The length of a blade of a helicopter is 5_m, and the blade spins at 350_rev/min. Find the centripetal acceleration of the tip of the blade. 5696 m/s? 5459 m/s² 6426̟m/s? 6155_m/s? 5943_m/s? 6717_m/s? А. D. В. Е. С. F.
The length of a blade of a helicopter is 5_m, and the blade spins at 350_rev/min. Find the centripetal acceleration of the tip of the blade. 5696 m/s? 5459 m/s² 6426̟m/s? 6155_m/s? 5943_m/s? 6717_m/s? А. D. В. Е. С. F.
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![**Problem:**
The length of a blade of a helicopter is 5 m, and the blade spins at 350 rev/min. Find the centripetal acceleration of the tip of the blade.
**Options:**
A. \(5696 \, \text{m/s}^2\)
B. \(5459 \, \text{m/s}^2\)
C. \(6426 \, \text{m/s}^2\)
D. \(6155 \, \text{m/s}^2\)
E. \(5943 \, \text{m/s}^2\)
F. \(6717 \, \text{m/s}^2\)
**Explanation:**
To solve for the centripetal acceleration (\(a_c\)) at the tip of the blade, use the formula:
\[ a_c = \omega^2 \times r \]
Where:
- \(\omega\) is the angular velocity in rad/s.
- \(r\) is the radius, which is the same as the length of the blade, \(5 \, \text{m}\).
First, convert revolutions per minute to radians per second to find \(\omega\):
- \(1 \, \text{rev} = 2\pi \, \text{rad}\)
\[ 350 \, \text{rev/min} = 350 \times 2\pi \, \text{rad/min} = 700\pi \, \text{rad/min} \]
Convert minutes to seconds:
\[ \omega = \frac{700\pi}{60} \, \text{rad/s} \]
Now, calculate:
\[ a_c = \left(\frac{700\pi}{60}\right)^2 \times 5 \]
Complete the calculation to find the correct answer from the options.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F32d80c3f-e8ca-4b33-9136-508eae27e90c%2F17268c3b-1579-4a69-87a3-465273e93d46%2F0v8n9g_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem:**
The length of a blade of a helicopter is 5 m, and the blade spins at 350 rev/min. Find the centripetal acceleration of the tip of the blade.
**Options:**
A. \(5696 \, \text{m/s}^2\)
B. \(5459 \, \text{m/s}^2\)
C. \(6426 \, \text{m/s}^2\)
D. \(6155 \, \text{m/s}^2\)
E. \(5943 \, \text{m/s}^2\)
F. \(6717 \, \text{m/s}^2\)
**Explanation:**
To solve for the centripetal acceleration (\(a_c\)) at the tip of the blade, use the formula:
\[ a_c = \omega^2 \times r \]
Where:
- \(\omega\) is the angular velocity in rad/s.
- \(r\) is the radius, which is the same as the length of the blade, \(5 \, \text{m}\).
First, convert revolutions per minute to radians per second to find \(\omega\):
- \(1 \, \text{rev} = 2\pi \, \text{rad}\)
\[ 350 \, \text{rev/min} = 350 \times 2\pi \, \text{rad/min} = 700\pi \, \text{rad/min} \]
Convert minutes to seconds:
\[ \omega = \frac{700\pi}{60} \, \text{rad/s} \]
Now, calculate:
\[ a_c = \left(\frac{700\pi}{60}\right)^2 \times 5 \]
Complete the calculation to find the correct answer from the options.
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