There is a clever kitchen gadget for drying lettuce leaves after you wash them. It consists of a cylindrical container mounted so that it can be rotated about its axis by turning a hand crank. The outer wall of the cylinder is perforated with small holes. You put the wet leaves in the container and turn the crank to spin off the water. The radius of the container is 12 cm. When the cylinder is rotating at 2.3 revolutions per second, what is the magnitude of the centripetal acceleration at the outer wall?
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To find the magnitude of the centripetal acceleration at the outer wall of the container, we can use the formula for centripetal acceleration:
a = rω^2
Where:
a is the centripetal acceleration,
r is the radius of the container, and
ω is the angular velocity of the container in radians per second.
Given that the radius of the container is 12 cm (converted to meters, 0.12 m) and the angular velocity is 2.3 revolutions per second, we need to convert revolutions to radians.
1 revolution = 2π radians
So, the angular velocity in radians per second is:
ω = 2.3 revolutions/s * 2π radians/revolution
= 14.46 radians/s
Now, we can substitute the values into the formula for centripetal acceleration:
a = 0.12 m * (14.46 radians/s)^2
Calculating this:
a = 0.12 m * (208.7316 radians^2/s^2)
≈ 25.05 m/s^2
Therefore, the magnitude of the centripetal acceleration at the outer wall of the container is approximately 25.05 m/s^2.