4. The figure above shows an 80-kg astronaut pushing on a spacecraft with force 𝐹𝐹, in outer space. The spacecraft has a mass of 1×104 kg. During the push, the astronaut accelerates to the right with an acceleration of 0.4 m/s2. Determine the magnitude of the acceleration of the spacecraft during the push.

m a = M A

80 kg * 0.4 m/s^2 = 1E4 kg * ?

To determine the magnitude of the acceleration of the spacecraft during the push, we can use Newton's second law of motion.

The formula for Newton's second law is:

𝐹 = 𝑚𝑎

Where:
𝐹 is the force applied,
𝑚 is the mass of the object, and
𝑎 is the acceleration.

In this case, the force being applied is the force exerted by the astronaut, denoted as 𝐹𝐹. The mass of the spacecraft is given as 1×10^4 kg.

We are given that the astronaut has a mass of 80 kg and accelerates to the right with an acceleration of 0.4 m/s^2.

Using Newton's second law, we can rearrange the formula to solve for acceleration:

𝐹 = 𝑚𝑎
𝐹 = (1×10^4 kg) × 𝑎

Now, we need to determine the force 𝐹𝐹 exerted by the astronaut. We know that the force exerted by an object can be calculated using the formula:

𝐹 = 𝑚 × 𝑎

Substituting the given values:

𝐹 = (80 kg) × (0.4 m/s^2)

Now we can substitute this value back into the initial formula and solve for acceleration:

(80 kg) × (0.4 m/s^2) = (1×10^4 kg) × 𝑎

Simplifying the equation:

32 N = 1×10^4 kg × 𝑎

Divide both sides of the equation by 1×10^4 kg:

𝑎 = 32 N / 1×10^4 kg

𝑎 = 0.0032 m/s^2

Therefore, the magnitude of the acceleration of the spacecraft during the push is 0.0032 m/s^2.