To find the mass of the second rocket that accelerates half as much as the first rocket, we can use Newton's second law, which states that \( F = ma \), where \( F \) is the force applied, \( m \) is the mass, and \( a \) is the acceleration.
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For the first rocket:
- Mass (\( m_1 \)) = 0.2 kg
- Force (\( F \)) = 100 N
- Using the equation \( F = ma \), we can find the acceleration (\( a_1 \)): \[ a_1 = \frac{F}{m_1} = \frac{100 , \text{N}}{0.2 , \text{kg}} = 500 , \text{m/s}^2 \]
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The second rocket is designed to accelerate half as much, so: \[ a_2 = \frac{a_1}{2} = \frac{500 , \text{m/s}^2}{2} = 250 , \text{m/s}^2 \]
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We know the force applied by the motor remains the same (100 N). Now we can find the mass of the second rocket (\( m_2 \)) that would result in this new acceleration: \[ F = m_2 a_2 \implies m_2 = \frac{F}{a_2} = \frac{100 , \text{N}}{250 , \text{m/s}^2} = 0.4 , \text{kg} \]
Therefore, to achieve half the acceleration of the first rocket, the mass of the second rocket should be 0.4 kg.
The correct response is: The mass of the second rocket should be 0.4 kg.
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