Question

A 70.0 kg astronaut pushes the 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.

A) 51. 4 m/s^2
B) 0.36 m/s^2
C) 2.5 X 10^-3 m/s^2
D) 7.0 X 10^-3 m/s^2
E) 3.97 X10^-4 m/s^2

Answer 1

The magnitude of the acceleration of the spacecraft is 2.52 x 10^-3 m/s^2.

Step-by-step explanation:

To determine the magnitude of the acceleration of the spacecraft, we can use Newton's second law, which states that the net force on an object is equal to the mass of the object times its acceleration (F = ma). In this case, the force exerted by the astronaut on the spacecraft is the net force. The force exerted by the astronaut can be calculated using the formula F = ma, where m is the mass of the astronaut (70.0 kg) and a is the acceleration of the astronaut (0.36 m/s^2). Plugging in the values, we get F = (70.0 kg)(0.36 m/s^2) = 25.2 N.

Now we can use the net force to calculate the acceleration of the spacecraft. The net force on the spacecraft is equal to the force exerted by the astronaut (25.2 N). The acceleration of the spacecraft can be calculated using the formula F = ma, where F is the net force on the spacecraft, m is the mass of the spacecraft (1.0 x 10^4 kg), and a is the acceleration of the spacecraft. Plugging in the values, we get 25.2 N = (1.0 x 10^4 kg)(a). Solving for a, we find a = (25.2 N) / (1.0 x 10^4 kg) = 2.52 x 10^-3 m/s^2.

Therefore, the magnitude of the acceleration of the spacecraft is 2.52 x 10^-3 m/s^2.