The weight of an object can be calculated using the formula:
Weight = Mass × Acceleration due to gravity
The gravitational force acting on the 75-kilogram object can be used to calculate the acceleration due to gravity. The formula for gravitational force is:
Force = (Gravitational constant × Mass of first object × Mass of second object) / (Distance between the objects)^2
Given that the force is 735 Newton, the mass of the Earth is approximately 5.972 × 10^24 kilograms, and the distance from the center of the Earth is 6400 km (which is 6400000 meters), we can rearrange the formula to solve for the acceleration due to gravity:
735 N = (Gravitational constant × 75 kg × 5.972 × 10^24 kg) / (6400000 m)^2
Solving for the gravitational constant gives:
Gravitational constant = (735 N × (6400000 m)^2) / (75 kg × 5.972 × 10^24 kg)
The gravitational constant, G, is approximately 6.674 × 10^-11 N(m/kg)^2.
Plugging in the values, we can calculate the gravitational constant:
Gravitational constant = (735 N × (6400000 m)^2) / (75 kg × 5.972 × 10^24 kg) Gravitational constant ≈ 6.674 × 10^-11 N(m/kg)^2
Now, we can calculate the acceleration due to gravity:
Acceleration due to gravity = (Gravitational constant × Mass of Earth) / (Distance from center of Earth)^2 Acceleration due to gravity ≈ (6.674 × 10^-11 N(m/kg)^2 × 5.972 × 10^24 kg) / (6400000 m)^2
With the value of the acceleration due to gravity, we can calculate the weight of an object. Assuming the object is on or near the Earth's surface, the standard value for acceleration due to gravity is approximately 9.8 m/s^2.
Weight = Mass × Acceleration due to gravity Weight ≈ Mass × 9.8 m/s^2
Please provide the mass of the object for a more specific weight calculation.