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The tip of a fan blade is 0.61 m from the center of the fan. The fan turns at a constant speed and completes 2 rotations every 1.0 second. What is the centripetal acceleration of the tip of the fan blade? Option 1: 6.0 m/s² Option 2: 48 m/s² Option 3: 53 m/s² Option 4: 96 m/s²

User Osaxma
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Answer: Here's my answer, I made it step-by-step so you can understand it! <3

Step-by-step explanation:

To find the centripetal acceleration of the tip of the fan blade, we can use the formula for centripetal acceleration:

a = (v^2) / r

where:

a is the centripetal acceleration,

v is the linear velocity, and

r is the radius of the circular path.

Given that the fan completes 2 rotations every 1.0 second, we can find the angular velocity (ω) using the formula:

ω = (2π * n) / t

where:

ω is the angular velocity,

π is a constant (approximately 3.14),

n is the number of rotations (2),

and t is the time taken (1.0 second).

Substituting the values into the formula, we have:

ω = (2π * 2) / 1.0 = 4π rad/s

Next, we can calculate the linear velocity (v) using the formula:

v = r * ω

Substituting the given radius value (0.61 m) and the angular velocity we found earlier, we have:

v = 0.61 * 4π = 2.44π m/s

Finally, we can calculate the centripetal acceleration (a) using the formula:

a = (v^2) / r

Substituting the linear velocity and the radius, we have:

a = (2.44π)^2 / 0.61 = 5.88π^2 / 0.61 ≈ 96 m/s²

Therefore, the centripetal acceleration of the tip of the fan blade is approximately 96 m/s² (Option 4).

User Jpsstack
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