To determine the mass of the second rocket needed to accelerate half as much as the first rocket with the same motor, we can use Newton's second law, which is \( F = ma \), where \( F \) is the force, \( m \) is the mass, and \( a \) is the acceleration.
For the first rocket:
- Mass (\( m_1 \)) = 0.2 kg
- Force (\( F \)) = 100 N
- Acceleration (\( a_1 \)) is calculated as follows:
\[ a_1 = \frac{F}{m_1} = \frac{100 , \text{N}}{0.2 , \text{kg}} = 500 , \text{m/s}^2 \]
For the second rocket, we want its acceleration (\( a_2 \)) to be half of that of the first rocket:
\[ a_2 = \frac{1}{2} a_1 = \frac{1}{2} \times 500 , \text{m/s}^2 = 250 , \text{m/s}^2 \]
Using the same motor which provides 100 N of force, we can find the required mass (\( m_2 \)) of the second rocket using the formula:
\[ a_2 = \frac{F}{m_2} \]
Rearranging gives:
\[ m_2 = \frac{F}{a_2} = \frac{100 , \text{N}}{250 , \text{m/s}^2} = 0.4 , \text{kg} \]
Thus, the mass of the second rocket should be 0.4 kg.
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