How Does Centripetal Force Affect the Angle of Water in a Microwave Carousel?

[physixnot4me]

2) 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 7.25s. What angle does the water surface make with the horizontal?

3) a person stands on a scale in the elevator. as the elevator starts, the scale has a constant reading of 591N. as the elevator later stops, the scale reading is 391N. assume the magnitude of the acceleration is the same starting and stopping, and determine:
(a) the weight of the person (b) the person's mass (c) the acceleration of the elevator--------------------------------------------------------------------------

for question #3) above with the elevator, every says to apply Newtons second law for BOTH cases ( i don't understand what the case(s) are)

is it: 591 = m(g+a) and 391= m(g-a) ?
is that how your suppose to find the weight? I really don't understand what I'm trying to be solving for.

as for question #2) above, for the microwave question, when solving for the angle why is it theta=arctan centripal acceleration/gravity? I've figured out that much, i just don't comprehend the theory behind it.

 

[HallsofIvy]

#3. Actually, the acceleration, starting and stopping can't be the same! One is the negative of the other. I assume they are referring the "magnitude" or absolute value of the acceleration. Yes, the "two cases" are the elevator starting and stopping. In one case, both weight, mg, and force causing the acceleration, ma, are in the same direction (downward): 591 = m(g+a). In the second case,weight, mg, is still downward but now ma is upward: 391= m(g-a).
"I really don't understand what I'm trying to be solving for. "
You are supposed to be solving for weight! Which is, of course, mg. You have two equations in the two "unknowns" m and a and I assume you know what g is.

"why is it theta=arctan centripal acceleration/gravity?"
Draw a force diagram. centripetal acceleration is horizontal, acceleration due to gravity is vertical. Use trigonometry! What is the definition of tangent of an angle?
(It might have been clearer if you had written "acceleration due to gravity" rather than just "gravity"!)