Final answer:
The force of gravitation between the Earth and a man with a mass of 80 kg can be calculated using Newton's universal law of gravitation and is found to be approximately 801.14 newtons.
Step-by-step explanation:
The force of gravitation between the Earth and a man can be calculated using Newton's universal law of gravitation, which states that the force of gravitation (F) is equal to the gravitational constant (G) multiplied by the mass of the first object (m1) and the mass of the second object (m2), divided by the square of the distance (r) between their centers of mass.
Using the provided values, which are the mass of Earth (6×1024 kg), the radius of Earth (6.32×106 m), and the mass of the man (80 kg), we can plug these into the universal law of gravitation formula:
F = G × (m1 × m2) / r2
Given that the gravitational constant (G) is 6.674×10-11 N·m2 kg-2. We calculate the force of gravitation as follows:
F = (6.674×10-11) × (80 kg × 6×1024 kg) / (6.32×106 m)2
F = (6.674×10-11) × (4.8×1026 kg2) / (3.9942×1013 m2)
F ≈ 801.14 N
Thus, the force of gravitation between the Earth and a man with a mass of 80 kg is approximately 801.14 newtons.