Suppose the mass of a fully loaded module in which astronauts take off from the moon is 10,000 kg. The thrust of its engines is 30,000 N.
Calculate its acceleration in a vertical takeoff from the moon.
When I set up my free body diagram, the force of thrust points upwards, and the force of weight points downward. The acceleration due to gravity on the moon is 1.63 m/s^2. When I calculate the acceleration of the rocket, I get 1.37m/s^2.
Does this answer make sense? I'm kind of confused about whether or not the acceleration of the rocket has to be greater than the acceleration of gravity for it to take off.
Calculate its acceleration in a vertical takeoff from the moon.
When I set up my free body diagram, the force of thrust points upwards, and the force of weight points downward. The acceleration due to gravity on the moon is 1.63 m/s^2. When I calculate the acceleration of the rocket, I get 1.37m/s^2.
Does this answer make sense? I'm kind of confused about whether or not the acceleration of the rocket has to be greater than the acceleration of gravity for it to take off.
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apply newton's second law
thrust (which causes the ground to push up on the rocket) - weight = ma
30,000N - 10,000kg*1.63m/s/s = 10,000 a
a = 1.37m/s/s
remember that this value of a is derived when you subtract the weight of the rocket from the thrust
as long as the thrust exceeds the weight on the moon, the rocket will accelerate upward; think about your question in terms of vectors...and recall that acceleration is a vector....the acceleration of this rocket is greater than the acceleration due to lunar gravity, since the former is +1.37m/s/s and the latter is - 1.63m/s/s
but what really matters is that thrust>weight; that will give the rocket a positive, upward acceleration
thrust (which causes the ground to push up on the rocket) - weight = ma
30,000N - 10,000kg*1.63m/s/s = 10,000 a
a = 1.37m/s/s
remember that this value of a is derived when you subtract the weight of the rocket from the thrust
as long as the thrust exceeds the weight on the moon, the rocket will accelerate upward; think about your question in terms of vectors...and recall that acceleration is a vector....the acceleration of this rocket is greater than the acceleration due to lunar gravity, since the former is +1.37m/s/s and the latter is - 1.63m/s/s
but what really matters is that thrust>weight; that will give the rocket a positive, upward acceleration
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Don't worry it makes sense. In physics if you are a couple of decimal places off its alright since everyone uses different sig figs and such. Its when the answer is "10^6": and you write "10^5" that you should be worried.