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## Homework Statement

Ball of mass=m on the frictionless table is connected to a string that passes in hole that is in table. The ball is set into a circular motion on a circle of radius = R. If the string pulled from the bottom, withe the force F, so that the radius of motion of ball would decrease, how would the final speed of ball change?

## Homework Equations

I know that centripetal force sets the ball into motion, it is given by the formula:

##F_C = \frac{mv^2}{r}##

where

m - mass of the body(m in my example)

v - velocity in my example:

## v_0 ##

r - radius of path - R in my example

F - force applied

So if the volocity is ##v_0##, mass is ##m## and the string that the ball is connected to, is pulled so that the radius of path is decreased, how would the final velocity change(the force F is applied to the string at its bottom)

## The Attempt at a Solution

**##F_C = \frac{mv^2}{r}##**

Therefore:

## v= \sqrt {\frac {R_f F_C} {m}} ## where:

## R_f = R-r ## and ## F_C = ## force applied at the bottom of string., so ##F_C = F##