Question

During lift off a rocket ship accelerates from rest to
about 28000 km/h and reaches an altitude of 300 km.
What is the apparent weight of a 75 kg astronaut during
this time (assume constant acceleration)? Explain why
does an astronaut feel weightless once in orbit?

Answer 1

As per the given question,

Initial velocity of the rocket ship (u)=0

Final velocity of the rocket ship (v)=28000 km/hour

Final height(h) = 300km

Now, applying newton's 3rd equation of motion,

$v^2= u^2+2ah$

$\Rightarrow a=\frac{v^2-u^2}{2h}$

Now, substituting the values,

$a=\frac{28000^2 -0}{2\times 300}=\frac{3920000k}{3} km/hour^2 =100.82 m/sec^2$

Hence, the apparent weight of the astronaut

$W= mg+ma =(75\times 9.8 + 75\times 100.82 )N$

$\Rightarrow W = 8296.5 N$

When he reached in the orbit then the gravitational force will be balanced by the centripetal force so the net reaction force on the astronaut will be zero. Hence He will experience weightlessness in the ship.