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 11.9 cm. When the cylinder is rotating at 1.26 revolutions per second, what is the magnitude of the centripetal acceleration at the outer wall

Answer 1

Centripetal acceleration;a_c = 7.46 m/s²

Step-by-step explanation:

In the concept of circular motion, if an object is moving in a circle of radius r with constant speed v, then the motion is said to be a uniform circular motion. It exhibits a centripetal acceleration directed towards it's centre with the formula;

Centripetal acceleration; a_c = v²/r

Where v is velocity and r is radius.

Now, we are not given the velocity but we know that velocity in uniform circular motion is given by the formula;

v = 2πr/T

Thus,

a_c = (2πr/T)²/r

a_c = 4π²r/T²

We are given;

Radius;r = 11.9cm = 0.119m

Frequency; f= 1.26 revs/s

Now,period;T = 1/f

Thus T = 1/1.26 = 0.7937 s

Thus;

a_c = 4π²(0.119)/(0.7937²)

a_c = 7.46 m/s²