What is the force?

Question

A spaceman of mass 80 kg is sitting in a spacecraft near the surface of the Earth. The spacecraft is accelerating upward at five times the acceleration due to gravity. What is the force of the spaceman on the spacecraft?

 

Answer: 4800 N

Answer 1

By Newton's 3rd law, the force of the spaceman on the spacecraft is equal and opposite to the force of the spacecraft on the spaceman, which is the normal force, F_n. From Newton's 2nd law,

F = F_n - mg = ma =m (5g)

F_n = 6mg = 6*80kg*9.8m/s² ≈ 4800 N.

Answer 2

Apply Newton's second law in vertical direction:

F - mg = ma

But a = 5g. So,

F = 6mg = 6*80*10 = 4800 N, where g = 10 m/sec^2