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 13.9 cm. When the cylinder is rotating at 1.38 revolutions per second, what is the magnitude of the centripetal acceleration at the outer wall?
To find the magnitude of the centripetal acceleration at the outer wall of the cylindrical container, we can use the centripetal acceleration formula:
a = ω^2 * r
Where:
a is the centripetal acceleration,
ω (omega) is the angular velocity, and
r is the radius.
Given that the radius is 13.9 cm and the cylinder is rotating at 1.38 revolutions per second, we need to convert the angular velocity to radians per second because the formula requires angular velocity in radians, not revolutions.
To convert revolutions per second to radians per second, we need to multiply by 2π since there are 2π radians in one revolution.
ω = (1.38 rev/s) * (2π rad/rev)
Now we can substitute the values into the formula:
a = (ω^2) * r
First, we calculate the angular velocity:
ω = (1.38 rev/s) * (2π rad/rev) = 2.38π rad/s
Next, substitute the values into the formula:
a = (2.38π rad/s)^2 * 0.139 m
Simplifying this:
a ≈ 5.93 * π^2 m/s^2
Finally, we can approximate the magnitude of the centripetal acceleration:
a ≈ 5.93 * 9.87 m/s^2
a ≈ 58.45 m/s^2
Therefore, the magnitude of the centripetal acceleration at the outer wall of the cylindrical container is approximately 58.45 m/s^2.
To find the magnitude of the centripetal acceleration at the outer wall of the cylindrical container, we can use the formula:
a = r * ω^2
Where:
a is the centripetal acceleration
r is the radius of the container
ω is the angular velocity in radians per second
Given:
r = 13.9 cm = 0.139 m (Converting to meters)
ω = 1.38 revolutions per second
First, we need to convert the angular velocity from revolutions per second to radians per second. Since one revolution is equal to 2π radians, we can multiply the given angular velocity by 2π:
ω = 1.38 rev/s * 2π rad/rev
ω ≈ 8.67 rad/s
Now we can substitute the values into the formula to calculate the centripetal acceleration:
a = 0.139 m * (8.67 rad/s)^2
a ≈ 10.87 m/s^2
Therefore, the magnitude of the centripetal acceleration at the outer wall of the container is approximately 10.87 m/s^2.
1.38*2pi radians/s = 8.67
8.67^2(.139) = 10.4 m/s^2
or about one g
Humm, why not leave it sitting in the collander ?