| 1B-6 : |
Force Required to Accelerate a Rocket |
4 pts |
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| Calculate the force necesssary to accelerate a 20,000 lbm rocket vertically upward at a rate of 100 ft/s2. |
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| Read : |
This is a direct application of Newton's 2nd Law of Motion in the AE System of units. |
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The key to solving this problem is a clear understanding of gc. |
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| Given : |
m |
20000 |
lbm |
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g |
32.174 |
ft/s2 |
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a |
100 |
ft/s2 |
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gc |
32.174 |
lbm-ft/lbf-s2 |
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| Solution : |
We begin with Newton's 2nd Law of Motion : |
Eqn 1 |
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The force required to lift the rocket and accelerate it upward depends on both the weight of the rocket (and therefore the acceleration of gravity) and the rate at which the rocket must be accelerated…100 ft/s2. Therefore : |
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Eqn 2 |
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We can now substitute Eqn 1 into Eqn 2 to get : |
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Eqn 3 |
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Now, we can plug in the values : |
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atotal |
132.174 |
ft/s2 |
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Fwt |
20000 |
lbf |
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Facc |
62162 |
lbf |
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Ftotal |
82162 |
lbf |
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Ftotal |
82200 |
lbf |
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Note, in the absence of gravity, weightlessness, it would still require a force of Facc = 62,162 lbf to accelerate the rocket at a rate of 100 ft/s2. |
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