Cone-shaped drain speed based on R and time

[Rileyss123]

Homework Statement

A basin surrounding a drain has a shape of a circular cone opening upward, having everywhere an angle of 35 with the horizontal. A 25 g ice cube is set sliding around the cone without friction in a horizontal circle of radius R.
(a) find the speed the ice cube must have based on r
(b) is any piece of data unnecessary for the solution? suppose R is two times larger
(c) will the required speed inc, dec, or stay constant? If it changes by what factor?
(d) will the time required for each revolution inc, dec, or constant? by what factor if it changes?
(e) do answers to part c and d seem contradictory? Explain how they are consistent

Homework Equations

Fc=mv^2/r
ac=v^2/r

The Attempt at a Solution

I don't know where to start. I wasn't even able to come up with a FBD
guessing if I use (SIGMA)Fr=mv^2/r
you can solve for speed for part a but what would be on the other side.
i really have no idea

 

[LowlyPion]

Homework Statement

A basin surrounding a drain has a shape of a circular cone opening upward, having everywhere an angle of 35 with the horizontal. A 25 g ice cube is set sliding around the cone without friction in a horizontal circle of radius R.
(a) find the speed the ice cube must have based on r
(b) is any piece of data unnecessary for the solution? suppose R is two times larger
(c) will the required speed inc, dec, or stay constant? If it changes by what factor?
(d) will the time required for each revolution inc, dec, or constant? by what factor if it changes?
(e) do answers to part c and d seem contradictory? Explain how they are consistent

Homework Equations

Fc=mv^2/r
ac=v^2/r

The Attempt at a Solution

I don't know where to start. I wasn't even able to come up with a FBD
guessing if I use (SIGMA)Fr=mv^2/r
you can solve for speed for part a but what would be on the other side.
i really have no idea

Think of it as a banked curve. What speed needs to be maintained so the centripetal acceleration will balance the downward force of gravity along the incline.
(Hint: The angle affects each. Which functions of the angle need to be applied to each?)

 

[Rileyss123]

SIGMA Fr=(mv^2)r
Nsin@=(mv^2)r

then from vertical component we find
Ncos@=mg
so N=(mg)/cos@
mg/cos@ * sin@ =(mv^2)r
tan@mg=(mv^2)r
do some work~~~~
v=sqrt(rtan@g)
did i do this right?

 

[Rileyss123]

mass is unnecessary because it is crossed out

 

[Rileyss123]

(c) inc by a factor of sqrt(2)

yes?

 

[Rileyss123]

then part d
T=(2*pi*R)/v

and then period will decrease by a factor of 1/sqrt(2)

 

[Rileyss123]

okay i think i got it.
haha THANKSS for the clue!

 

[LowlyPion]

v=sqrt(rtan@g)
did i do this right?

Good enough.

mass is unnecessary because it is crossed out

Good again.

(c) inc by a factor of sqrt(2)

You're on a roll.

then part d
T=(2*pi*R)/v
and then period will decrease by a factor of 1/sqrt(2)

Almost. V increases by Sqrt(2) bur R doubles in that equation.

 

[Rileyss123]

thanks again !