You\'re an engineer working on Ares I, NASA\'s replacement for the space shuttle

Question

You're an engineer working on Ares I, NASA's replacement for the space shuttles. Performance specs call for a first-stage rocket capable of accelerating a total mass of 630 Mg vertically from rest to 7600 km/h in 1.8 min. You're asked to determine the required engine thrust (force). What do you report? Express your answer to two significant figures and include the appropriate units. You're asked to determine the force exerted on a 80-kg astronaut during liftoff. What do you report? Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

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The initial velocity is 0, the final velocity is 7600 km/h = 2111 m/s

Assuming uniform acceleration, the acceleration is

a = (Vf - V0)/t = (2111 m/s - 0m/s)/(1.8 * 60s) = 19.54 m/s^2

Hence the force (thrust) on the mass 5.90 * 10^5 kg to achieve this acceleration against gravity is

F = m (a + g) = 630 * 10^6 kg * (19.54 m/s^2 - 9.8 m/s^2) = 6.136 * 10^9 N

The 80 kg astronaut will experience a force of

F = m (a + g) = 80 kg * (19.54 m/s^2 -9.8 m/s^2) = 779 N

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