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"!)

 

[quicknote]

I would like to provide a response to the content mentioned above.

Firstly, let's discuss apparent weight in elevators. Apparent weight is the weight that an object feels when it is in motion. In the case of an elevator, when it is accelerating upwards, the apparent weight will be greater than the actual weight, and when it is accelerating downwards, the apparent weight will be less than the actual weight. This is because of the normal force acting on the object, which is equal to the object's weight plus the force due to acceleration.

Now, let's move on to question #2 about the water container on a rotating carousel. In this situation, the water surface will make an angle with the horizontal, known as the angle of tilt. This angle can be calculated using the centripetal acceleration formula, where a = v^2/r. In this case, v is the tangential speed, and r is the radius of the carousel. Once you have calculated the centripetal acceleration, you can use the equation theta = arctan (a/g) to find the angle of tilt. This is because the centripetal acceleration acts in the same direction as the normal force, which is perpendicular to the surface of the water.

Now, for question #3 about the person standing on a scale in an elevator. You are correct in using Newton's second law to solve this problem. The two cases you mentioned are when the elevator is accelerating upwards (591 = m(g+a)) and when it is accelerating downwards (391 = m(g-a)). By solving these two equations simultaneously, you can find the weight of the person (m(g+a)) and their mass (m). The acceleration of the elevator can then be calculated by using a = (m(g+a))/m.

I hope this explanation helps to clarify the concepts and equations involved in these problems. Remember to always consider the forces acting on an object and use the appropriate equations to solve for the unknowns.