An astronaut is performing a space walk outside the International Space Station. The total mass of astronaut with her space suit and all lher gear is 127 kg. A small leak develps in her pulsion system and 5.84 g of gas are ejected each second into space with a speed of 754 m/s. She notices the leak 8.61 s after he start. How much will the gas leak have caused the from her original location in space by that time?
Assume astronaut starts form rest and the acceleration is constant...
Thanks anyways...
how did you do it?
To solve this problem, we need to calculate the displacement of the astronaut caused by the gas leak. We can use the equation:
displacement = initial velocity * time + (1/2) * acceleration * time^2
Given:
Mass of astronaut = 127 kg
Gas leakage rate = 5.84 g/s
Gas leakage speed = 754 m/s
Time from start to notice the leak = 8.61 s
First, let's convert the leakage rate from grams to kilograms:
Leakage rate = 5.84 g/s * (1 kg / 1000 g) = 0.00584 kg/s
To find the acceleration caused by the leakage, we can use Newton's second law:
Force = mass * acceleration
The force produced by the gas leakage is equal to the rate of change of momentum:
Force = rate of change of momentum = (mass of gas being leaked per second) * (velocity of gas being leaked)
Substituting the values:
Force = (0.00584 kg/s) * (754 m/s) = 4.40176 N
Since the gravitational force acting on the astronaut is 0 in space, the force from the gas leakage is the only force causing acceleration. Therefore, we can equate the two forces to find the acceleration:
Force = mass * acceleration
4.40176 N = (127 kg) * acceleration
Solving for acceleration:
acceleration = 4.40176 N / 127 kg ≈ 0.0347 m/s^2
Now we can calculate the displacement of the astronaut during the time the gas leak goes unnoticed (8.61 s):
displacement = (0 m/s) * (8.61 s) + (1/2) * (0.0347 m/s^2) * (8.61 s)^2
displacement ≈ 0 + 0.015 m ≈ 0.015 m
Therefore, the gas leak will have caused the astronaut to move approximately 0.015 meters from her original location in space.