According to Newton's Second Law, the acceleration (\(a\)) of an object is directly proportional to the net force (\(F\)) acting on it and inversely proportional to its mass (\(m\)). This relationship can be expressed with the formula:
\[ a = \frac{F}{m} \]
In the context of rockets, the net force is generated by the thrust produced by the rocket's engine. If we consider the thrust to be constant (which is often the case for the same motor being used), we can analyze how acceleration changes with varying mass.
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Constant Thrust: If the thrust produced by the rocket motor remains constant, as the mass of the rocket increases (due to fuel consumption, payload, or structural additions), the acceleration will decrease. This is because with a larger mass and the same amount of thrust, the ratio \(F/m\) becomes smaller, leading to reduced acceleration.
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Mathematically: For a rocket with constant thrust \(F\):
- As mass \(m\) increases, acceleration \(a\) is given by:
\[ a = \frac{F}{m} \] Thus, increasing \(m\) (mass) will result in a smaller value of \(a\) (acceleration).
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Practical Implication: This means that heavier rockets, under the same thrust conditions, will not accelerate as much as lighter rockets. In practice, this highlights the importance of optimizing the mass of a rocket to achieve the desired acceleration and performance.
In conclusion, as the mass of the rocket increases while maintaining a constant thrust from the same motor, the acceleration of the rocket is expected to decrease.