Example Problem with Complete Solution

1B-4 : Force Required to Accelerate a Rocket 4 pts
NASA would like a rocket to accelerate upward at a rate of 125 ft/s2. The mass of the rocket is 35,000 lbm. Determine the upward thrust force, in lbf, 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
Given: m 35000 lbm gc 32.174 lbm-ft/lbf-s2
a 125 ft/s2
Find: Fup ??? lbf
Assumptions: 1- Assume: g 32.174 ft/s2
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/s2.  Therefore:
Eqn 2
We can now substitute Eqn 1 into Eqn 2 to get :
Eqn 3
Now, we can plug in the values : atotal 157.174 ft/s2
Fwt 35000 lbf
Facc 135979 lbf
Ftotal 170979 lbf
Note, in the absence of gravity, weightlessness, it would still require a force of Facc = 135,979 lbf to accelerate the rocket at a rate of 125 ft/s2.
Answers: Fup 171000 lbf