An astronaut on a space walk bumps the shuttle and starts moving away at a velocity of 0.02m/s. The astronaut's mass is 100kg. He takes a 1kg "safety weight" and shoves it away in exactly the direction of his motion at a speed of 6m/s. at what speed does the astronaut move back towards the space shuttle
To answer this question, we can apply the principle of conservation of momentum. According to this principle, the total momentum of an isolated system remains constant unless acted upon by an external force.
Initially, the astronaut and the space shuttle are at rest, so their total momentum is zero. When the astronaut bumps into the shuttle and starts moving away, in order to retain the total momentum as zero, the shuttle should move in the opposite direction.
Let's calculate the initial momentum of the astronaut:
Initial momentum of the astronaut = mass of the astronaut × velocity of the astronaut
= 100 kg × 0.02 m/s
= 2 kg·m/s (in the direction away from the shuttle)
To bring the total momentum back to zero, the astronaut decides to push a "safety weight" in the opposite direction with a speed of 6 m/s. Here, we need to consider the momentum of the "safety weight" as well.
Momentum of the "safety weight" = mass of the "safety weight" × velocity of the "safety weight"
= 1 kg × 6 m/s
= 6 kg·m/s (in the direction towards the shuttle)
Now, let's combine the astronaut's momentum (away from the shuttle) and the "safety weight"'s momentum (towards the shuttle):
Total momentum after pushing the "safety weight" = momentum of the astronaut + momentum of the "safety weight"
= 2 kg·m/s (away from the shuttle) + 6 kg·m/s (towards the shuttle)
= 8 kg·m/s (opposite directions cancel out)
Since the total momentum after pushing the "safety weight" is in the opposite direction of the initial momentum, we can consider the speed at which the astronaut moves back towards the space shuttle as 8 m/s.
To calculate the final velocity of the astronaut moving back towards the space shuttle, we will first find the momentum of the astronaut before and after pushing the safety weight.
1. Calculate the initial momentum of the astronaut:
Momentum (p1) = mass (m1) × velocity (v1)
Given: mass of the astronaut (m1) = 100 kg
velocity of the astronaut before pushing the weight (v1) = 0.02 m/s
Therefore, p1 = m1 × v1
= 100 kg × 0.02 m/s
2. Calculate the momentum of the safety weight:
Given: mass of the safety weight (m2) = 1 kg
velocity of the safety weight (v2) = 6 m/s
Therefore, p2 = m2 × v2
= 1 kg × 6 m/s
3. Since momentum is conserved in an isolated system, the total momentum before and after pushing the safety weight will be equal.
p1 + p2 = p3 (momentum after pushing the safety weight)
Substituting the values we calculated:
100 kg × 0.02 m/s + 1 kg × 6 m/s = p3
4. Calculate the final momentum of the astronaut and safety weight combined (p3).
p3 = 100 kg × 0.02 m/s + 1 kg × 6 m/s
5. Find the final velocity of the astronaut moving back towards the space shuttle using the principle of conservation of momentum.
p3 = (m1 + m2) × v3 (where v3 is the final velocity of the astronaut moving back)
Rearranging the equation:
v3 = p3 / (m1 + m2)
Substituting the values from step 4:
v3 = (100 kg × 0.02 m/s + 1 kg × 6 m/s) / (100 kg + 1 kg)
Now you can perform the calculation to find the value of v3.