A deeper explenation of a pulley

[Mad_Eye]

hi,

http://img252.imageshack.us/img252/6325/23606963.png

so, if I'm not deadly wrong F here equals only to half m*g... and yeah, i can kind of feel it... but can anyone proof it and explain it to me..?

thanks a lot :D

 

[arildno]

1. The block exerts a force equal to mg downwards on the pulley.

2. If the pulley is to be at rest, the portion of the rope in touch with it must exert a total force of mg upwards on the pulley.

3. Thus, by Newton's 3.law, the pulley exerts a force of mg downwards on the portion of the rope it is in contact with.

4. Thus, if the contact portion of the rope is to be at rest, the two vertical strands of the rope must exert a total force of mg on the contact portion of the rope.

5. Since the tension in the rope is equal at all points, it must equal F, and thus, the two strands exerts a force 2*F on the contact portion of the rope.

6. We have from 4 and 5 the equation 2*F=mg, yielding F=mg/2.

7. The other half of mg is provided by the ceiling.