Newton's 2nd law involving pulley

[ysk1]

I came across some questions where one box's magnitude of acceleration differed from another box's magnitude of acceleration. Please explain why and how this can be true.
Thank you.

 

[andrevdh]

This can happen when the cable is not pulling in line with the box. That is the cable is pulling at some angle with respect to the direction of motion of the box.

 

[semc]

if the rope is extensible can also give u this result rite?

 

[Doc Al]

Depending upon the specific arrangement, not all parts of a pulley system move at the same rate. For example: When a pulley system gives you a mechanical advantage, the applied force must travel a greater distance than the load. If that applied force is given by a hanging box, its acceleration will be greater than the acceleration of the load. (You can figure this out by studying the configuration of the ropes.)

 

[ysk1]

How could you know which configuration of the ropes will give that condition?

 

[arildno]

As an example, conside a block sliding along a plane, a taut rope fixed to it going about a fixed pulley, then downwards and around a movable pulley, the rope then going upwards to be fixed in the ceiling.

In this case, inextensibility of rope requires that the acceleration of the movable pulley is only one-half of the acceleration of the block.

 

[ysk1]

Can inextensibility of rope also make acceleration of the movable pulley decrease to one-third, one-fourth, etc.?