What initial normal force would be exerted on an astronaut of mass m in a rocket

Question

What initial normal force would be exerted on an astronaut of mass m in a rocket traveling vertically upward with an acceleration a? Answer symbolically in terms of the positive quantities m, g, and a. (And others, see picture)

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LEARN MORE REMARKS Even taking gravity into account, the speed is sufficient to attain orbit. Some additional boost may be required to overcome air drag QUESTION What initial normal force would be exerted on an astronaut of mass m in a rocket traveling vertically upward with an acceleration a? Answer symbolically in terms of the positive quantities m, g, and a. OF=mg O F=m(a + g) 0 F = (m + Ma where M is the mass of the rocket O F=ma PRACTICE IT Use the worked example above to help you solve this problem. A rocket has a total mass of 1.15 x 105 kg and a burnout mass of 1.10 x 104 kg, including engines, shell and payload. The rocket blasts off from Earth and exhausts all its fuel in 3.97 min, burning the fuel at a steady rate with an exhaust velocity of v = 4.35 × 103 m/s. (a) If air friction and gravity are neglected, what is the speed of the rocket at burnout? m/s (b) What thrust does the engine develop at liftoff? (c) What is the initial acceleration of the rocket if gravity is not neglected? m/s (d) Estimate the speed at burnout if gravity isn't neglected m/s EXERCISE HINTS: GETTING STARTED I I'M STUCK! A spaceship with a mass of 4.50 x 104 kg is traveling at 6.32 x 103 m/s relative to a space station. What mass will the ship have after it fires its engines in order to reach a speed of 8.44 x 103 m/s? Assume an exhaust velocity of 4.12 x 103 m/s. kg

Explanation / Answer

The intial normal force will be:

F = m (a + g)

This is because, a is in upward direction and g acts downwards, so its -g

M = m (a - (-g)) = m (a + g)

Hence, F = m (a + g)

[Its a humble request to put one question at a time as per the guidelines. Pls put the other question separately. Kindly check and rate, let me know for any query in comment section. TIA and all the best].

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