²)
acceleration due to gravity ≈ 2.96 m/s²
4. Finally, we can calculate the weight of the space traveler on the other planet using the formula:
Weight = mass of the space traveler × acceleration due to gravity on the other planet
Weight = 63.27 kg × 2.96 m/s²
Weight ≈ 187.25 N
Therefore, the space traveler would weigh approximately 187.25 N on another planet with twice the mass of Earth and a radius three times that of Earth.