NASA
would like a rocket to accelerate upward at a rate of 125 ft/s^{2}. The mass of the rocket is 35,000 lb_{m}. Determine the upward thrust force,
in lb_{f}, that the rocket engine must produce. 











Read: 
This is a direct
application of Newton's 2nd Law of Motion in the AE System of units.
The key to solving this problem is a clear understanding of g_{c}. 










Given: 
m 
35000 
lb_{m} 


g_{c} 
32.174 
lb_{m}ft/lb_{f}s^{2} 

a 
125 
ft/s^{2} 
















Find: 
F_{up} 
??? 
lb_{f} 
















Assumptions: 
1 Assume: 
g 
32.174 
ft/s^{2} 














Equations
/ Data / Solve: 








We begin with Newton's
2nd Law of Motion : 



Eqn 1 











The force required to
lift the rocket and accelerate it upward depends on both the weight of the
rocket (and therefore the g)
and the rate at which the rocket must be accelerated…120 ft/s^{2}. Therefore: 



















Eqn 2 











We can now substitute Eqn 1 into Eqn 2 to get : 





















Eqn 3 











Now, we can plug in the
values : 



a_{total} 
157.174 
ft/s^{2} 







F_{wt} 
35000 
lb_{f} 







F_{acc} 
135979 
lb_{f} 

















F_{total} 
170979 
lb_{f} 











Note, in the absence
of gravity, weightlessness, it would still require a force of F_{acc} = 135,979 lb_{f} to accelerate the rocket at a rate of 125 ft/s^{2}. 










Answers: 
F_{up} 
171000 
lb_{f} 















