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?

Question

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?

Answer 1

velocity=2PIr*2.3, where r is .12mcheck that.

a= v^2/r

Answer 2

To find the magnitude of the centripetal acceleration at the outer wall of the cylindrical container, we can use the formula:

a = rω^2

where:
- a is the magnitude of the centripetal acceleration,
- r is the radius of the container, and
- ω is the angular velocity of the container in radians per second.

Given:
- r = 12 cm (converted to meters by dividing by 100, so r = 0.12 m),
- ω = 2.3 revolutions per second (converted to radians per second by multiplying by 2π).

First, let's convert 2.3 revolutions per second to radians per second:
ω = 2.3 revolutions per second * 2π radians per revolution = 2.3 * 2π radians per second.

Now, substitute the values into the formula and calculate the magnitude of the centripetal acceleration:
a = (0.12 m) * (2.3 * 2π radians per second)^2

a = 0.12 m * (13.84 radians per second)^2

a ≈ 0.12 m * (191.3856 radians^2 per second^2)

Answer 3

To find the magnitude of the centripetal acceleration at the outer wall of the cylindrical container, we can use the equation for centripetal acceleration:

a = ω²r

Where:
a = centripetal acceleration
ω = angular velocity (in this case, measured in revolutions per second)
r = radius of rotation

Given:
ω = 2.3 revolutions per second
r = 12 cm (or 0.12 meters)

First, let's convert the angular velocity from revolutions per second to radians per second. Since one revolution is equal to 2π radians, we can calculate:

ω = 2.3 revolutions/second * 2π radians/revolution

ω = 14.46 radians/second

Now, we can calculate the centripetal acceleration using the given formula:

a = (14.46 radians/second)² * 0.12 meters

a = 2.0903528 meters/second²

Therefore, the magnitude of the centripetal acceleration at the outer wall of the container is approximately 2.090 m/s².