How Much Work is Done to Change the Circular Path's Radius?

[thedark_master]

https://chip.physics.purdue.edu/protected/IEalgebraMimg/uiuc101-09-block.ie/pic.gif

A small block of mass 0.91 kg slides without friction on a horizontal table. Initially it moves in a circle of radius r0 = 0.63 m with a speed 1.5 m/s. It is held in its path by a string that passes through a small hole at the center of the circle. The string is then pulled down a distance of r0 - r1 = 0.12 m, leaving it at a radius of r1 = 0.51 m. It is pulled so slowly that the object continues to move in a circle of continually decreasing radius.

How much work was done by the force to change the radius from 0.63 m to 0.51 m?


basically i am completely lost, any help would be appreciated

 

[Mindscrape]

Well, you know that two things are always conserved, energy and momentum. A conservation theorem may be a good place to start.

 

[thedark_master]

ya i am still stuck

 

[Mindscrape]

First get a sense of what is happening. The ball is going around in a circle with a constant velocity. Some kind of force is keeping the ball from simply shooting outward. The whole time, energy will be conserved. Now, as the ball moves towards the center by whatever force, is energy still conserved?

 

[thedark_master]

no its not

 

[robb_]

Id start by looking at the work energy theorem.

 

[Mindscrape]

You don't believe that energy is still conserved? What would it lose energy to?

 

[robb_]

Well, one can't make a statement about energy conservation until the system is defined.

 

[Mindscrape]

Well, one can't make a statement about energy conservation until the system is defined.

Not really sure what you mean by this, but the system is defined enough to tell whether or not non-conservative forces are at play, and whether or not the work energy theorem can be used.

 

[robb_]

You and I may have a system in mind where energy is conserved, but the OP may not, i.e. just the rotating block?