Gravitational Forces - Questions

Question

1. A person weighs 950 N on Earth. Determine their weight on the moon if the gravitational field strength is 1.62 N/kg.
2. The asteroid Ceres has a mass 7.20 x 10^20 kg and a radius of 500 km. How much would a 720 N astronaut weigh on Ceres?

Answer 1

1.A person weighs 950 N on Earth. Determine their weight on the moon if the gravitational field strength is 1.62 N/kg.

The key to this problem is finding the mass of the individual in order to find the force of gravity on the moon (F_m)

F_e = ma_e

950N = (m)(9.8)

m = 950/9.8 = 96.94 kg

F_m = ma_m

F_m = (96.94 kg)(1.62N/kg) = 157.04 N

2.The asteroid Ceres has a mass 7.20 x 10^20 kg and a radius of 500 km. How much would a 720 N astronaut weigh on Ceres?

F_e = ma_e

720N = (m)(9.8)

m = 720/9.8 = 73.47 kg

F_c = k(m₁)(m_ceres)/r²

F_c = 6.67x10^-11(73.47)(7.20x10²⁰)/(500*10³)²

F_c = 14.11 N