Question: A 62 kg astronaut floats outside a 3200 kg spacecraft. She's initially stationary with respect to the spacecraft. Then she pushes against the spacecraft and moves away at .50m/s to the left.
I got an answer of .0096kg from doing 62*.50/3200 but that is incorrect.
Could you help me with this? I'm not sure how to answer this question.
moembntum is conserved.
62*.50+3200*V=0
V= - 31/3200 m/s the negative sign means to the right.
So if you are looking for the velocity of the spacecraft, it is .0096m/s to the right.
I have no idea why you put kg.
To answer this question, we need to use the principle of conservation of momentum. In this case, the momentum before the astronaut pushes off the spacecraft is equal to the momentum after she pushes off.
The momentum, p, of an object is calculated by multiplying its mass, m, by its velocity, v:
p = m * v
Initially, the astronaut is at rest with respect to the spacecraft, meaning her initial momentum is zero. The spacecraft has a mass of 3200 kg, so its initial momentum is also zero.
After the astronaut pushes off, she starts moving away from the spacecraft at a velocity of -0.50 m/s (negative because it is to the left). We can calculate her momentum using her mass of 62 kg and the velocity of -0.50 m/s:
momentum = mass * velocity = 62 kg * (-0.50 m/s) = -31 kg·m/s
According to the principle of conservation of momentum, the total momentum before the push-off must be equal to the total momentum after the push-off. Since the spacecraft has a mass of 3200 kg, its final velocity can be calculated as follows:
3200 kg * V = -31 kg·m/s (where V is the final velocity of the spacecraft)
Dividing both sides by 3200 kg:
V = -31 kg·m/s / 3200 kg ≈ -0.01 m/s
Therefore, the final velocity of the spacecraft is approximately -0.01 m/s (to the left). Note that the negative sign indicates the direction, so the velocity is to the left.
To summarize:
- The astronaut's final velocity is -0.50 m/s (to the left).
- The spacecraft's final velocity is approximately -0.01 m/s (to the left).
It seems your calculation of 0.0096 kg is incorrect. However, by following the principles of conservation of momentum, we can determine the correct final velocities for both the astronaut and the spacecraft.