To achieve half the acceleration of the first model rocket while using the same motor that provides a force of 100 N, you can adjust the mass of the second rocket.
According to Newton's second law of motion, acceleration \(a\) is given by the formula:
\[ F = m \cdot a \]
where \(F\) is the force applied, \(m\) is the mass of the object, and \(a\) is the acceleration. To find the acceleration, we can rearrange the equation as follows:
\[ a = \frac{F}{m} \]
For the first rocket:
- Mass (\(m_1\)) = 0.2 kg
- Force (\(F\)) = 100 N
Using the formula:
\[ a_1 = \frac{100 , \text{N}}{0.2 , \text{kg}} = 500 , \text{m/s}^2 \]
For the second rocket, which is designed to accelerate half as much (\(a_2 = \frac{1}{2} a_1\)), we want:
\[ a_2 = \frac{1}{2} \times 500 , \text{m/s}^2 = 250 , \text{m/s}^2 \]
Now we can use the same force to find the required mass for the second rocket that would give this acceleration:
\[ a_2 = \frac{F}{m_2} \implies m_2 = \frac{F}{a_2} \]
Substituting \(F\) and \(a_2\):
\[ m_2 = \frac{100 , \text{N}}{250 , \text{m/s}^2} = 0.4 , \text{kg} \]
Thus, to achieve half the acceleration, the second rocket should have a mass of 0.4 kg. In summary, to achieve the objective of the second model rocket accelerating at half the rate of the first, you can simply increase the mass of the rocket from 0.2 kg to 0.4 kg. This change modifies the rocket's mass to produce the desired lower acceleration while using the same motor force.