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) Responses The mass of the second rocket should be 0.4 kg. The mass of the second rocket should be 0.4 kg. The mass of the second rocket should be 0.1 kg. The mass of the second rocket should be 0.1 kg. The mass of the second rocket should be 0.01 kg. The mass of the second rocket should be 0.01 kg. The mass of the second rocket should be 0.2 kg.

Answer 1

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**.