the upward acceleration of saturn rocket shortly after blast-off is 80 m/s.when the saturn rocket is accelerating ,what is the apperent weight of the astourant ,that is ,what does the astourant experience as the weight of his body ?show calculations .answer must be in newtons?
Let the mass of the astronaut be M kg.
Acceleration a = 80 m/s^2 upward
Let `N_r` = normal reaction on the astronaut from the floor.
Apparent weight is the same as the normal reaction on the astronaut from the rocket floor.
Forces on the astronaut are:
1. `N_r` upward
2. `M*g` downward
3. `M*a` upward
Assuming, g remains unchanged shortly after blast-off, i.e. when the rocket is not too far away from the Earth, equating the forces in vertical direction:
`N_r-Mg = Ma`
`N_r = M(a + g)`
`N_r = M* (80 + 9.8)`
`N_r = M * 89.8 N`
Therefore, the apparent weight of the astronaut is 89.8*M Newtons.