Your an engineer working on Ares 1, NASA's replacement for the space shuttles, performance specs call for a first -stage rocket capable of accelerating a total mass of 660Mg vertically from rest to 7700 km/h in 1.7 min. Your asked to determine the required thrust (force). What do you report?

Question

Your an engineer working on Ares 1, NASA's replacement for the space shuttles, performance specs call for a first -stage rocket capable of accelerating a total mass of 660Mg vertically from rest to 7700 km/h in 1.7 min. Your asked to determine the required thrust (force).  What do you report?

shane_b · Answer

Ok, first I'd convert everything to the same units:

7700 km/h = 2138.89 m/s
660Mg = 660000kg
1.7min = 102s

Ok, let's see what our acceleration needs to be to reach that speed.  Using one of the kinematic equations you get:
$$V_f=V_i+at$$$$2138.89m/s=0m/s+a_{net}(102s)$$$$a_{net}=20.97m/s^2$$
Now let's not forget to add in the acceleration we need to overcome the acceleration due to gravity:$$a_{total}=a_{net}+a_g=20.97m/s^2 + 9.81m/s^2=30.78m/s^2$$
Ok finally, let's calculate the force needed now that we know the total acceleration required:$$F=ma=(660000kg)(30.78m/s^2)=20314800N=20.3148 MN$$