Does Using a Pulley Affect Acceleration in a Frictionless System?

[just.karl]

With a mass on a frictionless surface connected to a string that is sent over and down to a mass. Would that increase or decrease the acceleration compared to the equation, a=g(m). I'm just stumped on how to think of this. The pulley is not included in the equation but how would I figure out the difference?

 

[G01]

The extra mass attached to the rope will cause a tension in the rope correct? How does this tension affect the net force on the original block?

 

[just.karl]

It would decrease the net force on the original block, correct? But would it be just because of friction or is it something more complicated than that?

 

[G01]

Yes, the net force would decrease but not for the reason you are suggesting.

Consider the pulley to be frictionless. It's not the pulley that is decreasing the force on the block, but the weight of the second block that is added. The weight of the block causes a tension in the rope, and the rope thus pulls up on the first block, decreasing the net force on the first block. All the pulley really does is change the direction of the tension force so it pulls up on the block. This is why the pulley doesn't factor into the force equation, since it doesn't create any new forces.

(Of course, in reality, there is some friction in the pulley which will decrease the net force on the block, but it is not the primary cause of the decrease.)

Does this make sense? I suggest drawing a force/free-body diagram of the situation. It may help you visualize what's happening.

 

[tiny-tim]

make it as simple as possible first

With a mass on a frictionless surface connected to a string that is sent over and down to a mass. Would that increase or decrease the acceleration compared to the equation, a=g(m).

I assume by "frictionless surface", you mean a horizontal one, like a really smooth table?

Try an easier problem first: tilt the table, and put the pulley on the end of the table, so that the string always stays in the same direction.

Can you solve that problem?