Question

A 70.0-kg astronaut pushes to the left on a spacecraft with a force F in "gravity-free" space. The spacecraft has a total mass of 1.0 x 10^4 kg. During the push, the astronaut accelerates to the right with an acceleration of 0.36 m/s^2. Determine the magnitude of the acceleration of the spacecraft.

Answer 1

Answer:

$a_2=-0.00252\ m/s^2$

Explanation:

Given that,

Mass of the astronaut, m = 70 kg

Mass of the spacecraft, $m'=10^4\ kg$

Acceleration of the astronaut, $a_1=0.36\ m/s^2$

To find,

The magnitude of the acceleration of the spacecraft.

Solution,

The force acting on the astronaut is given by :

$F=m\times a_1$

$F=70\ kg\times 0.36\ m/s^2=25.2\ N$

During the push, the astronaut accelerates as a result a reaction force will also act on the spacecraft. Let $a_2$ is the acceleration of the spacecraft. It can be calculated as :

$a_2=\dfrac{-F}{m}$ (reaction force)

$a_2=\dfrac{-25.2}{10^4}$

$a_2=-0.00252\ m/s^2$

Therefore, the magnitude of the acceleration of the spacecraft is $0.00252\ m/s^2$. Hence, this is the required solution.