Question

A small container of water is placed on a carousel inside a microwave oven, at a radius of 12.0 cm from the center. The turntable rotates steadily, turning through one revolution in each 7.25 s. What angle does the water surface make with the horizontal?

Most people that have answered this question have answered it along the lines of this:

"The water is traveling in a circle whose radius, r, is .12m (I like to convert all units to kg/m/sec for simplicity). The speed of the water is the distance it travels divided by the time it takes. The circumference of the circle is 2*Pi*r = 0.7536m. It travels this is 7.25sec, so the speed is

0.7536m/7.25sec = .1039m/s

Now we find the centripetal acceleration required for the circular motion: a = v^2/r

plugging our velocity and radius:

a = (.1039m/s)^2/(.12m) = 0.09m/sec^2

Acceleration is a vector, so there is direction. In circular motion it is toward the center of the microwave. Due to the inertia of the water (it wants to go in a straight line, see Newton's Laws) the water will appear to be pulled outward, the "centrifugal force". Now we'll compare our acceleration (pointing horizontally outward) to gravity (pointing straight down).

We add these two vector accelerations to find the net acceleration. Since they are orthogonal (perpendicular) you get A = 0.09(x)+9.81(y). To find the angle of the water from horizontal, you find the direction of A.

This is Atan(x/y) = Atan(0/09/9.81)= 0.52 degrees "

I have come to terms that this is the correct answer to this problem however I cannot find any one that can explain why mg is being considered the x component for this problem, please help!

Answer 1

'mg' is the y component. Centrifugal force is acting in the x direction.

The shape of water surface depends on the forces acting on it.

For this problem, we have to find net acceleration of the water mass.(Consider water as a mass that can change it's shape)

To find the net acceleration, we must find net force.(Resultant of all the forces acting on the body)

As stated in the solution, one force is the centrifugal force.

Water has mass. It is constantly being pulled down by the gravity with an acceleration of 9.8m/s² . Assuming the mass of the water as m, Gravity force acting on the water is mg .

So, Net force on water = centrifugal(outwards) + mg(straight down)

x component y component