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).