# mechanics question to do with pulleys

Discussion in 'Mathematics' started by fudgesweets, Dec 12, 2011.

1. ### fudgesweetsNew commenter

Forgive me for my stupidity but I am not sure about a question involving a pulley and 2 objects hanging off it from a string:
'Explain how you have used the fact that the pulley is smooth in your calculations'
The answer states that the tension in the string remains either side of the pulley. However, I initially thought no friction. How does the same tension come about?

2. ### fudgesweetsNew commenter

Forgive me for my stupidity but I am not sure about a question involving a pulley and 2 objects hanging off it from a string:
'Explain how you have used the fact that the pulley is smooth in your calculations'
The answer states that the tension in the string remains either side of the pulley. However, I initially thought no friction. How does the same tension come about?

3. ### Maths_MikeNew commenter

Smooth pulley so no friction.
The tension in the string has nothing to do with the nature of the pulley. Even if the pulley were rough (which of couse in real life it must be) the tension in the string would still be constant otherwsie it would snap

4. ### DMNew commenter

That isn't correct Mike. In a rough pulley situation there are two equal and opposite tensions on one side of the pulley and two different equal and opposite tensions on the other side of the pulley.

5. ### Maths_MikeNew commenter

yep sry Dm is right if the pulley were rough then ofcourse the tensions either side of the pulley could be different - which i guess is the whole point - sry having a blonde moment - i realised me mistake and came back to correct but DM beat me to it.

6. ### fudgesweetsNew commenter

If the pully was rough why would tension on one side be different to the other?

7. ### DMNew commenter

If the pulley is rotating clockwise the string "catches" on the pulley and the tension on the right hand side increases because of this drag. On the left hand side the tension reduces as the string starts to become slack.
http://en.wikipedia.org/wiki/Belt_friction

8. ### DMNew commenter

Nive avatar for you fudge.

9. ### Maths_MikeNew commenter

would it be the left hand side for increased tension with the pulley going clockwise or am i being dim (again?)

10. ### DMNew commenter

Nope - not sure how to explain it apart from the friction at the pulley is acting against the direction of travel so it increases the tension on the right.

11. ### pipipi

Is there a collection of videos to demonstrate mechanics ideas? I have a group ( that I teach core to) who seem to really struggle about visualising what happens. I've drawn diagrams at lunchtimes but just wondered if there were animations around.

12. ### Maths_MikeNew commenter

Oh I assumed if the pulley was turning clockwise the string was moving left to right. Anyway I'll shut up and stop embarrassing myself.

13. ### Polecat

When a cable is wound around a bollard, for example when morring a boat, the tension in the cable varies according to exp(-mu x theta), where mu is the coefficient of friction and theta is the angle of winding. For each small length of cable the tensions pulling in opposite directions are different, but balanced by the friction and normal reaction acting on that small chunk.
If mu is zero, the tension is constant throughout the cable.