Question

a model rocket has a mass of 0.2 kg, with a motor that can provide a force of 100 n. a second model rocket is being built with the same motor, but it is being designed to accelerate half as much as the first rocket. what kind of change can be made in the design to achieve this objective? (1 point)
the mass of the second rocket should be 0.4 kg.
the mass of the second rocket should be 0.01 kg.
the mass of the second rocket should be 0.1 kg.
the mass of the second rocket should be 0.2 kg

Explanation:

Step1: Recall Newton's Second Law

Newton's second law is \( F = ma \), where \( F \) is force, \( m \) is mass, and \( a \) is acceleration. For the first rocket, \( F = 100\ N \) and \( m_1 = 0.2\ kg \). We can find its acceleration \( a_1 \) using \( a_1=\frac{F}{m_1} \).
\[ a_1=\frac{100}{0.2}= 500\ m/s^2 \]

Step2: Determine the desired acceleration for the second rocket

The second rocket should accelerate half as much as the first, so \( a_2=\frac{a_1}{2}=\frac{500}{2} = 250\ m/s^2 \). The force \( F \) is the same (100 N) for the second rocket. Using \( F = m_2a_2 \), we can solve for \( m_2 \) as \( m_2=\frac{F}{a_2} \).

Step3: Calculate the mass of the second rocket

Substitute \( F = 100\ N \) and \( a_2 = 250\ m/s^2 \) into the formula:
\[ m_2=\frac{100}{250}=0.4\ kg \]

Answer:

The mass of the second rocket should be 0.4 kg.