- #1
Satvik Pandey
- 591
- 12
Homework Statement
We have a disk of mass M and radius R placed on a horizontal plane. A cylindrical groove of radius r is made on a diameter.Now a sphere of mass m and radius r is placed in the groove at the circumference of the disk.
At t=0 the whole system is rotated with an angular velocity 1rad/s as shown in the figure.Also at the same time the sphere was projected with a velocity v towards the center of the disk.Find the minimum velocity of the sphere such that it is able to reach the other end of the groove.
Details and Assumptions
M=2kg
m=3kg
R=2m
r<<R
https://d18l82el6cdm1i.cloudfront.net/solvable/2676130fa9.119ef294cc.dlI6so.png
The disk is fixed about it's centre that is it can only rotate
Homework Equations
The Attempt at a Solution
I think if the ball crosses the center of the disk the centrifugal force will be enough to move that ball to the other side of the groove.
I think the minimum velocity in this case is the velocity which is enough to move the ball to the center of the disk.
Here the angular velocity of ball keeps changing, I think.
At distance x from the center of the disk let the angular velocity be ω_x.
I[itex]_{i}[/itex] ω[itex]_{i}[/itex]=I[itex]_{x}[/itex]ω[itex]_{x}[/itex]
ω[itex]_{x}[/itex]=MR2+2mR2)/(MR2+2mx2)
ω[itex]_{x}[/itex]=16/4+3x2
I think the total energy of the ball will be entirely converted to the potential energy.