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 0.2 kg.
The mass of the second rocket should be 0.2 kg.

The mass of the second rocket should be 0.01 kg.
The mass of the second rocket should be 0.01 kg.

1 answer

To determine the mass of the second rocket to achieve half the acceleration of the first rocket, we can use Newton's second law, which states that \( F = ma \) (where \( F \) is force, \( m \) is mass, and \( a \) is acceleration).

For the first rocket:

  • Mass \( m_1 = 0.2 , \text{kg} \)
  • Force \( F = 100 , \text{N} \)

The acceleration \( a_1 \) of the first rocket can be calculated as: \[ a_1 = \frac{F}{m_1} = \frac{100 , \text{N}}{0.2 , \text{kg}} = 500 , \text{m/s}^2 \]

For the second rocket, we want it to accelerate half as much, so: \[ a_2 = \frac{a_1}{2} = \frac{500 , \text{m/s}^2}{2} = 250 , \text{m/s}^2 \]

Using the same force of \( 100 , \text{N} \) for the second rocket, we can find the mass \( m_2 \): \[ m_2 = \frac{F}{a_2} = \frac{100 , \text{N}}{250 , \text{m/s}^2} = 0.4 , \text{kg} \]

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.