A weight attached to a wire is swung in a circular path. Its speed is 12 meters/sec, and it has a centripetal acceleration of 9.0 meters/sec2. Calculate the diameter of the circle.
1.3 meters
2.6 meters
16 meters
32 meters
To calculate the diameter of the circle, we first need to understand the relationship between speed, centripetal acceleration, and radius.
The centripetal acceleration (a) is given by the formula:
a = v² / r
Where:
a = centripetal acceleration
v = velocity (speed)
r = radius
In this case, the speed is given as 12 meters/sec and the centripetal acceleration is given as 9.0 meters/sec². We can use these values to find the radius.
Using the given values:
9.0 = 12² / r
To solve for r, we can rearrange the equation:
r = 12² / 9.0
r = 144 / 9.0
r ≈ 16 meters
Now that we have the radius, we can calculate the diameter of the circle. The diameter is simply twice the radius:
d = 2r
d = 2 * 16
d = 32 meters
Therefore, the diameter of the circle is 32 meters.
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