an astronaut rotates at the end of a test machine whose arm has a length of 10.0m. if the acceleration she experiences must not exceed 5g (g=10m/s^2? what is the maximum number of revolutions per minute of the arm?
I did what Bob did and got 134 rpm, which is wrong and crazy fast, but Jay's answer is only twice what the answer should be. What did you do?
Answer is 21 idk why and how
A=v^2/r
5g=50ms^-2
50ms=v^2/10m
V^2=500
V=22.26
Why did the astronaut become a human washing machine? Because they wanted to spin-dry their space suit, of course!
Now, let's calculate the maximum number of revolutions per minute the arm can have without exceeding 5g acceleration.
First, we need to convert the acceleration from 5g to m/s², so 5g is equal to 5 times 10 m/s², which is 50 m/s².
The acceleration in a circular motion can be calculated using the formula a = (4π²r/T²), where a is the acceleration, r is the radius, and T is the period or time it takes for one revolution.
Given the radius of the arm (r = 10.0 m), we can rearrange the formula to solve for T:
T² = (4π²r) / a
Now let's plug in the values:
T² = (4π² * 10.0) / 50
T² ≈ 2.5133
T ≈ √2.5133 ≈ 1.5867 seconds
Since we want the maximum number of revolutions per minute, we need to convert the period to minutes:
1 minute = 60 seconds
Number of revolutions per minute = 1 / T ≈ 1 / 1.5867 ≈ 0.6307
So, the maximum number of revolutions per minute the arm can have without exceeding 5g acceleration is approximately 0.6307. Keep your space suit clean, my friend!
To solve this problem, we need to consider the centripetal acceleration experienced by the astronaut as she rotates at the end of the test machine. The maximum acceleration is given as 5g, where g = 10 m/s².
The centripetal acceleration is given by the formula:
a = (ω² * r)
where:
a is the centripetal acceleration,
ω (omega) is the angular velocity in radians per second,
r is the radius (length of the arm in this case).
We can rearrange the formula to solve for ω:
ω = √(a / r)
In this case, the maximum acceleration (a) is given as 5g = 5 * 10 = 50 m/s², and the length of the arm (r) is 10.0 m.
ω = √(50 / 10.0)
= √5
≈ 2.24 rad/s
Now, we need to convert the angular velocity (ω) into revolutions per minute (RPM).
To convert radians per second to revolutions per minute, we can use the following conversion factor:
1 revolution = 2π radians
1 minute = 60 seconds
So, to convert ω from rad/s to RPM, we multiply ω by the conversion factor:
ω (in RPM) = (ω * 60) / (2π)
ω (in RPM) ≈ (2.24 * 60) / (2π)
≈ 67.24 / π
≈ 21.39 RPM
Therefore, the maximum number of revolutions per minute the arm can rotate is approximately 21.39 RPM.
5g>v^2/r
and v=RPM*1min/60sec * radius
5g>RPM^2 * 1/3660 * r
solve for RPM